Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(725))\).
|
Total |
New |
Old |
| Modular forms
| 21784 |
19863 |
1921 |
| Cusp forms
| 20217 |
18757 |
1460 |
| Eisenstein series
| 1567 |
1106 |
461 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(725))\)
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 |
| 725.2.a |
\(\chi_{725}(1, \cdot)\) |
725.2.a.a |
1 |
1 |
| 725.2.a.b |
2 |
| 725.2.a.c |
2 |
| 725.2.a.d |
3 |
| 725.2.a.e |
3 |
| 725.2.a.f |
4 |
| 725.2.a.g |
4 |
| 725.2.a.h |
5 |
| 725.2.a.i |
5 |
| 725.2.a.j |
5 |
| 725.2.a.k |
5 |
| 725.2.a.l |
6 |
| 725.2.b |
\(\chi_{725}(349, \cdot)\) |
725.2.b.a |
2 |
1 |
| 725.2.b.b |
4 |
| 725.2.b.c |
4 |
| 725.2.b.d |
6 |
| 725.2.b.e |
6 |
| 725.2.b.f |
10 |
| 725.2.b.g |
10 |
| 725.2.c |
\(\chi_{725}(376, \cdot)\) |
725.2.c.a |
2 |
1 |
| 725.2.c.b |
2 |
| 725.2.c.c |
2 |
| 725.2.c.d |
4 |
| 725.2.c.e |
6 |
| 725.2.c.f |
8 |
| 725.2.c.g |
10 |
| 725.2.c.h |
10 |
| 725.2.d |
\(\chi_{725}(724, \cdot)\) |
725.2.d.a |
4 |
1 |
| 725.2.d.b |
8 |
| 725.2.d.c |
12 |
| 725.2.d.d |
20 |
| 725.2.e |
\(\chi_{725}(157, \cdot)\) |
725.2.e.a |
4 |
2 |
| 725.2.e.b |
16 |
| 725.2.e.c |
26 |
| 725.2.e.d |
40 |
| 725.2.j |
\(\chi_{725}(307, \cdot)\) |
725.2.j.a |
4 |
2 |
| 725.2.j.b |
16 |
| 725.2.j.c |
26 |
| 725.2.j.d |
40 |
| 725.2.k |
\(\chi_{725}(146, \cdot)\) |
725.2.k.a |
4 |
4 |
| 725.2.k.b |
128 |
| 725.2.k.c |
148 |
| 725.2.l |
\(\chi_{725}(226, \cdot)\) |
725.2.l.a |
6 |
6 |
| 725.2.l.b |
6 |
| 725.2.l.c |
6 |
| 725.2.l.d |
24 |
| 725.2.l.e |
36 |
| 725.2.l.f |
54 |
| 725.2.l.g |
54 |
| 725.2.l.h |
84 |
| 725.2.m |
\(\chi_{725}(144, \cdot)\) |
725.2.m.a |
288 |
4 |
| 725.2.n |
\(\chi_{725}(59, \cdot)\) |
725.2.n.a |
128 |
4 |
| 725.2.n.b |
152 |
| 725.2.o |
\(\chi_{725}(86, \cdot)\) |
725.2.o.a |
296 |
4 |
| 725.2.p |
\(\chi_{725}(149, \cdot)\) |
725.2.p.a |
24 |
6 |
| 725.2.p.b |
48 |
| 725.2.p.c |
72 |
| 725.2.p.d |
120 |
| 725.2.q |
\(\chi_{725}(51, \cdot)\) |
725.2.q.a |
12 |
6 |
| 725.2.q.b |
24 |
| 725.2.q.c |
36 |
| 725.2.q.d |
60 |
| 725.2.q.e |
60 |
| 725.2.q.f |
72 |
| 725.2.r |
\(\chi_{725}(24, \cdot)\) |
725.2.r.a |
12 |
6 |
| 725.2.r.b |
12 |
| 725.2.r.c |
48 |
| 725.2.r.d |
72 |
| 725.2.r.e |
108 |
| 725.2.s |
\(\chi_{725}(17, \cdot)\) |
725.2.s.a |
584 |
8 |
| 725.2.x |
\(\chi_{725}(12, \cdot)\) |
725.2.x.a |
584 |
8 |
| 725.2.y |
\(\chi_{725}(18, \cdot)\) |
725.2.y.a |
120 |
12 |
| 725.2.y.b |
156 |
| 725.2.y.c |
240 |
| 725.2.bd |
\(\chi_{725}(43, \cdot)\) |
725.2.bd.a |
120 |
12 |
| 725.2.bd.b |
156 |
| 725.2.bd.c |
240 |
| 725.2.be |
\(\chi_{725}(16, \cdot)\) |
725.2.be.a |
1728 |
24 |
| 725.2.bf |
\(\chi_{725}(6, \cdot)\) |
725.2.bf.a |
1776 |
24 |
| 725.2.bg |
\(\chi_{725}(54, \cdot)\) |
725.2.bg.a |
1776 |
24 |
| 725.2.bh |
\(\chi_{725}(4, \cdot)\) |
725.2.bh.a |
1728 |
24 |
| 725.2.bi |
\(\chi_{725}(3, \cdot)\) |
725.2.bi.a |
3504 |
48 |
| 725.2.bn |
\(\chi_{725}(2, \cdot)\) |
725.2.bn.a |
3504 |
48 |
