Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3520))\).
|
Total |
New |
Old |
Modular forms
| 374400 |
188100 |
186300 |
Cusp forms
| 362881 |
185724 |
177157 |
Eisenstein series
| 11519 |
2376 |
9143 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3520))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
3520.2.a |
\(\chi_{3520}(1, \cdot)\) |
3520.2.a.a |
1 |
1 |
3520.2.a.b |
1 |
3520.2.a.c |
1 |
3520.2.a.d |
1 |
3520.2.a.e |
1 |
3520.2.a.f |
1 |
3520.2.a.g |
1 |
3520.2.a.h |
1 |
3520.2.a.i |
1 |
3520.2.a.j |
1 |
3520.2.a.k |
1 |
3520.2.a.l |
1 |
3520.2.a.m |
1 |
3520.2.a.n |
1 |
3520.2.a.o |
1 |
3520.2.a.p |
1 |
3520.2.a.q |
1 |
3520.2.a.r |
1 |
3520.2.a.s |
1 |
3520.2.a.t |
1 |
3520.2.a.u |
1 |
3520.2.a.v |
1 |
3520.2.a.w |
1 |
3520.2.a.x |
1 |
3520.2.a.y |
1 |
3520.2.a.z |
1 |
3520.2.a.ba |
1 |
3520.2.a.bb |
1 |
3520.2.a.bc |
1 |
3520.2.a.bd |
1 |
3520.2.a.be |
1 |
3520.2.a.bf |
1 |
3520.2.a.bg |
1 |
3520.2.a.bh |
1 |
3520.2.a.bi |
2 |
3520.2.a.bj |
2 |
3520.2.a.bk |
2 |
3520.2.a.bl |
2 |
3520.2.a.bm |
2 |
3520.2.a.bn |
2 |
3520.2.a.bo |
2 |
3520.2.a.bp |
2 |
3520.2.a.bq |
2 |
3520.2.a.br |
2 |
3520.2.a.bs |
2 |
3520.2.a.bt |
2 |
3520.2.a.bu |
3 |
3520.2.a.bv |
3 |
3520.2.a.bw |
3 |
3520.2.a.bx |
3 |
3520.2.a.by |
5 |
3520.2.a.bz |
5 |
3520.2.b |
\(\chi_{3520}(1409, \cdot)\) |
n/a |
120 |
1 |
3520.2.c |
\(\chi_{3520}(1759, \cdot)\) |
n/a |
144 |
1 |
3520.2.f |
\(\chi_{3520}(2111, \cdot)\) |
3520.2.f.a |
2 |
1 |
3520.2.f.b |
2 |
3520.2.f.c |
2 |
3520.2.f.d |
2 |
3520.2.f.e |
4 |
3520.2.f.f |
4 |
3520.2.f.g |
4 |
3520.2.f.h |
8 |
3520.2.f.i |
8 |
3520.2.f.j |
8 |
3520.2.f.k |
12 |
3520.2.f.l |
16 |
3520.2.f.m |
24 |
3520.2.g |
\(\chi_{3520}(1761, \cdot)\) |
3520.2.g.a |
2 |
1 |
3520.2.g.b |
2 |
3520.2.g.c |
2 |
3520.2.g.d |
2 |
3520.2.g.e |
2 |
3520.2.g.f |
2 |
3520.2.g.g |
4 |
3520.2.g.h |
4 |
3520.2.g.i |
4 |
3520.2.g.j |
4 |
3520.2.g.k |
6 |
3520.2.g.l |
6 |
3520.2.g.m |
8 |
3520.2.g.n |
8 |
3520.2.g.o |
12 |
3520.2.g.p |
12 |
3520.2.l |
\(\chi_{3520}(3169, \cdot)\) |
n/a |
120 |
1 |
3520.2.m |
\(\chi_{3520}(3519, \cdot)\) |
n/a |
140 |
1 |
3520.2.p |
\(\chi_{3520}(351, \cdot)\) |
3520.2.p.a |
4 |
1 |
3520.2.p.b |
4 |
3520.2.p.c |
12 |
3520.2.p.d |
12 |
3520.2.p.e |
32 |
3520.2.p.f |
32 |
3520.2.s |
\(\chi_{3520}(463, \cdot)\) |
n/a |
240 |
2 |
3520.2.t |
\(\chi_{3520}(593, \cdot)\) |
n/a |
280 |
2 |
3520.2.v |
\(\chi_{3520}(1231, \cdot)\) |
n/a |
192 |
2 |
3520.2.w |
\(\chi_{3520}(881, \cdot)\) |
n/a |
160 |
2 |
3520.2.z |
\(\chi_{3520}(287, \cdot)\) |
n/a |
240 |
2 |
3520.2.bb |
\(\chi_{3520}(417, \cdot)\) |
n/a |
288 |
2 |
3520.2.bd |
\(\chi_{3520}(1473, \cdot)\) |
n/a |
280 |
2 |
3520.2.bf |
\(\chi_{3520}(1343, \cdot)\) |
n/a |
240 |
2 |
3520.2.bh |
\(\chi_{3520}(529, \cdot)\) |
n/a |
240 |
2 |
3520.2.bi |
\(\chi_{3520}(879, \cdot)\) |
n/a |
280 |
2 |
3520.2.bk |
\(\chi_{3520}(1167, \cdot)\) |
n/a |
240 |
2 |
3520.2.bl |
\(\chi_{3520}(1297, \cdot)\) |
n/a |
280 |
2 |
3520.2.bo |
\(\chi_{3520}(641, \cdot)\) |
n/a |
384 |
4 |
3520.2.bp |
\(\chi_{3520}(727, \cdot)\) |
None |
0 |
4 |
3520.2.bs |
\(\chi_{3520}(153, \cdot)\) |
None |
0 |
4 |
3520.2.bt |
\(\chi_{3520}(439, \cdot)\) |
None |
0 |
4 |
3520.2.bv |
\(\chi_{3520}(441, \cdot)\) |
None |
0 |
4 |
3520.2.by |
\(\chi_{3520}(791, \cdot)\) |
None |
0 |
4 |
3520.2.ca |
\(\chi_{3520}(89, \cdot)\) |
None |
0 |
4 |
3520.2.cc |
\(\chi_{3520}(857, \cdot)\) |
None |
0 |
4 |
3520.2.cd |
\(\chi_{3520}(23, \cdot)\) |
None |
0 |
4 |
3520.2.cf |
\(\chi_{3520}(1311, \cdot)\) |
n/a |
384 |
4 |
3520.2.ci |
\(\chi_{3520}(959, \cdot)\) |
n/a |
560 |
4 |
3520.2.cj |
\(\chi_{3520}(289, \cdot)\) |
n/a |
576 |
4 |
3520.2.co |
\(\chi_{3520}(801, \cdot)\) |
n/a |
384 |
4 |
3520.2.cp |
\(\chi_{3520}(831, \cdot)\) |
n/a |
384 |
4 |
3520.2.cs |
\(\chi_{3520}(479, \cdot)\) |
n/a |
576 |
4 |
3520.2.ct |
\(\chi_{3520}(449, \cdot)\) |
n/a |
560 |
4 |
3520.2.cv |
\(\chi_{3520}(197, \cdot)\) |
n/a |
4576 |
8 |
3520.2.cx |
\(\chi_{3520}(67, \cdot)\) |
n/a |
3840 |
8 |
3520.2.cz |
\(\chi_{3520}(309, \cdot)\) |
n/a |
3840 |
8 |
3520.2.da |
\(\chi_{3520}(221, \cdot)\) |
n/a |
2560 |
8 |
3520.2.dd |
\(\chi_{3520}(219, \cdot)\) |
n/a |
4576 |
8 |
3520.2.de |
\(\chi_{3520}(131, \cdot)\) |
n/a |
3072 |
8 |
3520.2.dg |
\(\chi_{3520}(373, \cdot)\) |
n/a |
4576 |
8 |
3520.2.di |
\(\chi_{3520}(243, \cdot)\) |
n/a |
3840 |
8 |
3520.2.dm |
\(\chi_{3520}(17, \cdot)\) |
n/a |
1120 |
8 |
3520.2.dn |
\(\chi_{3520}(207, \cdot)\) |
n/a |
1120 |
8 |
3520.2.do |
\(\chi_{3520}(79, \cdot)\) |
n/a |
1120 |
8 |
3520.2.dr |
\(\chi_{3520}(49, \cdot)\) |
n/a |
1120 |
8 |
3520.2.ds |
\(\chi_{3520}(193, \cdot)\) |
n/a |
1120 |
8 |
3520.2.du |
\(\chi_{3520}(383, \cdot)\) |
n/a |
1120 |
8 |
3520.2.dw |
\(\chi_{3520}(223, \cdot)\) |
n/a |
1152 |
8 |
3520.2.dy |
\(\chi_{3520}(673, \cdot)\) |
n/a |
1152 |
8 |
3520.2.ea |
\(\chi_{3520}(81, \cdot)\) |
n/a |
768 |
8 |
3520.2.ed |
\(\chi_{3520}(271, \cdot)\) |
n/a |
768 |
8 |
3520.2.ee |
\(\chi_{3520}(497, \cdot)\) |
n/a |
1120 |
8 |
3520.2.ef |
\(\chi_{3520}(47, \cdot)\) |
n/a |
1120 |
8 |
3520.2.ei |
\(\chi_{3520}(57, \cdot)\) |
None |
0 |
16 |
3520.2.el |
\(\chi_{3520}(487, \cdot)\) |
None |
0 |
16 |
3520.2.em |
\(\chi_{3520}(9, \cdot)\) |
None |
0 |
16 |
3520.2.eo |
\(\chi_{3520}(151, \cdot)\) |
None |
0 |
16 |
3520.2.er |
\(\chi_{3520}(201, \cdot)\) |
None |
0 |
16 |
3520.2.et |
\(\chi_{3520}(39, \cdot)\) |
None |
0 |
16 |
3520.2.ev |
\(\chi_{3520}(103, \cdot)\) |
None |
0 |
16 |
3520.2.ew |
\(\chi_{3520}(457, \cdot)\) |
None |
0 |
16 |
3520.2.ez |
\(\chi_{3520}(3, \cdot)\) |
n/a |
18304 |
32 |
3520.2.fb |
\(\chi_{3520}(237, \cdot)\) |
n/a |
18304 |
32 |
3520.2.fd |
\(\chi_{3520}(51, \cdot)\) |
n/a |
12288 |
32 |
3520.2.fe |
\(\chi_{3520}(19, \cdot)\) |
n/a |
18304 |
32 |
3520.2.fh |
\(\chi_{3520}(141, \cdot)\) |
n/a |
12288 |
32 |
3520.2.fi |
\(\chi_{3520}(69, \cdot)\) |
n/a |
18304 |
32 |
3520.2.fk |
\(\chi_{3520}(147, \cdot)\) |
n/a |
18304 |
32 |
3520.2.fm |
\(\chi_{3520}(13, \cdot)\) |
n/a |
18304 |
32 |
"n/a" means that newforms for that character have not been added to the database yet