Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(325))\).
|
Total |
New |
Old |
| Modular forms
| 4536 |
4051 |
485 |
| Cusp forms
| 3865 |
3601 |
264 |
| Eisenstein series
| 671 |
450 |
221 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)
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 |
| 325.2.a |
\(\chi_{325}(1, \cdot)\) |
325.2.a.a |
1 |
1 |
| 325.2.a.b |
1 |
| 325.2.a.c |
1 |
| 325.2.a.d |
1 |
| 325.2.a.e |
1 |
| 325.2.a.f |
2 |
| 325.2.a.g |
2 |
| 325.2.a.h |
2 |
| 325.2.a.i |
2 |
| 325.2.a.j |
3 |
| 325.2.a.k |
3 |
| 325.2.b |
\(\chi_{325}(274, \cdot)\) |
325.2.b.a |
2 |
1 |
| 325.2.b.b |
2 |
| 325.2.b.c |
2 |
| 325.2.b.d |
4 |
| 325.2.b.e |
4 |
| 325.2.b.f |
4 |
| 325.2.c |
\(\chi_{325}(51, \cdot)\) |
325.2.c.a |
2 |
1 |
| 325.2.c.b |
2 |
| 325.2.c.c |
2 |
| 325.2.c.d |
2 |
| 325.2.c.e |
2 |
| 325.2.c.f |
2 |
| 325.2.c.g |
6 |
| 325.2.d |
\(\chi_{325}(324, \cdot)\) |
325.2.d.a |
2 |
1 |
| 325.2.d.b |
2 |
| 325.2.d.c |
2 |
| 325.2.d.d |
2 |
| 325.2.d.e |
6 |
| 325.2.d.f |
6 |
| 325.2.e |
\(\chi_{325}(126, \cdot)\) |
325.2.e.a |
4 |
2 |
| 325.2.e.b |
4 |
| 325.2.e.c |
10 |
| 325.2.e.d |
10 |
| 325.2.e.e |
12 |
| 325.2.f |
\(\chi_{325}(18, \cdot)\) |
325.2.f.a |
2 |
2 |
| 325.2.f.b |
8 |
| 325.2.f.c |
12 |
| 325.2.f.d |
16 |
| 325.2.k |
\(\chi_{325}(57, \cdot)\) |
325.2.k.a |
2 |
2 |
| 325.2.k.b |
8 |
| 325.2.k.c |
12 |
| 325.2.k.d |
16 |
| 325.2.l |
\(\chi_{325}(66, \cdot)\) |
325.2.l.a |
4 |
4 |
| 325.2.l.b |
56 |
| 325.2.l.c |
60 |
| 325.2.m |
\(\chi_{325}(49, \cdot)\) |
325.2.m.a |
4 |
2 |
| 325.2.m.b |
8 |
| 325.2.m.c |
8 |
| 325.2.m.d |
20 |
| 325.2.n |
\(\chi_{325}(101, \cdot)\) |
325.2.n.a |
2 |
2 |
| 325.2.n.b |
4 |
| 325.2.n.c |
4 |
| 325.2.n.d |
8 |
| 325.2.n.e |
10 |
| 325.2.n.f |
10 |
| 325.2.o |
\(\chi_{325}(74, \cdot)\) |
325.2.o.a |
8 |
2 |
| 325.2.o.b |
8 |
| 325.2.o.c |
20 |
| 325.2.p |
\(\chi_{325}(64, \cdot)\) |
325.2.p.a |
128 |
4 |
| 325.2.q |
\(\chi_{325}(116, \cdot)\) |
325.2.q.a |
136 |
4 |
| 325.2.r |
\(\chi_{325}(14, \cdot)\) |
325.2.r.a |
120 |
4 |
| 325.2.s |
\(\chi_{325}(32, \cdot)\) |
325.2.s.a |
16 |
4 |
| 325.2.s.b |
20 |
| 325.2.s.c |
40 |
| 325.2.x |
\(\chi_{325}(7, \cdot)\) |
325.2.x.a |
16 |
4 |
| 325.2.x.b |
20 |
| 325.2.x.c |
40 |
| 325.2.y |
\(\chi_{325}(16, \cdot)\) |
325.2.y.a |
256 |
8 |
| 325.2.z |
\(\chi_{325}(8, \cdot)\) |
325.2.z.a |
8 |
8 |
| 325.2.z.b |
256 |
| 325.2.be |
\(\chi_{325}(47, \cdot)\) |
325.2.be.a |
8 |
8 |
| 325.2.be.b |
256 |
| 325.2.bf |
\(\chi_{325}(9, \cdot)\) |
325.2.bf.a |
272 |
8 |
| 325.2.bg |
\(\chi_{325}(36, \cdot)\) |
325.2.bg.a |
272 |
8 |
| 325.2.bh |
\(\chi_{325}(4, \cdot)\) |
325.2.bh.a |
256 |
8 |
| 325.2.bi |
\(\chi_{325}(28, \cdot)\) |
325.2.bi.a |
528 |
16 |
| 325.2.bn |
\(\chi_{325}(2, \cdot)\) |
325.2.bn.a |
528 |
16 |
