Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2240))\).
|
Total |
New |
Old |
Modular forms
| 445824 |
219252 |
226572 |
Cusp forms
| 438912 |
217932 |
220980 |
Eisenstein series
| 6912 |
1320 |
5592 |
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2240))\)
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 available newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
2240.4.a |
\(\chi_{2240}(1, \cdot)\) |
2240.4.a.a |
1 |
1 |
2240.4.a.b |
1 |
2240.4.a.c |
1 |
2240.4.a.d |
1 |
2240.4.a.e |
1 |
2240.4.a.f |
1 |
2240.4.a.g |
1 |
2240.4.a.h |
1 |
2240.4.a.i |
1 |
2240.4.a.j |
1 |
2240.4.a.k |
1 |
2240.4.a.l |
1 |
2240.4.a.m |
1 |
2240.4.a.n |
1 |
2240.4.a.o |
1 |
2240.4.a.p |
1 |
2240.4.a.q |
1 |
2240.4.a.r |
1 |
2240.4.a.s |
1 |
2240.4.a.t |
1 |
2240.4.a.u |
1 |
2240.4.a.v |
1 |
2240.4.a.w |
1 |
2240.4.a.x |
1 |
2240.4.a.y |
1 |
2240.4.a.z |
1 |
2240.4.a.ba |
1 |
2240.4.a.bb |
1 |
2240.4.a.bc |
1 |
2240.4.a.bd |
1 |
2240.4.a.be |
1 |
2240.4.a.bf |
1 |
2240.4.a.bg |
1 |
2240.4.a.bh |
1 |
2240.4.a.bi |
1 |
2240.4.a.bj |
1 |
2240.4.a.bk |
1 |
2240.4.a.bl |
1 |
2240.4.a.bm |
2 |
2240.4.a.bn |
2 |
2240.4.a.bo |
2 |
2240.4.a.bp |
2 |
2240.4.a.bq |
3 |
2240.4.a.br |
3 |
2240.4.a.bs |
3 |
2240.4.a.bt |
3 |
2240.4.a.bu |
3 |
2240.4.a.bv |
3 |
2240.4.a.bw |
3 |
2240.4.a.bx |
3 |
2240.4.a.by |
3 |
2240.4.a.bz |
3 |
2240.4.a.ca |
4 |
2240.4.a.cb |
4 |
2240.4.a.cc |
4 |
2240.4.a.cd |
4 |
2240.4.a.ce |
4 |
2240.4.a.cf |
4 |
2240.4.a.cg |
4 |
2240.4.a.ch |
4 |
2240.4.a.ci |
4 |
2240.4.a.cj |
4 |
2240.4.a.ck |
4 |
2240.4.a.cl |
4 |
2240.4.a.cm |
5 |
2240.4.a.cn |
5 |
2240.4.a.co |
5 |
2240.4.a.cp |
5 |
2240.4.b |
\(\chi_{2240}(1121, \cdot)\) |
n/a |
144 |
1 |
2240.4.e |
\(\chi_{2240}(2239, \cdot)\) |
n/a |
284 |
1 |
2240.4.g |
\(\chi_{2240}(449, \cdot)\) |
n/a |
216 |
1 |
2240.4.h |
\(\chi_{2240}(671, \cdot)\) |
n/a |
192 |
1 |
2240.4.k |
\(\chi_{2240}(1791, \cdot)\) |
n/a |
192 |
1 |
2240.4.l |
\(\chi_{2240}(1569, \cdot)\) |
n/a |
216 |
1 |
2240.4.n |
\(\chi_{2240}(1119, \cdot)\) |
n/a |
288 |
1 |
2240.4.q |
\(\chi_{2240}(641, \cdot)\) |
n/a |
384 |
2 |
2240.4.r |
\(\chi_{2240}(433, \cdot)\) |
n/a |
568 |
2 |
2240.4.t |
\(\chi_{2240}(463, \cdot)\) |
n/a |
432 |
2 |
2240.4.w |
\(\chi_{2240}(97, \cdot)\) |
n/a |
576 |
2 |
2240.4.x |
\(\chi_{2240}(127, \cdot)\) |
n/a |
432 |
2 |
2240.4.bb |
\(\chi_{2240}(1009, \cdot)\) |
n/a |
432 |
2 |
2240.4.bc |
\(\chi_{2240}(111, \cdot)\) |
n/a |
384 |
2 |
2240.4.bd |
\(\chi_{2240}(561, \cdot)\) |
n/a |
288 |
2 |
2240.4.be |
\(\chi_{2240}(559, \cdot)\) |
n/a |
568 |
2 |
2240.4.bi |
\(\chi_{2240}(1247, \cdot)\) |
n/a |
432 |
2 |
2240.4.bj |
\(\chi_{2240}(1217, \cdot)\) |
n/a |
568 |
2 |
2240.4.bl |
\(\chi_{2240}(1583, \cdot)\) |
n/a |
432 |
2 |
2240.4.bn |
\(\chi_{2240}(1553, \cdot)\) |
n/a |
568 |
2 |
2240.4.bq |
\(\chi_{2240}(159, \cdot)\) |
n/a |
576 |
2 |
2240.4.bs |
\(\chi_{2240}(831, \cdot)\) |
n/a |
384 |
2 |
2240.4.bv |
\(\chi_{2240}(289, \cdot)\) |
n/a |
576 |
2 |
2240.4.bw |
\(\chi_{2240}(1089, \cdot)\) |
n/a |
568 |
2 |
2240.4.bz |
\(\chi_{2240}(31, \cdot)\) |
n/a |
384 |
2 |
2240.4.cb |
\(\chi_{2240}(1761, \cdot)\) |
n/a |
384 |
2 |
2240.4.cc |
\(\chi_{2240}(1279, \cdot)\) |
n/a |
568 |
2 |
2240.4.cg |
\(\chi_{2240}(281, \cdot)\) |
None |
0 |
4 |
2240.4.ch |
\(\chi_{2240}(279, \cdot)\) |
None |
0 |
4 |
2240.4.ci |
\(\chi_{2240}(377, \cdot)\) |
None |
0 |
4 |
2240.4.cj |
\(\chi_{2240}(407, \cdot)\) |
None |
0 |
4 |
2240.4.cm |
\(\chi_{2240}(183, \cdot)\) |
None |
0 |
4 |
2240.4.cn |
\(\chi_{2240}(153, \cdot)\) |
None |
0 |
4 |
2240.4.cs |
\(\chi_{2240}(391, \cdot)\) |
None |
0 |
4 |
2240.4.ct |
\(\chi_{2240}(169, \cdot)\) |
None |
0 |
4 |
2240.4.cv |
\(\chi_{2240}(207, \cdot)\) |
n/a |
1136 |
4 |
2240.4.cx |
\(\chi_{2240}(593, \cdot)\) |
n/a |
1136 |
4 |
2240.4.cy |
\(\chi_{2240}(257, \cdot)\) |
n/a |
1136 |
4 |
2240.4.db |
\(\chi_{2240}(543, \cdot)\) |
n/a |
1152 |
4 |
2240.4.de |
\(\chi_{2240}(719, \cdot)\) |
n/a |
1136 |
4 |
2240.4.df |
\(\chi_{2240}(81, \cdot)\) |
n/a |
768 |
4 |
2240.4.dg |
\(\chi_{2240}(271, \cdot)\) |
n/a |
768 |
4 |
2240.4.dh |
\(\chi_{2240}(529, \cdot)\) |
n/a |
1136 |
4 |
2240.4.dk |
\(\chi_{2240}(767, \cdot)\) |
n/a |
1136 |
4 |
2240.4.dn |
\(\chi_{2240}(33, \cdot)\) |
n/a |
1152 |
4 |
2240.4.dp |
\(\chi_{2240}(17, \cdot)\) |
n/a |
1136 |
4 |
2240.4.dr |
\(\chi_{2240}(1103, \cdot)\) |
n/a |
1136 |
4 |
2240.4.du |
\(\chi_{2240}(13, \cdot)\) |
n/a |
9184 |
8 |
2240.4.dv |
\(\chi_{2240}(43, \cdot)\) |
n/a |
6912 |
8 |
2240.4.dw |
\(\chi_{2240}(139, \cdot)\) |
n/a |
9184 |
8 |
2240.4.dx |
\(\chi_{2240}(141, \cdot)\) |
n/a |
4608 |
8 |
2240.4.dy |
\(\chi_{2240}(251, \cdot)\) |
n/a |
6144 |
8 |
2240.4.dz |
\(\chi_{2240}(29, \cdot)\) |
n/a |
6912 |
8 |
2240.4.eg |
\(\chi_{2240}(267, \cdot)\) |
n/a |
6912 |
8 |
2240.4.eh |
\(\chi_{2240}(237, \cdot)\) |
n/a |
9184 |
8 |
2240.4.ei |
\(\chi_{2240}(9, \cdot)\) |
None |
0 |
8 |
2240.4.ej |
\(\chi_{2240}(311, \cdot)\) |
None |
0 |
8 |
2240.4.eo |
\(\chi_{2240}(23, \cdot)\) |
None |
0 |
8 |
2240.4.ep |
\(\chi_{2240}(297, \cdot)\) |
None |
0 |
8 |
2240.4.es |
\(\chi_{2240}(73, \cdot)\) |
None |
0 |
8 |
2240.4.et |
\(\chi_{2240}(247, \cdot)\) |
None |
0 |
8 |
2240.4.eu |
\(\chi_{2240}(199, \cdot)\) |
None |
0 |
8 |
2240.4.ev |
\(\chi_{2240}(121, \cdot)\) |
None |
0 |
8 |
2240.4.ey |
\(\chi_{2240}(157, \cdot)\) |
n/a |
18368 |
16 |
2240.4.ez |
\(\chi_{2240}(107, \cdot)\) |
n/a |
18368 |
16 |
2240.4.fg |
\(\chi_{2240}(109, \cdot)\) |
n/a |
18368 |
16 |
2240.4.fh |
\(\chi_{2240}(131, \cdot)\) |
n/a |
12288 |
16 |
2240.4.fi |
\(\chi_{2240}(221, \cdot)\) |
n/a |
12288 |
16 |
2240.4.fj |
\(\chi_{2240}(19, \cdot)\) |
n/a |
18368 |
16 |
2240.4.fk |
\(\chi_{2240}(67, \cdot)\) |
n/a |
18368 |
16 |
2240.4.fl |
\(\chi_{2240}(117, \cdot)\) |
n/a |
18368 |
16 |
"n/a" means that newforms for that character have not been added to the database yet