Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2624))\).
|
Total |
New |
Old |
Modular forms
| 217920 |
121674 |
96246 |
Cusp forms
| 212161 |
119958 |
92203 |
Eisenstein series
| 5759 |
1716 |
4043 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2624))\)
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 |
2624.2.a |
\(\chi_{2624}(1, \cdot)\) |
2624.2.a.a |
1 |
1 |
2624.2.a.b |
1 |
2624.2.a.c |
1 |
2624.2.a.d |
1 |
2624.2.a.e |
1 |
2624.2.a.f |
1 |
2624.2.a.g |
1 |
2624.2.a.h |
1 |
2624.2.a.i |
2 |
2624.2.a.j |
2 |
2624.2.a.k |
2 |
2624.2.a.l |
2 |
2624.2.a.m |
2 |
2624.2.a.n |
3 |
2624.2.a.o |
3 |
2624.2.a.p |
3 |
2624.2.a.q |
3 |
2624.2.a.r |
3 |
2624.2.a.s |
3 |
2624.2.a.t |
3 |
2624.2.a.u |
3 |
2624.2.a.v |
4 |
2624.2.a.w |
4 |
2624.2.a.x |
4 |
2624.2.a.y |
4 |
2624.2.a.z |
7 |
2624.2.a.ba |
7 |
2624.2.a.bb |
8 |
2624.2.b |
\(\chi_{2624}(1313, \cdot)\) |
2624.2.b.a |
2 |
1 |
2624.2.b.b |
2 |
2624.2.b.c |
4 |
2624.2.b.d |
4 |
2624.2.b.e |
12 |
2624.2.b.f |
28 |
2624.2.b.g |
28 |
2624.2.d |
\(\chi_{2624}(2049, \cdot)\) |
2624.2.d.a |
2 |
1 |
2624.2.d.b |
2 |
2624.2.d.c |
2 |
2624.2.d.d |
2 |
2624.2.d.e |
2 |
2624.2.d.f |
2 |
2624.2.d.g |
2 |
2624.2.d.h |
2 |
2624.2.d.i |
2 |
2624.2.d.j |
4 |
2624.2.d.k |
4 |
2624.2.d.l |
4 |
2624.2.d.m |
4 |
2624.2.d.n |
6 |
2624.2.d.o |
6 |
2624.2.d.p |
8 |
2624.2.d.q |
8 |
2624.2.d.r |
10 |
2624.2.d.s |
10 |
2624.2.g |
\(\chi_{2624}(737, \cdot)\) |
2624.2.g.a |
4 |
1 |
2624.2.g.b |
8 |
2624.2.g.c |
16 |
2624.2.g.d |
56 |
2624.2.i |
\(\chi_{2624}(337, \cdot)\) |
n/a |
164 |
2 |
2624.2.l |
\(\chi_{2624}(2305, \cdot)\) |
n/a |
164 |
2 |
2624.2.n |
\(\chi_{2624}(657, \cdot)\) |
n/a |
160 |
2 |
2624.2.o |
\(\chi_{2624}(81, \cdot)\) |
n/a |
164 |
2 |
2624.2.r |
\(\chi_{2624}(993, \cdot)\) |
n/a |
168 |
2 |
2624.2.t |
\(\chi_{2624}(401, \cdot)\) |
n/a |
164 |
2 |
2624.2.u |
\(\chi_{2624}(385, \cdot)\) |
n/a |
328 |
4 |
2624.2.v |
\(\chi_{2624}(167, \cdot)\) |
None |
0 |
4 |
2624.2.x |
\(\chi_{2624}(79, \cdot)\) |
n/a |
328 |
4 |
2624.2.ba |
\(\chi_{2624}(73, \cdot)\) |
None |
0 |
4 |
2624.2.bc |
\(\chi_{2624}(407, \cdot)\) |
None |
0 |
4 |
2624.2.be |
\(\chi_{2624}(519, \cdot)\) |
None |
0 |
4 |
2624.2.bf |
\(\chi_{2624}(329, \cdot)\) |
None |
0 |
4 |
2624.2.bj |
\(\chi_{2624}(735, \cdot)\) |
n/a |
336 |
4 |
2624.2.bk |
\(\chi_{2624}(191, \cdot)\) |
n/a |
328 |
4 |
2624.2.bm |
\(\chi_{2624}(409, \cdot)\) |
None |
0 |
4 |
2624.2.bo |
\(\chi_{2624}(9, \cdot)\) |
None |
0 |
4 |
2624.2.bp |
\(\chi_{2624}(495, \cdot)\) |
n/a |
328 |
4 |
2624.2.bs |
\(\chi_{2624}(55, \cdot)\) |
None |
0 |
4 |
2624.2.bu |
\(\chi_{2624}(769, \cdot)\) |
n/a |
328 |
4 |
2624.2.bw |
\(\chi_{2624}(1185, \cdot)\) |
n/a |
336 |
4 |
2624.2.by |
\(\chi_{2624}(353, \cdot)\) |
n/a |
336 |
4 |
2624.2.ca |
\(\chi_{2624}(219, \cdot)\) |
n/a |
2672 |
8 |
2624.2.cd |
\(\chi_{2624}(173, \cdot)\) |
n/a |
2672 |
8 |
2624.2.ce |
\(\chi_{2624}(245, \cdot)\) |
n/a |
2672 |
8 |
2624.2.cf |
\(\chi_{2624}(165, \cdot)\) |
n/a |
2560 |
8 |
2624.2.cg |
\(\chi_{2624}(355, \cdot)\) |
n/a |
2672 |
8 |
2624.2.ch |
\(\chi_{2624}(331, \cdot)\) |
n/a |
2672 |
8 |
2624.2.cm |
\(\chi_{2624}(237, \cdot)\) |
n/a |
2672 |
8 |
2624.2.co |
\(\chi_{2624}(3, \cdot)\) |
n/a |
2672 |
8 |
2624.2.cr |
\(\chi_{2624}(241, \cdot)\) |
n/a |
656 |
8 |
2624.2.cs |
\(\chi_{2624}(33, \cdot)\) |
n/a |
672 |
8 |
2624.2.cv |
\(\chi_{2624}(113, \cdot)\) |
n/a |
656 |
8 |
2624.2.cw |
\(\chi_{2624}(305, \cdot)\) |
n/a |
656 |
8 |
2624.2.cy |
\(\chi_{2624}(449, \cdot)\) |
n/a |
656 |
8 |
2624.2.da |
\(\chi_{2624}(49, \cdot)\) |
n/a |
656 |
8 |
2624.2.dd |
\(\chi_{2624}(135, \cdot)\) |
None |
0 |
16 |
2624.2.df |
\(\chi_{2624}(15, \cdot)\) |
n/a |
1312 |
16 |
2624.2.dg |
\(\chi_{2624}(169, \cdot)\) |
None |
0 |
16 |
2624.2.di |
\(\chi_{2624}(199, \cdot)\) |
None |
0 |
16 |
2624.2.dk |
\(\chi_{2624}(151, \cdot)\) |
None |
0 |
16 |
2624.2.dm |
\(\chi_{2624}(25, \cdot)\) |
None |
0 |
16 |
2624.2.do |
\(\chi_{2624}(63, \cdot)\) |
n/a |
1312 |
16 |
2624.2.dp |
\(\chi_{2624}(95, \cdot)\) |
n/a |
1344 |
16 |
2624.2.dt |
\(\chi_{2624}(57, \cdot)\) |
None |
0 |
16 |
2624.2.du |
\(\chi_{2624}(121, \cdot)\) |
None |
0 |
16 |
2624.2.dx |
\(\chi_{2624}(47, \cdot)\) |
n/a |
1312 |
16 |
2624.2.dy |
\(\chi_{2624}(7, \cdot)\) |
None |
0 |
16 |
2624.2.eb |
\(\chi_{2624}(259, \cdot)\) |
n/a |
10688 |
32 |
2624.2.ed |
\(\chi_{2624}(5, \cdot)\) |
n/a |
10688 |
32 |
2624.2.ei |
\(\chi_{2624}(67, \cdot)\) |
n/a |
10688 |
32 |
2624.2.ej |
\(\chi_{2624}(11, \cdot)\) |
n/a |
10688 |
32 |
2624.2.ek |
\(\chi_{2624}(37, \cdot)\) |
n/a |
10688 |
32 |
2624.2.el |
\(\chi_{2624}(45, \cdot)\) |
n/a |
10688 |
32 |
2624.2.em |
\(\chi_{2624}(197, \cdot)\) |
n/a |
10688 |
32 |
2624.2.ep |
\(\chi_{2624}(275, \cdot)\) |
n/a |
10688 |
32 |
"n/a" means that newforms for that character have not been added to the database yet