Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1425))\).
|
Total |
New |
Old |
Modular forms
| 74016 |
50190 |
23826 |
Cusp forms
| 69985 |
48794 |
21191 |
Eisenstein series
| 4031 |
1396 |
2635 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1425))\)
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 |
1425.2.a |
\(\chi_{1425}(1, \cdot)\) |
1425.2.a.a |
1 |
1 |
1425.2.a.b |
1 |
1425.2.a.c |
1 |
1425.2.a.d |
1 |
1425.2.a.e |
1 |
1425.2.a.f |
1 |
1425.2.a.g |
1 |
1425.2.a.h |
1 |
1425.2.a.i |
1 |
1425.2.a.j |
1 |
1425.2.a.k |
2 |
1425.2.a.l |
2 |
1425.2.a.m |
2 |
1425.2.a.n |
2 |
1425.2.a.o |
2 |
1425.2.a.p |
2 |
1425.2.a.q |
2 |
1425.2.a.r |
2 |
1425.2.a.s |
3 |
1425.2.a.t |
3 |
1425.2.a.u |
3 |
1425.2.a.v |
3 |
1425.2.a.w |
3 |
1425.2.a.x |
3 |
1425.2.a.y |
7 |
1425.2.a.z |
7 |
1425.2.b |
\(\chi_{1425}(1424, \cdot)\) |
n/a |
116 |
1 |
1425.2.c |
\(\chi_{1425}(799, \cdot)\) |
1425.2.c.a |
2 |
1 |
1425.2.c.b |
2 |
1425.2.c.c |
2 |
1425.2.c.d |
2 |
1425.2.c.e |
2 |
1425.2.c.f |
2 |
1425.2.c.g |
2 |
1425.2.c.h |
2 |
1425.2.c.i |
4 |
1425.2.c.j |
4 |
1425.2.c.k |
4 |
1425.2.c.l |
4 |
1425.2.c.m |
4 |
1425.2.c.n |
4 |
1425.2.c.o |
6 |
1425.2.c.p |
6 |
1425.2.h |
\(\chi_{1425}(626, \cdot)\) |
n/a |
120 |
1 |
1425.2.i |
\(\chi_{1425}(676, \cdot)\) |
n/a |
128 |
2 |
1425.2.k |
\(\chi_{1425}(818, \cdot)\) |
n/a |
216 |
2 |
1425.2.m |
\(\chi_{1425}(493, \cdot)\) |
n/a |
120 |
2 |
1425.2.n |
\(\chi_{1425}(286, \cdot)\) |
n/a |
352 |
4 |
1425.2.q |
\(\chi_{1425}(1076, \cdot)\) |
n/a |
240 |
2 |
1425.2.r |
\(\chi_{1425}(449, \cdot)\) |
n/a |
232 |
2 |
1425.2.s |
\(\chi_{1425}(49, \cdot)\) |
n/a |
120 |
2 |
1425.2.v |
\(\chi_{1425}(226, \cdot)\) |
n/a |
378 |
6 |
1425.2.y |
\(\chi_{1425}(56, \cdot)\) |
n/a |
784 |
4 |
1425.2.z |
\(\chi_{1425}(229, \cdot)\) |
n/a |
368 |
4 |
1425.2.ba |
\(\chi_{1425}(284, \cdot)\) |
n/a |
784 |
4 |
1425.2.bd |
\(\chi_{1425}(68, \cdot)\) |
n/a |
464 |
4 |
1425.2.bf |
\(\chi_{1425}(943, \cdot)\) |
n/a |
240 |
4 |
1425.2.bh |
\(\chi_{1425}(106, \cdot)\) |
n/a |
800 |
8 |
1425.2.bi |
\(\chi_{1425}(326, \cdot)\) |
n/a |
726 |
6 |
1425.2.bn |
\(\chi_{1425}(199, \cdot)\) |
n/a |
360 |
6 |
1425.2.bo |
\(\chi_{1425}(224, \cdot)\) |
n/a |
696 |
6 |
1425.2.bp |
\(\chi_{1425}(37, \cdot)\) |
n/a |
800 |
8 |
1425.2.br |
\(\chi_{1425}(77, \cdot)\) |
n/a |
1440 |
8 |
1425.2.bt |
\(\chi_{1425}(64, \cdot)\) |
n/a |
800 |
8 |
1425.2.bu |
\(\chi_{1425}(164, \cdot)\) |
n/a |
1568 |
8 |
1425.2.bz |
\(\chi_{1425}(221, \cdot)\) |
n/a |
1568 |
8 |
1425.2.cb |
\(\chi_{1425}(193, \cdot)\) |
n/a |
720 |
12 |
1425.2.cc |
\(\chi_{1425}(218, \cdot)\) |
n/a |
1392 |
12 |
1425.2.ce |
\(\chi_{1425}(16, \cdot)\) |
n/a |
2400 |
24 |
1425.2.cg |
\(\chi_{1425}(88, \cdot)\) |
n/a |
1600 |
16 |
1425.2.ci |
\(\chi_{1425}(83, \cdot)\) |
n/a |
3136 |
16 |
1425.2.cl |
\(\chi_{1425}(41, \cdot)\) |
n/a |
4704 |
24 |
1425.2.cm |
\(\chi_{1425}(14, \cdot)\) |
n/a |
4704 |
24 |
1425.2.cn |
\(\chi_{1425}(4, \cdot)\) |
n/a |
2400 |
24 |
1425.2.cr |
\(\chi_{1425}(17, \cdot)\) |
n/a |
9408 |
48 |
1425.2.cs |
\(\chi_{1425}(13, \cdot)\) |
n/a |
4800 |
48 |
"n/a" means that newforms for that character have not been added to the database yet