Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1275))\).
|
Total |
New |
Old |
Modular forms
| 59392 |
40154 |
19238 |
Cusp forms
| 55809 |
38922 |
16887 |
Eisenstein series
| 3583 |
1232 |
2351 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1275))\)
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 the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
1275.2.a |
\(\chi_{1275}(1, \cdot)\) |
1275.2.a.a |
1 |
1 |
1275.2.a.b |
1 |
1275.2.a.c |
1 |
1275.2.a.d |
1 |
1275.2.a.e |
1 |
1275.2.a.f |
1 |
1275.2.a.g |
1 |
1275.2.a.h |
2 |
1275.2.a.i |
2 |
1275.2.a.j |
2 |
1275.2.a.k |
2 |
1275.2.a.l |
2 |
1275.2.a.m |
2 |
1275.2.a.n |
2 |
1275.2.a.o |
3 |
1275.2.a.p |
3 |
1275.2.a.q |
3 |
1275.2.a.r |
3 |
1275.2.a.s |
3 |
1275.2.a.t |
4 |
1275.2.a.u |
5 |
1275.2.a.v |
5 |
1275.2.b |
\(\chi_{1275}(1174, \cdot)\) |
1275.2.b.a |
2 |
1 |
1275.2.b.b |
2 |
1275.2.b.c |
2 |
1275.2.b.d |
4 |
1275.2.b.e |
4 |
1275.2.b.f |
4 |
1275.2.b.g |
4 |
1275.2.b.h |
6 |
1275.2.b.i |
6 |
1275.2.b.j |
6 |
1275.2.b.k |
8 |
1275.2.d |
\(\chi_{1275}(424, \cdot)\) |
1275.2.d.a |
2 |
1 |
1275.2.d.b |
2 |
1275.2.d.c |
2 |
1275.2.d.d |
2 |
1275.2.d.e |
4 |
1275.2.d.f |
4 |
1275.2.d.g |
8 |
1275.2.d.h |
8 |
1275.2.d.i |
12 |
1275.2.d.j |
12 |
1275.2.g |
\(\chi_{1275}(526, \cdot)\) |
1275.2.g.a |
2 |
1 |
1275.2.g.b |
2 |
1275.2.g.c |
4 |
1275.2.g.d |
8 |
1275.2.g.e |
12 |
1275.2.g.f |
12 |
1275.2.g.g |
16 |
1275.2.j |
\(\chi_{1275}(676, \cdot)\) |
n/a |
112 |
2 |
1275.2.k |
\(\chi_{1275}(1007, \cdot)\) |
n/a |
208 |
2 |
1275.2.m |
\(\chi_{1275}(443, \cdot)\) |
n/a |
192 |
2 |
1275.2.o |
\(\chi_{1275}(407, \cdot)\) |
n/a |
208 |
2 |
1275.2.r |
\(\chi_{1275}(293, \cdot)\) |
n/a |
208 |
2 |
1275.2.s |
\(\chi_{1275}(574, \cdot)\) |
n/a |
112 |
2 |
1275.2.u |
\(\chi_{1275}(256, \cdot)\) |
n/a |
320 |
4 |
1275.2.w |
\(\chi_{1275}(332, \cdot)\) |
n/a |
416 |
4 |
1275.2.x |
\(\chi_{1275}(76, \cdot)\) |
n/a |
232 |
4 |
1275.2.ba |
\(\chi_{1275}(49, \cdot)\) |
n/a |
208 |
4 |
1275.2.bb |
\(\chi_{1275}(32, \cdot)\) |
n/a |
416 |
4 |
1275.2.bd |
\(\chi_{1275}(16, \cdot)\) |
n/a |
368 |
4 |
1275.2.bh |
\(\chi_{1275}(154, \cdot)\) |
n/a |
320 |
4 |
1275.2.bj |
\(\chi_{1275}(169, \cdot)\) |
n/a |
352 |
4 |
1275.2.bl |
\(\chi_{1275}(7, \cdot)\) |
n/a |
432 |
8 |
1275.2.bm |
\(\chi_{1275}(74, \cdot)\) |
n/a |
832 |
8 |
1275.2.bo |
\(\chi_{1275}(176, \cdot)\) |
n/a |
864 |
8 |
1275.2.bq |
\(\chi_{1275}(82, \cdot)\) |
n/a |
432 |
8 |
1275.2.bt |
\(\chi_{1275}(4, \cdot)\) |
n/a |
704 |
8 |
1275.2.bv |
\(\chi_{1275}(98, \cdot)\) |
n/a |
1408 |
8 |
1275.2.bw |
\(\chi_{1275}(152, \cdot)\) |
n/a |
1408 |
8 |
1275.2.by |
\(\chi_{1275}(137, \cdot)\) |
n/a |
1280 |
8 |
1275.2.ca |
\(\chi_{1275}(38, \cdot)\) |
n/a |
1408 |
8 |
1275.2.cc |
\(\chi_{1275}(106, \cdot)\) |
n/a |
736 |
8 |
1275.2.ce |
\(\chi_{1275}(2, \cdot)\) |
n/a |
2816 |
16 |
1275.2.cg |
\(\chi_{1275}(19, \cdot)\) |
n/a |
1472 |
16 |
1275.2.cj |
\(\chi_{1275}(121, \cdot)\) |
n/a |
1408 |
16 |
1275.2.cl |
\(\chi_{1275}(53, \cdot)\) |
n/a |
2816 |
16 |
1275.2.cn |
\(\chi_{1275}(22, \cdot)\) |
n/a |
2880 |
32 |
1275.2.cp |
\(\chi_{1275}(11, \cdot)\) |
n/a |
5632 |
32 |
1275.2.cr |
\(\chi_{1275}(14, \cdot)\) |
n/a |
5632 |
32 |
1275.2.cs |
\(\chi_{1275}(73, \cdot)\) |
n/a |
2880 |
32 |
"n/a" means that newforms for that character have not been added to the database yet