Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(624))\).
|
Total |
New |
Old |
Modular forms
| 11424 |
4582 |
6842 |
Cusp forms
| 10081 |
4382 |
5699 |
Eisenstein series
| 1343 |
200 |
1143 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)
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 |
624.2.a |
\(\chi_{624}(1, \cdot)\) |
624.2.a.a |
1 |
1 |
624.2.a.b |
1 |
624.2.a.c |
1 |
624.2.a.d |
1 |
624.2.a.e |
1 |
624.2.a.f |
1 |
624.2.a.g |
1 |
624.2.a.h |
1 |
624.2.a.i |
1 |
624.2.a.j |
1 |
624.2.a.k |
2 |
624.2.c |
\(\chi_{624}(337, \cdot)\) |
624.2.c.a |
2 |
1 |
624.2.c.b |
2 |
624.2.c.c |
2 |
624.2.c.d |
2 |
624.2.c.e |
2 |
624.2.c.f |
2 |
624.2.c.g |
2 |
624.2.d |
\(\chi_{624}(287, \cdot)\) |
624.2.d.a |
2 |
1 |
624.2.d.b |
2 |
624.2.d.c |
2 |
624.2.d.d |
2 |
624.2.d.e |
2 |
624.2.d.f |
2 |
624.2.d.g |
4 |
624.2.d.h |
4 |
624.2.d.i |
4 |
624.2.g |
\(\chi_{624}(313, \cdot)\) |
None |
0 |
1 |
624.2.h |
\(\chi_{624}(311, \cdot)\) |
None |
0 |
1 |
624.2.j |
\(\chi_{624}(599, \cdot)\) |
None |
0 |
1 |
624.2.m |
\(\chi_{624}(25, \cdot)\) |
None |
0 |
1 |
624.2.n |
\(\chi_{624}(623, \cdot)\) |
624.2.n.a |
2 |
1 |
624.2.n.b |
2 |
624.2.n.c |
4 |
624.2.n.d |
4 |
624.2.n.e |
8 |
624.2.n.f |
8 |
624.2.q |
\(\chi_{624}(289, \cdot)\) |
624.2.q.a |
2 |
2 |
624.2.q.b |
2 |
624.2.q.c |
2 |
624.2.q.d |
2 |
624.2.q.e |
2 |
624.2.q.f |
2 |
624.2.q.g |
2 |
624.2.q.h |
4 |
624.2.q.i |
4 |
624.2.q.j |
6 |
624.2.r |
\(\chi_{624}(499, \cdot)\) |
624.2.r.a |
112 |
2 |
624.2.u |
\(\chi_{624}(5, \cdot)\) |
624.2.u.a |
4 |
2 |
624.2.u.b |
4 |
624.2.u.c |
208 |
624.2.v |
\(\chi_{624}(155, \cdot)\) |
624.2.v.a |
16 |
2 |
624.2.v.b |
200 |
624.2.x |
\(\chi_{624}(157, \cdot)\) |
624.2.x.a |
40 |
2 |
624.2.x.b |
56 |
624.2.bb |
\(\chi_{624}(151, \cdot)\) |
None |
0 |
2 |
624.2.bc |
\(\chi_{624}(31, \cdot)\) |
624.2.bc.a |
2 |
2 |
624.2.bc.b |
2 |
624.2.bc.c |
4 |
624.2.bc.d |
4 |
624.2.bc.e |
8 |
624.2.bc.f |
8 |
624.2.bf |
\(\chi_{624}(161, \cdot)\) |
624.2.bf.a |
4 |
2 |
624.2.bf.b |
4 |
624.2.bf.c |
4 |
624.2.bf.d |
4 |
624.2.bf.e |
8 |
624.2.bf.f |
12 |
624.2.bf.g |
16 |
624.2.bg |
\(\chi_{624}(281, \cdot)\) |
None |
0 |
2 |
624.2.bh |
\(\chi_{624}(131, \cdot)\) |
624.2.bh.a |
192 |
2 |
624.2.bj |
\(\chi_{624}(181, \cdot)\) |
624.2.bj.a |
112 |
2 |
624.2.bm |
\(\chi_{624}(317, \cdot)\) |
624.2.bm.a |
4 |
2 |
624.2.bm.b |
4 |
624.2.bm.c |
208 |
624.2.bn |
\(\chi_{624}(187, \cdot)\) |
624.2.bn.a |
112 |
2 |
624.2.bq |
\(\chi_{624}(23, \cdot)\) |
None |
0 |
2 |
624.2.br |
\(\chi_{624}(217, \cdot)\) |
None |
0 |
2 |
624.2.bu |
\(\chi_{624}(191, \cdot)\) |
624.2.bu.a |
2 |
2 |
624.2.bu.b |
2 |
624.2.bu.c |
2 |
624.2.bu.d |
2 |
624.2.bu.e |
2 |
624.2.bu.f |
2 |
624.2.bu.g |
2 |
624.2.bu.h |
2 |
624.2.bu.i |
4 |
624.2.bu.j |
4 |
624.2.bu.k |
6 |
624.2.bu.l |
6 |
624.2.bu.m |
6 |
624.2.bu.n |
6 |
624.2.bu.o |
8 |
624.2.bv |
\(\chi_{624}(49, \cdot)\) |
624.2.bv.a |
2 |
2 |
624.2.bv.b |
2 |
624.2.bv.c |
4 |
624.2.bv.d |
4 |
624.2.bv.e |
4 |
624.2.bv.f |
4 |
624.2.bv.g |
8 |
624.2.bz |
\(\chi_{624}(95, \cdot)\) |
624.2.bz.a |
2 |
2 |
624.2.bz.b |
2 |
624.2.bz.c |
2 |
624.2.bz.d |
2 |
624.2.bz.e |
8 |
624.2.bz.f |
8 |
624.2.bz.g |
16 |
624.2.bz.h |
16 |
624.2.ca |
\(\chi_{624}(121, \cdot)\) |
None |
0 |
2 |
624.2.cd |
\(\chi_{624}(263, \cdot)\) |
None |
0 |
2 |
624.2.ce |
\(\chi_{624}(149, \cdot)\) |
624.2.ce.a |
432 |
4 |
624.2.ch |
\(\chi_{624}(19, \cdot)\) |
624.2.ch.a |
224 |
4 |
624.2.cj |
\(\chi_{624}(205, \cdot)\) |
624.2.cj.a |
224 |
4 |
624.2.cl |
\(\chi_{624}(35, \cdot)\) |
624.2.cl.a |
432 |
4 |
624.2.cm |
\(\chi_{624}(41, \cdot)\) |
None |
0 |
4 |
624.2.cn |
\(\chi_{624}(305, \cdot)\) |
624.2.cn.a |
4 |
4 |
624.2.cn.b |
4 |
624.2.cn.c |
8 |
624.2.cn.d |
16 |
624.2.cn.e |
16 |
624.2.cn.f |
56 |
624.2.cq |
\(\chi_{624}(175, \cdot)\) |
624.2.cq.a |
8 |
4 |
624.2.cq.b |
8 |
624.2.cq.c |
8 |
624.2.cq.d |
8 |
624.2.cq.e |
12 |
624.2.cq.f |
12 |
624.2.cr |
\(\chi_{624}(7, \cdot)\) |
None |
0 |
4 |
624.2.cv |
\(\chi_{624}(61, \cdot)\) |
624.2.cv.a |
224 |
4 |
624.2.cx |
\(\chi_{624}(179, \cdot)\) |
624.2.cx.a |
432 |
4 |
624.2.cz |
\(\chi_{624}(115, \cdot)\) |
624.2.cz.a |
224 |
4 |
624.2.da |
\(\chi_{624}(245, \cdot)\) |
624.2.da.a |
432 |
4 |