Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(975))\).
|
Total |
New |
Old |
Modular forms
| 1466 |
545 |
921 |
Cusp forms
| 122 |
95 |
27 |
Eisenstein series
| 1344 |
450 |
894 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(975))\)
We only show spaces with odd 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 |
975.1.d |
\(\chi_{975}(326, \cdot)\) |
None |
0 |
1 |
975.1.e |
\(\chi_{975}(974, \cdot)\) |
975.1.e.a |
2 |
1 |
975.1.f |
\(\chi_{975}(599, \cdot)\) |
None |
0 |
1 |
975.1.g |
\(\chi_{975}(701, \cdot)\) |
975.1.g.a |
1 |
1 |
975.1.g.b |
2 |
975.1.g.c |
2 |
975.1.j |
\(\chi_{975}(593, \cdot)\) |
975.1.j.a |
4 |
2 |
975.1.l |
\(\chi_{975}(493, \cdot)\) |
None |
0 |
2 |
975.1.p |
\(\chi_{975}(151, \cdot)\) |
None |
0 |
2 |
975.1.q |
\(\chi_{975}(424, \cdot)\) |
None |
0 |
2 |
975.1.r |
\(\chi_{975}(118, \cdot)\) |
None |
0 |
2 |
975.1.u |
\(\chi_{975}(632, \cdot)\) |
975.1.u.a |
4 |
2 |
975.1.x |
\(\chi_{975}(101, \cdot)\) |
975.1.x.a |
2 |
2 |
975.1.x.b |
2 |
975.1.y |
\(\chi_{975}(74, \cdot)\) |
975.1.y.a |
4 |
2 |
975.1.z |
\(\chi_{975}(374, \cdot)\) |
975.1.z.a |
4 |
2 |
975.1.ba |
\(\chi_{975}(776, \cdot)\) |
975.1.ba.a |
2 |
2 |
975.1.ba.b |
2 |
975.1.bd |
\(\chi_{975}(116, \cdot)\) |
975.1.bd.a |
4 |
4 |
975.1.bd.b |
4 |
975.1.bd.c |
8 |
975.1.be |
\(\chi_{975}(14, \cdot)\) |
None |
0 |
4 |
975.1.bi |
\(\chi_{975}(194, \cdot)\) |
975.1.bi.a |
16 |
4 |
975.1.bj |
\(\chi_{975}(131, \cdot)\) |
None |
0 |
4 |
975.1.bk |
\(\chi_{975}(332, \cdot)\) |
975.1.bk.a |
8 |
4 |
975.1.bm |
\(\chi_{975}(568, \cdot)\) |
None |
0 |
4 |
975.1.bq |
\(\chi_{975}(124, \cdot)\) |
None |
0 |
4 |
975.1.br |
\(\chi_{975}(76, \cdot)\) |
None |
0 |
4 |
975.1.bs |
\(\chi_{975}(43, \cdot)\) |
None |
0 |
4 |
975.1.bv |
\(\chi_{975}(32, \cdot)\) |
975.1.bv.a |
8 |
4 |
975.1.by |
\(\chi_{975}(47, \cdot)\) |
None |
0 |
8 |
975.1.ca |
\(\chi_{975}(313, \cdot)\) |
None |
0 |
8 |
975.1.cb |
\(\chi_{975}(34, \cdot)\) |
None |
0 |
8 |
975.1.cc |
\(\chi_{975}(31, \cdot)\) |
None |
0 |
8 |
975.1.cg |
\(\chi_{975}(103, \cdot)\) |
None |
0 |
8 |
975.1.ch |
\(\chi_{975}(8, \cdot)\) |
None |
0 |
8 |
975.1.cj |
\(\chi_{975}(146, \cdot)\) |
975.1.cj.a |
16 |
8 |
975.1.ck |
\(\chi_{975}(134, \cdot)\) |
None |
0 |
8 |
975.1.co |
\(\chi_{975}(29, \cdot)\) |
None |
0 |
8 |
975.1.cp |
\(\chi_{975}(56, \cdot)\) |
None |
0 |
8 |
975.1.cr |
\(\chi_{975}(2, \cdot)\) |
None |
0 |
16 |
975.1.ct |
\(\chi_{975}(88, \cdot)\) |
None |
0 |
16 |
975.1.cu |
\(\chi_{975}(46, \cdot)\) |
None |
0 |
16 |
975.1.cv |
\(\chi_{975}(19, \cdot)\) |
None |
0 |
16 |
975.1.cz |
\(\chi_{975}(22, \cdot)\) |
None |
0 |
16 |
975.1.da |
\(\chi_{975}(137, \cdot)\) |
None |
0 |
16 |