Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2233))\).
|
Total |
New |
Old |
Modular forms
| 204960 |
191959 |
13001 |
Cusp forms
| 198241 |
187103 |
11138 |
Eisenstein series
| 6719 |
4856 |
1863 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2233))\)
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 |
2233.2.a |
\(\chi_{2233}(1, \cdot)\) |
2233.2.a.a |
1 |
1 |
2233.2.a.b |
1 |
2233.2.a.c |
2 |
2233.2.a.d |
3 |
2233.2.a.e |
5 |
2233.2.a.f |
8 |
2233.2.a.g |
13 |
2233.2.a.h |
14 |
2233.2.a.i |
16 |
2233.2.a.j |
17 |
2233.2.a.k |
17 |
2233.2.a.l |
21 |
2233.2.a.m |
21 |
2233.2.b |
\(\chi_{2233}(1770, \cdot)\) |
n/a |
224 |
1 |
2233.2.c |
\(\chi_{2233}(463, \cdot)\) |
n/a |
152 |
1 |
2233.2.h |
\(\chi_{2233}(2232, \cdot)\) |
n/a |
236 |
1 |
2233.2.i |
\(\chi_{2233}(639, \cdot)\) |
n/a |
376 |
2 |
2233.2.k |
\(\chi_{2233}(505, \cdot)\) |
n/a |
360 |
2 |
2233.2.m |
\(\chi_{2233}(650, \cdot)\) |
n/a |
400 |
2 |
2233.2.n |
\(\chi_{2233}(610, \cdot)\) |
n/a |
672 |
4 |
2233.2.o |
\(\chi_{2233}(318, \cdot)\) |
n/a |
472 |
2 |
2233.2.t |
\(\chi_{2233}(144, \cdot)\) |
n/a |
400 |
2 |
2233.2.u |
\(\chi_{2233}(1132, \cdot)\) |
n/a |
448 |
2 |
2233.2.v |
\(\chi_{2233}(78, \cdot)\) |
n/a |
888 |
6 |
2233.2.w |
\(\chi_{2233}(811, \cdot)\) |
n/a |
944 |
4 |
2233.2.bb |
\(\chi_{2233}(1072, \cdot)\) |
n/a |
720 |
4 |
2233.2.bc |
\(\chi_{2233}(349, \cdot)\) |
n/a |
896 |
4 |
2233.2.be |
\(\chi_{2233}(12, \cdot)\) |
n/a |
800 |
4 |
2233.2.bg |
\(\chi_{2233}(186, \cdot)\) |
n/a |
944 |
4 |
2233.2.bh |
\(\chi_{2233}(615, \cdot)\) |
n/a |
1416 |
6 |
2233.2.bm |
\(\chi_{2233}(386, \cdot)\) |
n/a |
912 |
6 |
2233.2.bn |
\(\chi_{2233}(384, \cdot)\) |
n/a |
1416 |
6 |
2233.2.bo |
\(\chi_{2233}(291, \cdot)\) |
n/a |
1792 |
8 |
2233.2.bp |
\(\chi_{2233}(104, \cdot)\) |
n/a |
1888 |
8 |
2233.2.br |
\(\chi_{2233}(162, \cdot)\) |
n/a |
1440 |
8 |
2233.2.bt |
\(\chi_{2233}(23, \cdot)\) |
n/a |
2400 |
12 |
2233.2.bu |
\(\chi_{2233}(188, \cdot)\) |
n/a |
2400 |
12 |
2233.2.bw |
\(\chi_{2233}(43, \cdot)\) |
n/a |
2160 |
12 |
2233.2.by |
\(\chi_{2233}(117, \cdot)\) |
n/a |
1792 |
8 |
2233.2.bz |
\(\chi_{2233}(86, \cdot)\) |
n/a |
1888 |
8 |
2233.2.ce |
\(\chi_{2233}(173, \cdot)\) |
n/a |
1888 |
8 |
2233.2.cf |
\(\chi_{2233}(36, \cdot)\) |
n/a |
4320 |
24 |
2233.2.cg |
\(\chi_{2233}(54, \cdot)\) |
n/a |
2832 |
12 |
2233.2.ch |
\(\chi_{2233}(67, \cdot)\) |
n/a |
2400 |
12 |
2233.2.cm |
\(\chi_{2233}(208, \cdot)\) |
n/a |
2832 |
12 |
2233.2.cn |
\(\chi_{2233}(46, \cdot)\) |
n/a |
3776 |
16 |
2233.2.cp |
\(\chi_{2233}(75, \cdot)\) |
n/a |
3776 |
16 |
2233.2.cr |
\(\chi_{2233}(83, \cdot)\) |
n/a |
5664 |
24 |
2233.2.cs |
\(\chi_{2233}(64, \cdot)\) |
n/a |
4320 |
24 |
2233.2.cx |
\(\chi_{2233}(6, \cdot)\) |
n/a |
5664 |
24 |
2233.2.cy |
\(\chi_{2233}(32, \cdot)\) |
n/a |
5664 |
24 |
2233.2.da |
\(\chi_{2233}(89, \cdot)\) |
n/a |
4800 |
24 |
2233.2.dc |
\(\chi_{2233}(16, \cdot)\) |
n/a |
11328 |
48 |
2233.2.de |
\(\chi_{2233}(8, \cdot)\) |
n/a |
8640 |
48 |
2233.2.dg |
\(\chi_{2233}(27, \cdot)\) |
n/a |
11328 |
48 |
2233.2.dh |
\(\chi_{2233}(96, \cdot)\) |
n/a |
11328 |
48 |
2233.2.dm |
\(\chi_{2233}(4, \cdot)\) |
n/a |
11328 |
48 |
2233.2.dn |
\(\chi_{2233}(24, \cdot)\) |
n/a |
11328 |
48 |
2233.2.dp |
\(\chi_{2233}(3, \cdot)\) |
n/a |
22656 |
96 |
2233.2.dr |
\(\chi_{2233}(2, \cdot)\) |
n/a |
22656 |
96 |
"n/a" means that newforms for that character have not been added to the database yet