Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5648))\).
|
Total |
New |
Old |
| Modular forms
| 1001792 |
562306 |
439486 |
| Cusp forms
| 991937 |
559148 |
432789 |
| Eisenstein series
| 9855 |
3158 |
6697 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5648))\)
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 |
| 5648.2.a |
\(\chi_{5648}(1, \cdot)\) |
5648.2.a.a |
1 |
1 |
| 5648.2.a.b |
1 |
| 5648.2.a.c |
1 |
| 5648.2.a.d |
1 |
| 5648.2.a.e |
1 |
| 5648.2.a.f |
1 |
| 5648.2.a.g |
2 |
| 5648.2.a.h |
2 |
| 5648.2.a.i |
2 |
| 5648.2.a.j |
3 |
| 5648.2.a.k |
5 |
| 5648.2.a.l |
8 |
| 5648.2.a.m |
10 |
| 5648.2.a.n |
11 |
| 5648.2.a.o |
11 |
| 5648.2.a.p |
14 |
| 5648.2.a.q |
15 |
| 5648.2.a.r |
17 |
| 5648.2.a.s |
20 |
| 5648.2.a.t |
23 |
| 5648.2.a.u |
27 |
| 5648.2.b |
\(\chi_{5648}(705, \cdot)\) |
n/a |
176 |
1 |
| 5648.2.c |
\(\chi_{5648}(2825, \cdot)\) |
None |
0 |
1 |
| 5648.2.h |
\(\chi_{5648}(3529, \cdot)\) |
None |
0 |
1 |
| 5648.2.j |
\(\chi_{5648}(2429, \cdot)\) |
n/a |
1412 |
2 |
| 5648.2.l |
\(\chi_{5648}(1413, \cdot)\) |
n/a |
1408 |
2 |
| 5648.2.m |
\(\chi_{5648}(1017, \cdot)\) |
None |
0 |
2 |
| 5648.2.o |
\(\chi_{5648}(2513, \cdot)\) |
n/a |
352 |
2 |
| 5648.2.r |
\(\chi_{5648}(2117, \cdot)\) |
n/a |
1412 |
2 |
| 5648.2.s |
\(\chi_{5648}(1101, \cdot)\) |
n/a |
1412 |
2 |
| 5648.2.u |
\(\chi_{5648}(1649, \cdot)\) |
n/a |
704 |
4 |
| 5648.2.w |
\(\chi_{5648}(237, \cdot)\) |
n/a |
2824 |
4 |
| 5648.2.z |
\(\chi_{5648}(469, \cdot)\) |
n/a |
2824 |
4 |
| 5648.2.bb |
\(\chi_{5648}(1129, \cdot)\) |
None |
0 |
4 |
| 5648.2.bc |
\(\chi_{5648}(337, \cdot)\) |
n/a |
1760 |
10 |
| 5648.2.be |
\(\chi_{5648}(389, \cdot)\) |
n/a |
5648 |
8 |
| 5648.2.bf |
\(\chi_{5648}(49, \cdot)\) |
n/a |
1408 |
8 |
| 5648.2.bh |
\(\chi_{5648}(1705, \cdot)\) |
None |
0 |
8 |
| 5648.2.bj |
\(\chi_{5648}(253, \cdot)\) |
n/a |
5648 |
8 |
| 5648.2.bl |
\(\chi_{5648}(489, \cdot)\) |
None |
0 |
10 |
| 5648.2.bq |
\(\chi_{5648}(97, \cdot)\) |
n/a |
1760 |
10 |
| 5648.2.br |
\(\chi_{5648}(185, \cdot)\) |
None |
0 |
10 |
| 5648.2.bt |
\(\chi_{5648}(347, \cdot)\) |
n/a |
11296 |
16 |
| 5648.2.bu |
\(\chi_{5648}(639, \cdot)\) |
n/a |
2832 |
16 |
| 5648.2.bx |
\(\chi_{5648}(7, \cdot)\) |
None |
0 |
16 |
| 5648.2.bz |
\(\chi_{5648}(59, \cdot)\) |
n/a |
11296 |
16 |
| 5648.2.cb |
\(\chi_{5648}(741, \cdot)\) |
n/a |
14120 |
20 |
| 5648.2.cc |
\(\chi_{5648}(493, \cdot)\) |
n/a |
14120 |
20 |
| 5648.2.cf |
\(\chi_{5648}(289, \cdot)\) |
n/a |
3520 |
20 |
| 5648.2.ch |
\(\chi_{5648}(121, \cdot)\) |
None |
0 |
20 |
| 5648.2.ci |
\(\chi_{5648}(213, \cdot)\) |
n/a |
14120 |
20 |
| 5648.2.ck |
\(\chi_{5648}(349, \cdot)\) |
n/a |
14120 |
20 |
| 5648.2.cm |
\(\chi_{5648}(73, \cdot)\) |
None |
0 |
40 |
| 5648.2.co |
\(\chi_{5648}(21, \cdot)\) |
n/a |
28240 |
40 |
| 5648.2.cr |
\(\chi_{5648}(109, \cdot)\) |
n/a |
28240 |
40 |
| 5648.2.ct |
\(\chi_{5648}(17, \cdot)\) |
n/a |
7040 |
40 |
| 5648.2.cv |
\(\chi_{5648}(181, \cdot)\) |
n/a |
56480 |
80 |
| 5648.2.cx |
\(\chi_{5648}(9, \cdot)\) |
None |
0 |
80 |
| 5648.2.cz |
\(\chi_{5648}(65, \cdot)\) |
n/a |
14080 |
80 |
| 5648.2.da |
\(\chi_{5648}(93, \cdot)\) |
n/a |
56480 |
80 |
| 5648.2.dc |
\(\chi_{5648}(3, \cdot)\) |
n/a |
112960 |
160 |
| 5648.2.de |
\(\chi_{5648}(55, \cdot)\) |
None |
0 |
160 |
| 5648.2.dh |
\(\chi_{5648}(31, \cdot)\) |
n/a |
28320 |
160 |
| 5648.2.di |
\(\chi_{5648}(115, \cdot)\) |
n/a |
112960 |
160 |
"n/a" means that newforms for that character have not been added to the database yet
