Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(585))\).
|
Total |
New |
Old |
| Modular forms
| 37056 |
26320 |
10736 |
| Cusp forms
| 35520 |
25724 |
9796 |
| Eisenstein series
| 1536 |
596 |
940 |
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(585))\)
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 |
| 585.4.a |
\(\chi_{585}(1, \cdot)\) |
585.4.a.a |
1 |
1 |
| 585.4.a.b |
1 |
| 585.4.a.c |
1 |
| 585.4.a.d |
1 |
| 585.4.a.e |
1 |
| 585.4.a.f |
2 |
| 585.4.a.g |
2 |
| 585.4.a.h |
2 |
| 585.4.a.i |
2 |
| 585.4.a.j |
3 |
| 585.4.a.k |
3 |
| 585.4.a.l |
4 |
| 585.4.a.m |
4 |
| 585.4.a.n |
4 |
| 585.4.a.o |
5 |
| 585.4.a.p |
5 |
| 585.4.a.q |
5 |
| 585.4.a.r |
7 |
| 585.4.a.s |
7 |
| 585.4.b |
\(\chi_{585}(181, \cdot)\) |
585.4.b.a |
2 |
1 |
| 585.4.b.b |
2 |
| 585.4.b.c |
2 |
| 585.4.b.d |
8 |
| 585.4.b.e |
14 |
| 585.4.b.f |
14 |
| 585.4.b.g |
28 |
| 585.4.c |
\(\chi_{585}(469, \cdot)\) |
585.4.c.a |
2 |
1 |
| 585.4.c.b |
2 |
| 585.4.c.c |
12 |
| 585.4.c.d |
16 |
| 585.4.c.e |
22 |
| 585.4.c.f |
36 |
| 585.4.h |
\(\chi_{585}(64, \cdot)\) |
n/a |
104 |
1 |
| 585.4.i |
\(\chi_{585}(196, \cdot)\) |
n/a |
288 |
2 |
| 585.4.j |
\(\chi_{585}(406, \cdot)\) |
n/a |
140 |
2 |
| 585.4.k |
\(\chi_{585}(61, \cdot)\) |
n/a |
336 |
2 |
| 585.4.l |
\(\chi_{585}(16, \cdot)\) |
n/a |
336 |
2 |
| 585.4.n |
\(\chi_{585}(307, \cdot)\) |
n/a |
206 |
2 |
| 585.4.p |
\(\chi_{585}(53, \cdot)\) |
n/a |
144 |
2 |
| 585.4.q |
\(\chi_{585}(44, \cdot)\) |
n/a |
168 |
2 |
| 585.4.r |
\(\chi_{585}(161, \cdot)\) |
n/a |
112 |
2 |
| 585.4.v |
\(\chi_{585}(233, \cdot)\) |
n/a |
168 |
2 |
| 585.4.w |
\(\chi_{585}(73, \cdot)\) |
n/a |
206 |
2 |
| 585.4.ba |
\(\chi_{585}(121, \cdot)\) |
n/a |
336 |
2 |
| 585.4.bb |
\(\chi_{585}(139, \cdot)\) |
n/a |
496 |
2 |
| 585.4.be |
\(\chi_{585}(259, \cdot)\) |
n/a |
496 |
2 |
| 585.4.bf |
\(\chi_{585}(199, \cdot)\) |
n/a |
208 |
2 |
| 585.4.bk |
\(\chi_{585}(49, \cdot)\) |
n/a |
496 |
2 |
| 585.4.bl |
\(\chi_{585}(94, \cdot)\) |
n/a |
496 |
2 |
| 585.4.bm |
\(\chi_{585}(166, \cdot)\) |
n/a |
336 |
2 |
| 585.4.br |
\(\chi_{585}(79, \cdot)\) |
n/a |
432 |
2 |
| 585.4.bs |
\(\chi_{585}(289, \cdot)\) |
n/a |
204 |
2 |
| 585.4.bt |
\(\chi_{585}(376, \cdot)\) |
n/a |
336 |
2 |
| 585.4.bu |
\(\chi_{585}(316, \cdot)\) |
n/a |
140 |
2 |
| 585.4.bx |
\(\chi_{585}(4, \cdot)\) |
n/a |
496 |
2 |
| 585.4.ca |
\(\chi_{585}(58, \cdot)\) |
n/a |
992 |
4 |
| 585.4.cc |
\(\chi_{585}(67, \cdot)\) |
n/a |
992 |
4 |
| 585.4.cf |
\(\chi_{585}(163, \cdot)\) |
n/a |
412 |
4 |
| 585.4.cg |
\(\chi_{585}(187, \cdot)\) |
n/a |
992 |
4 |
| 585.4.ci |
\(\chi_{585}(113, \cdot)\) |
n/a |
992 |
4 |
| 585.4.cm |
\(\chi_{585}(11, \cdot)\) |
n/a |
672 |
4 |
| 585.4.cn |
\(\chi_{585}(59, \cdot)\) |
n/a |
992 |
4 |
| 585.4.co |
\(\chi_{585}(212, \cdot)\) |
n/a |
992 |
4 |
| 585.4.cr |
\(\chi_{585}(23, \cdot)\) |
n/a |
992 |
4 |
| 585.4.cs |
\(\chi_{585}(38, \cdot)\) |
n/a |
992 |
4 |
| 585.4.cv |
\(\chi_{585}(17, \cdot)\) |
n/a |
336 |
4 |
| 585.4.cw |
\(\chi_{585}(71, \cdot)\) |
n/a |
224 |
4 |
| 585.4.cx |
\(\chi_{585}(89, \cdot)\) |
n/a |
336 |
4 |
| 585.4.dc |
\(\chi_{585}(164, \cdot)\) |
n/a |
992 |
4 |
| 585.4.dd |
\(\chi_{585}(41, \cdot)\) |
n/a |
672 |
4 |
| 585.4.de |
\(\chi_{585}(254, \cdot)\) |
n/a |
992 |
4 |
| 585.4.df |
\(\chi_{585}(86, \cdot)\) |
n/a |
672 |
4 |
| 585.4.dj |
\(\chi_{585}(92, \cdot)\) |
n/a |
864 |
4 |
| 585.4.dk |
\(\chi_{585}(68, \cdot)\) |
n/a |
992 |
4 |
| 585.4.dn |
\(\chi_{585}(107, \cdot)\) |
n/a |
336 |
4 |
| 585.4.dp |
\(\chi_{585}(28, \cdot)\) |
n/a |
412 |
4 |
| 585.4.dq |
\(\chi_{585}(112, \cdot)\) |
n/a |
992 |
4 |
| 585.4.dt |
\(\chi_{585}(7, \cdot)\) |
n/a |
992 |
4 |
| 585.4.dv |
\(\chi_{585}(292, \cdot)\) |
n/a |
992 |
4 |
"n/a" means that newforms for that character have not been added to the database yet
