Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1205))\).
|
Total |
New |
Old |
Modular forms
| 59040 |
53955 |
5085 |
Cusp forms
| 57121 |
52519 |
4602 |
Eisenstein series
| 1919 |
1436 |
483 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1205))\)
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 |
1205.2.a |
\(\chi_{1205}(1, \cdot)\) |
1205.2.a.a |
5 |
1 |
1205.2.a.b |
11 |
1205.2.a.c |
15 |
1205.2.a.d |
25 |
1205.2.a.e |
25 |
1205.2.b |
\(\chi_{1205}(724, \cdot)\) |
1205.2.b.a |
4 |
1 |
1205.2.b.b |
4 |
1205.2.b.c |
46 |
1205.2.b.d |
66 |
1205.2.c |
\(\chi_{1205}(1204, \cdot)\) |
n/a |
120 |
1 |
1205.2.d |
\(\chi_{1205}(481, \cdot)\) |
1205.2.d.a |
6 |
1 |
1205.2.d.b |
34 |
1205.2.d.c |
42 |
1205.2.e |
\(\chi_{1205}(256, \cdot)\) |
n/a |
160 |
2 |
1205.2.f |
\(\chi_{1205}(546, \cdot)\) |
n/a |
164 |
2 |
1205.2.k |
\(\chi_{1205}(64, \cdot)\) |
n/a |
240 |
2 |
1205.2.l |
\(\chi_{1205}(91, \cdot)\) |
n/a |
328 |
4 |
1205.2.m |
\(\chi_{1205}(16, \cdot)\) |
n/a |
160 |
2 |
1205.2.n |
\(\chi_{1205}(739, \cdot)\) |
n/a |
240 |
2 |
1205.2.o |
\(\chi_{1205}(979, \cdot)\) |
n/a |
240 |
2 |
1205.2.q |
\(\chi_{1205}(249, \cdot)\) |
n/a |
472 |
4 |
1205.2.r |
\(\chi_{1205}(211, \cdot)\) |
n/a |
328 |
4 |
1205.2.t |
\(\chi_{1205}(154, \cdot)\) |
n/a |
480 |
4 |
1205.2.u |
\(\chi_{1205}(339, \cdot)\) |
n/a |
480 |
4 |
1205.2.v |
\(\chi_{1205}(36, \cdot)\) |
n/a |
328 |
4 |
1205.2.w |
\(\chi_{1205}(4, \cdot)\) |
n/a |
480 |
4 |
1205.2.bb |
\(\chi_{1205}(181, \cdot)\) |
n/a |
320 |
4 |
1205.2.bc |
\(\chi_{1205}(231, \cdot)\) |
n/a |
640 |
8 |
1205.2.bd |
\(\chi_{1205}(352, \cdot)\) |
n/a |
952 |
8 |
1205.2.be |
\(\chi_{1205}(197, \cdot)\) |
n/a |
952 |
8 |
1205.2.bh |
\(\chi_{1205}(6, \cdot)\) |
n/a |
656 |
8 |
1205.2.bm |
\(\chi_{1205}(729, \cdot)\) |
n/a |
960 |
8 |
1205.2.bo |
\(\chi_{1205}(121, \cdot)\) |
n/a |
640 |
8 |
1205.2.bp |
\(\chi_{1205}(209, \cdot)\) |
n/a |
944 |
8 |
1205.2.br |
\(\chi_{1205}(81, \cdot)\) |
n/a |
640 |
8 |
1205.2.bs |
\(\chi_{1205}(24, \cdot)\) |
n/a |
960 |
8 |
1205.2.bt |
\(\chi_{1205}(299, \cdot)\) |
n/a |
960 |
8 |
1205.2.bv |
\(\chi_{1205}(41, \cdot)\) |
n/a |
1312 |
16 |
1205.2.bw |
\(\chi_{1205}(79, \cdot)\) |
n/a |
1888 |
16 |
1205.2.ca |
\(\chi_{1205}(38, \cdot)\) |
n/a |
1904 |
16 |
1205.2.cb |
\(\chi_{1205}(22, \cdot)\) |
n/a |
1904 |
16 |
1205.2.cc |
\(\chi_{1205}(9, \cdot)\) |
n/a |
1920 |
16 |
1205.2.ch |
\(\chi_{1205}(96, \cdot)\) |
n/a |
1280 |
16 |
1205.2.ck |
\(\chi_{1205}(33, \cdot)\) |
n/a |
3808 |
32 |
1205.2.cl |
\(\chi_{1205}(17, \cdot)\) |
n/a |
3808 |
32 |
1205.2.cn |
\(\chi_{1205}(29, \cdot)\) |
n/a |
3776 |
32 |
1205.2.co |
\(\chi_{1205}(161, \cdot)\) |
n/a |
2560 |
32 |
1205.2.cq |
\(\chi_{1205}(52, \cdot)\) |
n/a |
7616 |
64 |
1205.2.cr |
\(\chi_{1205}(7, \cdot)\) |
n/a |
7616 |
64 |
"n/a" means that newforms for that character have not been added to the database yet