Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1775))\).
|
Total |
New |
Old |
Modular forms
| 2055 |
1487 |
568 |
Cusp forms
| 95 |
72 |
23 |
Eisenstein series
| 1960 |
1415 |
545 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1775))\)
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 |
1775.1.c |
\(\chi_{1775}(1774, \cdot)\) |
1775.1.c.a |
6 |
1 |
1775.1.d |
\(\chi_{1775}(851, \cdot)\) |
1775.1.d.a |
1 |
1 |
1775.1.d.b |
3 |
1775.1.d.c |
6 |
1775.1.f |
\(\chi_{1775}(143, \cdot)\) |
None |
0 |
2 |
1775.1.n |
\(\chi_{1775}(259, \cdot)\) |
None |
0 |
4 |
1775.1.p |
\(\chi_{1775}(141, \cdot)\) |
1775.1.p.a |
4 |
4 |
1775.1.p.b |
24 |
1775.1.q |
\(\chi_{1775}(301, \cdot)\) |
None |
0 |
4 |
1775.1.r |
\(\chi_{1775}(66, \cdot)\) |
None |
0 |
4 |
1775.1.s |
\(\chi_{1775}(1111, \cdot)\) |
None |
0 |
4 |
1775.1.t |
\(\chi_{1775}(46, \cdot)\) |
None |
0 |
4 |
1775.1.u |
\(\chi_{1775}(869, \cdot)\) |
None |
0 |
4 |
1775.1.x |
\(\chi_{1775}(14, \cdot)\) |
None |
0 |
4 |
1775.1.y |
\(\chi_{1775}(724, \cdot)\) |
None |
0 |
4 |
1775.1.bb |
\(\chi_{1775}(354, \cdot)\) |
1775.1.bb.a |
4 |
4 |
1775.1.bb.b |
24 |
1775.1.bc |
\(\chi_{1775}(159, \cdot)\) |
None |
0 |
4 |
1775.1.be |
\(\chi_{1775}(156, \cdot)\) |
None |
0 |
4 |
1775.1.bf |
\(\chi_{1775}(26, \cdot)\) |
None |
0 |
6 |
1775.1.bg |
\(\chi_{1775}(449, \cdot)\) |
None |
0 |
6 |
1775.1.bj |
\(\chi_{1775}(147, \cdot)\) |
None |
0 |
8 |
1775.1.bk |
\(\chi_{1775}(267, \cdot)\) |
None |
0 |
8 |
1775.1.bm |
\(\chi_{1775}(167, \cdot)\) |
None |
0 |
8 |
1775.1.bn |
\(\chi_{1775}(72, \cdot)\) |
None |
0 |
8 |
1775.1.bo |
\(\chi_{1775}(57, \cdot)\) |
None |
0 |
8 |
1775.1.bs |
\(\chi_{1775}(128, \cdot)\) |
None |
0 |
8 |
1775.1.bu |
\(\chi_{1775}(32, \cdot)\) |
None |
0 |
12 |
1775.1.cc |
\(\chi_{1775}(61, \cdot)\) |
None |
0 |
24 |
1775.1.ce |
\(\chi_{1775}(44, \cdot)\) |
None |
0 |
24 |
1775.1.cf |
\(\chi_{1775}(34, \cdot)\) |
None |
0 |
24 |
1775.1.ci |
\(\chi_{1775}(99, \cdot)\) |
None |
0 |
24 |
1775.1.cj |
\(\chi_{1775}(59, \cdot)\) |
None |
0 |
24 |
1775.1.cm |
\(\chi_{1775}(209, \cdot)\) |
None |
0 |
24 |
1775.1.cn |
\(\chi_{1775}(56, \cdot)\) |
None |
0 |
24 |
1775.1.co |
\(\chi_{1775}(11, \cdot)\) |
None |
0 |
24 |
1775.1.cp |
\(\chi_{1775}(31, \cdot)\) |
None |
0 |
24 |
1775.1.cq |
\(\chi_{1775}(126, \cdot)\) |
None |
0 |
24 |
1775.1.cr |
\(\chi_{1775}(41, \cdot)\) |
None |
0 |
24 |
1775.1.ct |
\(\chi_{1775}(189, \cdot)\) |
None |
0 |
24 |
1775.1.cv |
\(\chi_{1775}(2, \cdot)\) |
None |
0 |
48 |
1775.1.cz |
\(\chi_{1775}(12, \cdot)\) |
None |
0 |
48 |
1775.1.da |
\(\chi_{1775}(18, \cdot)\) |
None |
0 |
48 |
1775.1.db |
\(\chi_{1775}(37, \cdot)\) |
None |
0 |
48 |
1775.1.dd |
\(\chi_{1775}(3, \cdot)\) |
None |
0 |
48 |
1775.1.de |
\(\chi_{1775}(152, \cdot)\) |
None |
0 |
48 |