Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2365))\).
|
Total |
New |
Old |
Modular forms
| 225120 |
201891 |
23229 |
Cusp forms
| 218401 |
197467 |
20934 |
Eisenstein series
| 6719 |
4424 |
2295 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2365))\)
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 |
2365.2.a |
\(\chi_{2365}(1, \cdot)\) |
2365.2.a.a |
1 |
1 |
2365.2.a.b |
1 |
2365.2.a.c |
1 |
2365.2.a.d |
1 |
2365.2.a.e |
1 |
2365.2.a.f |
2 |
2365.2.a.g |
2 |
2365.2.a.h |
9 |
2365.2.a.i |
13 |
2365.2.a.j |
16 |
2365.2.a.k |
17 |
2365.2.a.l |
17 |
2365.2.a.m |
18 |
2365.2.a.n |
20 |
2365.2.a.o |
20 |
2365.2.b |
\(\chi_{2365}(474, \cdot)\) |
n/a |
212 |
1 |
2365.2.e |
\(\chi_{2365}(2364, \cdot)\) |
n/a |
260 |
1 |
2365.2.f |
\(\chi_{2365}(1891, \cdot)\) |
n/a |
176 |
1 |
2365.2.i |
\(\chi_{2365}(221, \cdot)\) |
n/a |
296 |
2 |
2365.2.k |
\(\chi_{2365}(87, \cdot)\) |
n/a |
504 |
2 |
2365.2.m |
\(\chi_{2365}(1332, \cdot)\) |
n/a |
440 |
2 |
2365.2.n |
\(\chi_{2365}(861, \cdot)\) |
n/a |
672 |
4 |
2365.2.o |
\(\chi_{2365}(824, \cdot)\) |
n/a |
520 |
2 |
2365.2.r |
\(\chi_{2365}(694, \cdot)\) |
n/a |
440 |
2 |
2365.2.u |
\(\chi_{2365}(351, \cdot)\) |
n/a |
352 |
2 |
2365.2.v |
\(\chi_{2365}(441, \cdot)\) |
n/a |
864 |
6 |
2365.2.y |
\(\chi_{2365}(171, \cdot)\) |
n/a |
704 |
4 |
2365.2.z |
\(\chi_{2365}(644, \cdot)\) |
n/a |
1040 |
4 |
2365.2.bc |
\(\chi_{2365}(1334, \cdot)\) |
n/a |
1008 |
4 |
2365.2.bd |
\(\chi_{2365}(738, \cdot)\) |
n/a |
880 |
4 |
2365.2.bf |
\(\chi_{2365}(208, \cdot)\) |
n/a |
1040 |
4 |
2365.2.bj |
\(\chi_{2365}(131, \cdot)\) |
n/a |
1056 |
6 |
2365.2.bk |
\(\chi_{2365}(604, \cdot)\) |
n/a |
1560 |
6 |
2365.2.bn |
\(\chi_{2365}(914, \cdot)\) |
n/a |
1320 |
6 |
2365.2.bo |
\(\chi_{2365}(36, \cdot)\) |
n/a |
1408 |
8 |
2365.2.bp |
\(\chi_{2365}(42, \cdot)\) |
n/a |
2080 |
8 |
2365.2.br |
\(\chi_{2365}(173, \cdot)\) |
n/a |
2016 |
8 |
2365.2.bt |
\(\chi_{2365}(56, \cdot)\) |
n/a |
1776 |
12 |
2365.2.bu |
\(\chi_{2365}(428, \cdot)\) |
n/a |
3120 |
12 |
2365.2.bw |
\(\chi_{2365}(452, \cdot)\) |
n/a |
2640 |
12 |
2365.2.by |
\(\chi_{2365}(381, \cdot)\) |
n/a |
1408 |
8 |
2365.2.cb |
\(\chi_{2365}(49, \cdot)\) |
n/a |
2080 |
8 |
2365.2.ce |
\(\chi_{2365}(424, \cdot)\) |
n/a |
2080 |
8 |
2365.2.cf |
\(\chi_{2365}(16, \cdot)\) |
n/a |
4224 |
24 |
2365.2.cg |
\(\chi_{2365}(76, \cdot)\) |
n/a |
2112 |
12 |
2365.2.cj |
\(\chi_{2365}(144, \cdot)\) |
n/a |
2640 |
12 |
2365.2.cm |
\(\chi_{2365}(329, \cdot)\) |
n/a |
3120 |
12 |
2365.2.co |
\(\chi_{2365}(178, \cdot)\) |
n/a |
4160 |
16 |
2365.2.cq |
\(\chi_{2365}(37, \cdot)\) |
n/a |
4160 |
16 |
2365.2.cr |
\(\chi_{2365}(4, \cdot)\) |
n/a |
6240 |
24 |
2365.2.cu |
\(\chi_{2365}(39, \cdot)\) |
n/a |
6240 |
24 |
2365.2.cv |
\(\chi_{2365}(51, \cdot)\) |
n/a |
4224 |
24 |
2365.2.cz |
\(\chi_{2365}(12, \cdot)\) |
n/a |
5280 |
24 |
2365.2.db |
\(\chi_{2365}(142, \cdot)\) |
n/a |
6240 |
24 |
2365.2.dc |
\(\chi_{2365}(31, \cdot)\) |
n/a |
8448 |
48 |
2365.2.de |
\(\chi_{2365}(27, \cdot)\) |
n/a |
12480 |
48 |
2365.2.dg |
\(\chi_{2365}(107, \cdot)\) |
n/a |
12480 |
48 |
2365.2.dh |
\(\chi_{2365}(19, \cdot)\) |
n/a |
12480 |
48 |
2365.2.dk |
\(\chi_{2365}(9, \cdot)\) |
n/a |
12480 |
48 |
2365.2.dn |
\(\chi_{2365}(46, \cdot)\) |
n/a |
8448 |
48 |
2365.2.do |
\(\chi_{2365}(13, \cdot)\) |
n/a |
24960 |
96 |
2365.2.dq |
\(\chi_{2365}(3, \cdot)\) |
n/a |
24960 |
96 |
"n/a" means that newforms for that character have not been added to the database yet