Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(465))\).
|
Total |
New |
Old |
Modular forms
| 8160 |
5443 |
2717 |
Cusp forms
| 7201 |
5099 |
2102 |
Eisenstein series
| 959 |
344 |
615 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)
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 |
465.2.a |
\(\chi_{465}(1, \cdot)\) |
465.2.a.a |
1 |
1 |
465.2.a.b |
1 |
465.2.a.c |
2 |
465.2.a.d |
2 |
465.2.a.e |
3 |
465.2.a.f |
3 |
465.2.a.g |
3 |
465.2.a.h |
4 |
465.2.c |
\(\chi_{465}(94, \cdot)\) |
465.2.c.a |
10 |
1 |
465.2.c.b |
22 |
465.2.e |
\(\chi_{465}(371, \cdot)\) |
465.2.e.a |
44 |
1 |
465.2.g |
\(\chi_{465}(464, \cdot)\) |
465.2.g.a |
4 |
1 |
465.2.g.b |
4 |
465.2.g.c |
4 |
465.2.g.d |
8 |
465.2.g.e |
8 |
465.2.g.f |
32 |
465.2.i |
\(\chi_{465}(211, \cdot)\) |
465.2.i.a |
2 |
2 |
465.2.i.b |
4 |
465.2.i.c |
6 |
465.2.i.d |
8 |
465.2.i.e |
10 |
465.2.i.f |
14 |
465.2.j |
\(\chi_{465}(247, \cdot)\) |
465.2.j.a |
64 |
2 |
465.2.k |
\(\chi_{465}(32, \cdot)\) |
465.2.k.a |
60 |
2 |
465.2.k.b |
60 |
465.2.n |
\(\chi_{465}(16, \cdot)\) |
465.2.n.a |
4 |
4 |
465.2.n.b |
4 |
465.2.n.c |
8 |
465.2.n.d |
16 |
465.2.n.e |
20 |
465.2.n.f |
28 |
465.2.o |
\(\chi_{465}(26, \cdot)\) |
465.2.o.a |
84 |
2 |
465.2.q |
\(\chi_{465}(304, \cdot)\) |
465.2.q.a |
4 |
2 |
465.2.q.b |
60 |
465.2.t |
\(\chi_{465}(119, \cdot)\) |
465.2.t.a |
4 |
2 |
465.2.t.b |
4 |
465.2.t.c |
8 |
465.2.t.d |
104 |
465.2.w |
\(\chi_{465}(29, \cdot)\) |
465.2.w.a |
8 |
4 |
465.2.w.b |
8 |
465.2.w.c |
224 |
465.2.y |
\(\chi_{465}(116, \cdot)\) |
465.2.y.a |
176 |
4 |
465.2.ba |
\(\chi_{465}(4, \cdot)\) |
465.2.ba.a |
128 |
4 |
465.2.be |
\(\chi_{465}(98, \cdot)\) |
465.2.be.a |
240 |
4 |
465.2.bf |
\(\chi_{465}(37, \cdot)\) |
465.2.bf.a |
128 |
4 |
465.2.bg |
\(\chi_{465}(76, \cdot)\) |
465.2.bg.a |
32 |
8 |
465.2.bg.b |
40 |
465.2.bg.c |
48 |
465.2.bg.d |
56 |
465.2.bj |
\(\chi_{465}(2, \cdot)\) |
465.2.bj.a |
480 |
8 |
465.2.bk |
\(\chi_{465}(58, \cdot)\) |
465.2.bk.a |
256 |
8 |
465.2.bm |
\(\chi_{465}(44, \cdot)\) |
465.2.bm.a |
8 |
8 |
465.2.bm.b |
8 |
465.2.bm.c |
8 |
465.2.bm.d |
8 |
465.2.bm.e |
448 |
465.2.bp |
\(\chi_{465}(19, \cdot)\) |
465.2.bp.a |
256 |
8 |
465.2.br |
\(\chi_{465}(11, \cdot)\) |
465.2.br.a |
336 |
8 |
465.2.bs |
\(\chi_{465}(13, \cdot)\) |
465.2.bs.a |
512 |
16 |
465.2.bt |
\(\chi_{465}(38, \cdot)\) |
465.2.bt.a |
960 |
16 |