Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1375))\).
|
Total |
New |
Old |
Modular forms
| 1909 |
1240 |
669 |
Cusp forms
| 109 |
88 |
21 |
Eisenstein series
| 1800 |
1152 |
648 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1375))\)
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 available newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
1375.1.c |
\(\chi_{1375}(626, \cdot)\) |
1375.1.c.a |
4 |
1 |
1375.1.c.b |
4 |
1375.1.d |
\(\chi_{1375}(1374, \cdot)\) |
1375.1.d.a |
2 |
1 |
1375.1.d.b |
2 |
1375.1.d.c |
4 |
1375.1.f |
\(\chi_{1375}(1057, \cdot)\) |
None |
0 |
2 |
1375.1.m |
\(\chi_{1375}(51, \cdot)\) |
None |
0 |
4 |
1375.1.o |
\(\chi_{1375}(24, \cdot)\) |
None |
0 |
4 |
1375.1.p |
\(\chi_{1375}(299, \cdot)\) |
None |
0 |
4 |
1375.1.q |
\(\chi_{1375}(249, \cdot)\) |
1375.1.q.a |
4 |
4 |
1375.1.r |
\(\chi_{1375}(349, \cdot)\) |
None |
0 |
4 |
1375.1.s |
\(\chi_{1375}(274, \cdot)\) |
1375.1.s.a |
4 |
4 |
1375.1.s.b |
8 |
1375.1.u |
\(\chi_{1375}(976, \cdot)\) |
None |
0 |
4 |
1375.1.v |
\(\chi_{1375}(76, \cdot)\) |
1375.1.v.a |
4 |
4 |
1375.1.v.b |
8 |
1375.1.w |
\(\chi_{1375}(151, \cdot)\) |
None |
0 |
4 |
1375.1.x |
\(\chi_{1375}(376, \cdot)\) |
1375.1.x.a |
4 |
4 |
1375.1.bc |
\(\chi_{1375}(101, \cdot)\) |
None |
0 |
4 |
1375.1.bd |
\(\chi_{1375}(149, \cdot)\) |
None |
0 |
4 |
1375.1.be |
\(\chi_{1375}(168, \cdot)\) |
None |
0 |
8 |
1375.1.bh |
\(\chi_{1375}(157, \cdot)\) |
None |
0 |
8 |
1375.1.bi |
\(\chi_{1375}(232, \cdot)\) |
None |
0 |
8 |
1375.1.bj |
\(\chi_{1375}(82, \cdot)\) |
None |
0 |
8 |
1375.1.bk |
\(\chi_{1375}(432, \cdot)\) |
None |
0 |
8 |
1375.1.bp |
\(\chi_{1375}(93, \cdot)\) |
None |
0 |
8 |
1375.1.bw |
\(\chi_{1375}(41, \cdot)\) |
None |
0 |
20 |
1375.1.bx |
\(\chi_{1375}(39, \cdot)\) |
None |
0 |
20 |
1375.1.by |
\(\chi_{1375}(19, \cdot)\) |
None |
0 |
20 |
1375.1.bz |
\(\chi_{1375}(54, \cdot)\) |
1375.1.bz.a |
20 |
20 |
1375.1.ca |
\(\chi_{1375}(79, \cdot)\) |
None |
0 |
20 |
1375.1.cc |
\(\chi_{1375}(6, \cdot)\) |
None |
0 |
20 |
1375.1.cd |
\(\chi_{1375}(61, \cdot)\) |
None |
0 |
20 |
1375.1.cg |
\(\chi_{1375}(116, \cdot)\) |
None |
0 |
20 |
1375.1.ch |
\(\chi_{1375}(21, \cdot)\) |
1375.1.ch.a |
20 |
20 |
1375.1.cj |
\(\chi_{1375}(139, \cdot)\) |
None |
0 |
20 |
1375.1.ck |
\(\chi_{1375}(3, \cdot)\) |
None |
0 |
40 |
1375.1.cp |
\(\chi_{1375}(42, \cdot)\) |
None |
0 |
40 |
1375.1.cq |
\(\chi_{1375}(12, \cdot)\) |
None |
0 |
40 |
1375.1.cr |
\(\chi_{1375}(38, \cdot)\) |
None |
0 |
40 |
1375.1.cs |
\(\chi_{1375}(37, \cdot)\) |
None |
0 |
40 |