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Merge pull request LMFDB#6282 from fchapoton/doc_siegel_from_html_to_rst
turn doc in bad file into rst syntax (roughly)
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‎lmfdb/siegel_modular_forms/dimensions.py‎

Lines changed: 91 additions & 112 deletions
Original file line numberDiff line numberDiff line change
@@ -54,91 +54,76 @@ def parse_dim_args(dim_args, default_dim_args):
5454

5555
def dimension_Gamma_2(wt_range, j):
5656
r"""
57-
<ul>
58-
<li>First entry of the respective triple: The full space.</li>
59-
<li>Second entry: The codimension of the subspace of cusp forms.</li>
60-
<li>Third entry: The subspace of cusp forms.</li>
61-
</ul>
62-
<p> More precisely, The triple $[a,b,c]$ in
63-
<ul>
64-
<li>
65-
row <span class="emph">All</span>
66-
and in the $k$th column shows the dimension of
67-
the full space $M_{k,j}(\Gamma(2))$,
68-
of the non cusp forms, and of the cusp forms.</li>
69-
<li>
70-
in row <span class="emph">$p$</span>, where $p$ is a partition of $6$,
71-
and in the $k$th column shows the multiplicity of the
72-
$\mathrm{Sp}(4,\Z)$-representation
73-
associated to $p$ in the full $\mathrm{Sp}(4,\Z)$-module
74-
$M_{k,j}(\Gamma(2))$,
75-
in the submodule of non cusp forms and of cusp forms.
76-
(See below for details.)
77-
</li>
78-
</ul>
57+
First entry of the respective triple: The full space.
58+
Second entry: The codimension of the subspace of cusp forms.
59+
Third entry: The subspace of cusp forms.
7960
61+
More precisely, The triple $[a,b,c]$ in
62+
63+
row All
64+
and in the $k$th column shows the dimension of
65+
the full space $M_{k,j}(\Gamma(2))$,
66+
of the non cusp forms, and of the cusp forms.
67+
68+
in row $p$, where $p$ is a partition of $6$,
69+
and in the $k$th column shows the multiplicity of the
70+
$\mathrm{Sp}(4,\Z)$-representation
71+
associated to $p$ in the full $\mathrm{Sp}(4,\Z)$-module
72+
$M_{k,j}(\Gamma(2))$,
73+
in the submodule of non cusp forms and of cusp forms.
74+
(See below for details.)
8075
"""
8176
return _dimension_Gamma_2(wt_range, j, group='Gamma(2)')
8277

8378

8479
def dimension_Gamma1_2(wt_range, j):
8580
r"""
86-
<ul>
87-
<li>First entry of the respective triple: The full space.</li>
88-
<li>Second entry: The codimension of the subspace of cusp forms.</li>
89-
<li>Third entry: The subspace of cusp forms.</li>
90-
</ul>
91-
<p> More precisely, The triple $[a,b,c]$ in
92-
<ul>
93-
<li>
94-
row <span class="emph">All</span>
95-
and in the $k$th column shows the dimension of
96-
the full space $M_{k,j}(\Gamma(2))$,
97-
of the non cusp forms, and of the cusp forms.</li>
98-
<li>
99-
in row <span class="emph">$p$</span>, where $p$ is a partition of $3$,
100-
and in the $k$th column shows the multiplicity of the
101-
$\Gamma_1(2)$-representation
102-
associated to $p$ in the full $\Gamma_1(2)$-module $M_{k,j}(\Gamma(2))$,
103-
in the submodule of non cusp forms and of cusp forms.
104-
(See below for details.)
105-
</li>
106-
</ul>
81+
First entry of the respective triple: The full space.
82+
Second entry: The codimension of the subspace of cusp forms.
83+
Third entry: The subspace of cusp forms.
84+
85+
More precisely, The triple $[a,b,c]$ in
86+
87+
row All
88+
and in the $k$th column shows the dimension of
89+
the full space $M_{k,j}(\Gamma(2))$,
90+
of the non cusp forms, and of the cusp forms.
91+
92+
in row $p$, where $p$ is a partition of $3$,
93+
and in the $k$th column shows the multiplicity of the
94+
$\Gamma_1(2)$-representation
95+
associated to $p$ in the full $\Gamma_1(2)$-module $M_{k,j}(\Gamma(2))$,
96+
in the submodule of non cusp forms and of cusp forms.
97+
(See below for details.)
10798
"""
10899
return _dimension_Gamma_2(wt_range, j, group='Gamma1(2)')
109100

110101

111102
def dimension_Gamma0_2(wt_range, j):
112103
"""
113-
<ul>
114-
<li><span class="emph">Total</span>: The full space.</li>
115-
<li><span class="emph">Non cusp</span>: The codimension of the subspace of cusp forms.</li>
116-
<li><span class="emph">Cusp</span>: The subspace of cusp forms.</li>
117-
</ul>
104+
<span class="emph">Total</span>: The full space.
105+
<span class="emph">Non cusp</span>: The codimension of the subspace of cusp forms.
106+
<span class="emph">Cusp</span>: The subspace of cusp forms.
118107
"""
119108
return _dimension_Gamma_2(wt_range, j, group='Gamma0(2)')
120109

121110

122111
def dimension_Sp4Z(wt_range):
123112
"""
124-
<ul>
125-
<li><span class="emph">Total</span>: The full space.</li>
126-
<li><span class="emph">Eisenstein</span>: The subspace of Siegel Eisenstein series.</li>
127-
<li><span class="emph">Klingen</span>: The subspace of Klingen Eisenstein series.</li>
128-
<li><span class="emph">Maass</span>: The subspace of Maass liftings.</li>
129-
<li><span class="emph">Interesting</span>: The subspace spanned by cuspidal eigenforms that are not Maass liftings.</li>
130-
</ul>
113+
<span class="emph">Total</span>: The full space.
114+
<span class="emph">Eisenstein</span>: The subspace of Siegel Eisenstein series.
115+
<span class="emph">Klingen</span>: The subspace of Klingen Eisenstein series.
116+
<span class="emph">Maass</span>: The subspace of Maass liftings.
117+
<span class="emph">Interesting</span>: The subspace spanned by cuspidal eigenforms that are not Maass liftings.
131118
"""
132119
return _dimension_Sp4Z(wt_range)
133120

134121

135122
def dimension_Sp4Z_2(wt_range):
136123
"""
137-
<ul>
138-
<li><span class="emph">Total</span>: The full space.</li>
139-
<li><span class="emph">Non cusp</span>: The subspace of non cusp forms.</li>
140-
<li><span class="emph">Cusp</span>: The subspace of cusp forms.</li>
141-
</ul>
124+
<span class="emph">Total</span>: The full space.
125+
<span class="emph">Non cusp</span>: The subspace of non cusp forms.
126+
<span class="emph">Cusp</span>: The subspace of cusp forms.
142127
"""
143128
return _dimension_Gamma_2(wt_range, 2, group='Sp4(Z)')
144129

@@ -160,11 +145,9 @@ def dimension_table_Sp4Z_j(wt_range, j_range):
160145

161146
def dimension_Sp4Z_j(wt_range, j):
162147
"""
163-
<ul>
164-
<li><span class="emph">Total</span>: The full space.</li>
165-
<li><span class="emph">Non cusp</span>: The subspace of non cusp forms.</li>
166-
<li><span class="emph">Cusp</span>: The subspace of cusp forms.</li>
167-
</ul>
148+
<span class="emph">Total</span>: The full space.
149+
<span class="emph">Non cusp</span>: The subspace of non cusp forms.
150+
<span class="emph">Cusp</span>: The subspace of cusp forms.
168151
"""
169152
return _dimension_Gamma_2(wt_range, j, group='Sp4(Z)')
170153

@@ -307,12 +290,10 @@ def _dimension_Gamma_2(wt_range, j, group='Gamma(2)'):
307290

308291
def dimension_Sp6Z(wt_range):
309292
"""
310-
<ul>
311-
<li><span class="emph">Total</span>: The full space.</li>
312-
<li><span class="emph">Miyawaki lifts I</span>: The subspace of Miyawaki lifts of type I.</li>
313-
<li><span class="emph">Miyawaki lifts II</span>: The subspace of (conjectured) Miyawaki lifts of type II.</li>
314-
<li><span class="emph">Other</span>: The subspace of cusp forms which are not Miyawaki lifts of type I or II.</li>
315-
</ul>
293+
<span class="emph">Total</span>: The full space.
294+
<span class="emph">Miyawaki lifts I</span>: The subspace of Miyawaki lifts of type I.
295+
<span class="emph">Miyawaki lifts II</span>: The subspace of (conjectured) Miyawaki lifts of type II.
296+
<span class="emph">Other</span>: The subspace of cusp forms which are not Miyawaki lifts of type I or II.
316297
"""
317298
return _dimension_Sp6Z(wt_range)
318299

@@ -365,12 +346,10 @@ def __dimension_Sp6Z(wt):
365346

366347
def dimension_Sp8Z(wt_range):
367348
"""
368-
<ul>
369-
<li><span class="emph">Total</span>: The subspace of cusp forms.</li>
370-
<li><span class="emph">Ikeda lifts</span>: The subspace of Ikeda lifts.</li>
371-
<li><span class="emph">Miyawaki lifts</span>: The subspace of Miyawaki lifts.</li>
372-
<li><span class="emph">Other</span>: The subspace that are not Ikeda or Miyawaki lifts.</li>
373-
</ul>
349+
<span class="emph">Total</span>: The subspace of cusp forms.
350+
<span class="emph">Ikeda lifts</span>: The subspace of Ikeda lifts.
351+
<span class="emph">Miyawaki lifts</span>: The subspace of Miyawaki lifts.
352+
<span class="emph">Other</span>: The subspace that are not Ikeda or Miyawaki lifts.
374353
"""
375354
headers = ['Total', 'Ikeda lifts', 'Miyawaki lifts', 'Other']
376355
dct = {}
@@ -429,11 +408,9 @@ def _dimension_Sp8Z(wt):
429408

430409
def dimension_Gamma0_4_half(wt_range):
431410
"""
432-
<ul>
433-
<li><span class="emph">Total</span>: The full space.</li>
434-
<li><span class="emph">Non cusp</span>: The codimension of the subspace of cusp forms.</li>
435-
<li><span class="emph">Cusp</span>: The subspace of cusp forms.</li>
436-
</ul>
411+
<span class="emph">Total</span>: The full space.
412+
<span class="emph">Non cusp</span>: The codimension of the subspace of cusp forms.
413+
<span class="emph">Cusp</span>: The subspace of cusp forms.
437414
"""
438415
headers = ['Total', 'Non cusp', 'Cusp']
439416
dct = {}
@@ -449,14 +426,17 @@ def _dimension_Gamma0_4_half(k):
449426
of half integral weight k - 1/2.
450427
451428
INPUT
452-
The realweight is k-1/2
429+
430+
The realweight is k-1/2
453431
454432
OUTPUT
455-
('Total', 'Non cusp', 'Cusp')
433+
434+
('Total', 'Non cusp', 'Cusp')
456435
457436
REMARK
458-
Note that formula from Hayashida's and Ibukiyama's paper has formula
459-
that coefficient of x^w is for weight (w+1/2). So here w=k-1.
437+
438+
Note that formula from Hayashida's and Ibukiyama's paper has formula
439+
that coefficient of x^w is for weight (w+1/2). So here w=k-1.
460440
"""
461441
if k < 1:
462442
raise ValueError("$k$ must be a positive integer")
@@ -475,9 +455,7 @@ def _dimension_Gamma0_4_half(k):
475455

476456
def dimension_Gamma0_3_psi_3(wt_range):
477457
"""
478-
<ul>
479-
<li><span class="emph">Total</span>: The full space.</li>
480-
</ul>
458+
<span class="emph">Total</span>: The full space.
481459
"""
482460
headers = ['Total']
483461
dct = {}
@@ -493,10 +471,12 @@ def _dimension_Gamma0_3_psi_3(wt):
493471
on $Gamma_0(3)$ with character $\psi_3$.
494472
495473
OUTPUT
496-
("Total")
474+
475+
("Total")
497476
498477
REMARK
499-
Not completely implemented
478+
479+
Not completely implemented
500480
"""
501481
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
502482
(x,) = R._first_ngens(1)
@@ -515,10 +495,9 @@ def _dimension_Gamma0_3_psi_3(wt):
515495

516496
def dimension_Gamma0_4_psi_4(wt_range):
517497
"""
518-
<ul>
519-
<li><span class="emph">Total</span>: The full space.</li>
520-
</ul>
521-
<p> Odd weights are not yet implemented.</p>
498+
<span class="emph">Total</span>: The full space.
499+
500+
Odd weights are not yet implemented.
522501
"""
523502
headers = ['Total']
524503
dct = {}
@@ -537,10 +516,12 @@ def _dimension_Gamma0_4_psi_4(wt):
537516
with character $\psi_4$.
538517
539518
OUTPUT
540-
("Total")
519+
520+
("Total")
541521
542522
REMARK
543-
The formula for odd weights is unknown or not obvious from the paper.
523+
524+
The formula for odd weights is unknown or not obvious from the paper.
544525
"""
545526
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
546527
(x,) = R._first_ngens(1)
@@ -556,9 +537,7 @@ def _dimension_Gamma0_4_psi_4(wt):
556537

557538
def dimension_Gamma0_4(wt_range):
558539
"""
559-
<ul>
560-
<li><span class="emph">Total</span>: The full space.</li>
561-
</ul>
540+
<span class="emph">Total</span>: The full space.
562541
"""
563542
headers = ['Total']
564543
dct = {}
@@ -573,10 +552,12 @@ def _dimension_Gamma0_4(wt):
573552
Return the dimensions of subspaces of Siegel modular forms on $Gamma0(4)$.
574553
575554
OUTPUT
576-
("Total",)
555+
556+
("Total",)
577557
578558
REMARK
579-
Not completely implemented
559+
560+
Not completely implemented
580561
"""
581562
R = PowerSeriesRing(ZZ, 'x')
582563
x = R.gen().O(wt + 1)
@@ -590,9 +571,7 @@ def _dimension_Gamma0_4(wt):
590571

591572
def dimension_Gamma0_3(wt_range):
592573
"""
593-
<ul>
594-
<li><span class="emph">Total</span>: The full space.</li>
595-
</ul>
574+
<span class="emph">Total</span>: The full space.
596575
"""
597576
headers = ['Total']
598577
dct = {}
@@ -607,10 +586,12 @@ def _dimension_Gamma0_3(wt):
607586
Return the dimensions of subspaces of Siegel modular forms on $Gamma0(3)$.
608587
609588
OUTPUT
610-
("Total")
589+
590+
("Total")
611591
612592
REMARK
613-
Only total dimension implemented.
593+
594+
Only total dimension implemented.
614595
"""
615596
R = PowerSeriesRing(ZZ, 'x')
616597
x = R.gen().O(wt + 1)
@@ -624,11 +605,9 @@ def _dimension_Gamma0_3(wt):
624605

625606
def dimension_Dummy_0(wt_range):
626607
"""
627-
<ul>
628-
<li><span class="emph">Total</span>: The subspace of cusp forms.</li>
629-
<li><span class="emph">Yoda lifts</span>: The subspace of Master Yoda lifts.</li>
630-
<li><span class="emph">Hinkelstein series</span>: The subspace of Hinkelstein series.</li>
631-
</ul>
608+
<span class="emph">Total</span>: The subspace of cusp forms.
609+
<span class="emph">Yoda lifts</span>: The subspace of Master Yoda lifts.
610+
<span class="emph">Hinkelstein series</span>: The subspace of Hinkelstein series.
632611
"""
633612
headers = ['Total', 'Yoda lifts', 'Hinkelstein series']
634613
dct = {}

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