Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4624))\).
|
Total |
New |
Old |
| Modular forms
| 671456 |
373615 |
297841 |
| Cusp forms
| 660257 |
370298 |
289959 |
| Eisenstein series
| 11199 |
3317 |
7882 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4624))\)
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 |
| 4624.2.a |
\(\chi_{4624}(1, \cdot)\) |
4624.2.a.a |
1 |
1 |
| 4624.2.a.b |
1 |
| 4624.2.a.c |
1 |
| 4624.2.a.d |
1 |
| 4624.2.a.e |
1 |
| 4624.2.a.f |
1 |
| 4624.2.a.g |
2 |
| 4624.2.a.h |
2 |
| 4624.2.a.i |
2 |
| 4624.2.a.j |
2 |
| 4624.2.a.k |
2 |
| 4624.2.a.l |
2 |
| 4624.2.a.m |
2 |
| 4624.2.a.n |
2 |
| 4624.2.a.o |
2 |
| 4624.2.a.p |
2 |
| 4624.2.a.q |
2 |
| 4624.2.a.r |
2 |
| 4624.2.a.s |
2 |
| 4624.2.a.t |
2 |
| 4624.2.a.u |
2 |
| 4624.2.a.v |
2 |
| 4624.2.a.w |
2 |
| 4624.2.a.x |
2 |
| 4624.2.a.y |
2 |
| 4624.2.a.z |
3 |
| 4624.2.a.ba |
3 |
| 4624.2.a.bb |
3 |
| 4624.2.a.bc |
3 |
| 4624.2.a.bd |
3 |
| 4624.2.a.be |
3 |
| 4624.2.a.bf |
3 |
| 4624.2.a.bg |
3 |
| 4624.2.a.bh |
3 |
| 4624.2.a.bi |
3 |
| 4624.2.a.bj |
3 |
| 4624.2.a.bk |
3 |
| 4624.2.a.bl |
4 |
| 4624.2.a.bm |
4 |
| 4624.2.a.bn |
4 |
| 4624.2.a.bo |
4 |
| 4624.2.a.bp |
4 |
| 4624.2.a.bq |
4 |
| 4624.2.a.br |
6 |
| 4624.2.a.bs |
6 |
| 4624.2.a.bt |
12 |
| 4624.2.b |
\(\chi_{4624}(577, \cdot)\) |
n/a |
128 |
1 |
| 4624.2.c |
\(\chi_{4624}(2313, \cdot)\) |
None |
0 |
1 |
| 4624.2.h |
\(\chi_{4624}(2889, \cdot)\) |
None |
0 |
1 |
| 4624.2.j |
\(\chi_{4624}(829, \cdot)\) |
n/a |
1052 |
2 |
| 4624.2.l |
\(\chi_{4624}(1157, \cdot)\) |
n/a |
1054 |
2 |
| 4624.2.m |
\(\chi_{4624}(905, \cdot)\) |
None |
0 |
2 |
| 4624.2.o |
\(\chi_{4624}(1985, \cdot)\) |
n/a |
256 |
2 |
| 4624.2.r |
\(\chi_{4624}(1733, \cdot)\) |
n/a |
1052 |
2 |
| 4624.2.s |
\(\chi_{4624}(2061, \cdot)\) |
n/a |
1052 |
2 |
| 4624.2.v |
\(\chi_{4624}(977, \cdot)\) |
n/a |
512 |
4 |
| 4624.2.w |
\(\chi_{4624}(733, \cdot)\) |
n/a |
2104 |
4 |
| 4624.2.y |
\(\chi_{4624}(3045, \cdot)\) |
n/a |
2104 |
4 |
| 4624.2.ba |
\(\chi_{4624}(1001, \cdot)\) |
None |
0 |
4 |
| 4624.2.bd |
\(\chi_{4624}(75, \cdot)\) |
n/a |
4208 |
8 |
| 4624.2.bf |
\(\chi_{4624}(447, \cdot)\) |
n/a |
1080 |
8 |
| 4624.2.bg |
\(\chi_{4624}(503, \cdot)\) |
None |
0 |
8 |
| 4624.2.bj |
\(\chi_{4624}(2387, \cdot)\) |
n/a |
4208 |
8 |
| 4624.2.bk |
\(\chi_{4624}(273, \cdot)\) |
n/a |
2432 |
16 |
| 4624.2.bl |
\(\chi_{4624}(169, \cdot)\) |
None |
0 |
16 |
| 4624.2.bq |
\(\chi_{4624}(137, \cdot)\) |
None |
0 |
16 |
| 4624.2.br |
\(\chi_{4624}(33, \cdot)\) |
n/a |
2432 |
16 |
| 4624.2.bt |
\(\chi_{4624}(149, \cdot)\) |
n/a |
19520 |
32 |
| 4624.2.bu |
\(\chi_{4624}(101, \cdot)\) |
n/a |
19520 |
32 |
| 4624.2.bx |
\(\chi_{4624}(81, \cdot)\) |
n/a |
4864 |
32 |
| 4624.2.bz |
\(\chi_{4624}(89, \cdot)\) |
None |
0 |
32 |
| 4624.2.ca |
\(\chi_{4624}(69, \cdot)\) |
n/a |
19520 |
32 |
| 4624.2.cc |
\(\chi_{4624}(13, \cdot)\) |
n/a |
19520 |
32 |
| 4624.2.cf |
\(\chi_{4624}(9, \cdot)\) |
None |
0 |
64 |
| 4624.2.ch |
\(\chi_{4624}(53, \cdot)\) |
n/a |
39040 |
64 |
| 4624.2.cj |
\(\chi_{4624}(189, \cdot)\) |
n/a |
39040 |
64 |
| 4624.2.ck |
\(\chi_{4624}(49, \cdot)\) |
n/a |
9728 |
64 |
| 4624.2.cm |
\(\chi_{4624}(107, \cdot)\) |
n/a |
78080 |
128 |
| 4624.2.cp |
\(\chi_{4624}(7, \cdot)\) |
None |
0 |
128 |
| 4624.2.cq |
\(\chi_{4624}(31, \cdot)\) |
n/a |
19584 |
128 |
| 4624.2.cs |
\(\chi_{4624}(3, \cdot)\) |
n/a |
78080 |
128 |
"n/a" means that newforms for that character have not been added to the database yet
