Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(775))\).
|
Total |
New |
Old |
Modular forms
| 879 |
625 |
254 |
Cusp forms
| 39 |
30 |
9 |
Eisenstein series
| 840 |
595 |
245 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(775))\)
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 |
775.1.c |
\(\chi_{775}(774, \cdot)\) |
775.1.c.a |
2 |
1 |
775.1.d |
\(\chi_{775}(526, \cdot)\) |
775.1.d.a |
1 |
1 |
775.1.d.b |
1 |
775.1.d.c |
2 |
775.1.g |
\(\chi_{775}(32, \cdot)\) |
None |
0 |
2 |
775.1.n |
\(\chi_{775}(99, \cdot)\) |
None |
0 |
2 |
775.1.p |
\(\chi_{775}(26, \cdot)\) |
None |
0 |
2 |
775.1.q |
\(\chi_{775}(339, \cdot)\) |
None |
0 |
4 |
775.1.s |
\(\chi_{775}(246, \cdot)\) |
None |
0 |
4 |
775.1.t |
\(\chi_{775}(151, \cdot)\) |
None |
0 |
4 |
775.1.u |
\(\chi_{775}(91, \cdot)\) |
None |
0 |
4 |
775.1.v |
\(\chi_{775}(46, \cdot)\) |
None |
0 |
4 |
775.1.w |
\(\chi_{775}(61, \cdot)\) |
775.1.w.a |
4 |
4 |
775.1.w.b |
8 |
775.1.y |
\(\chi_{775}(399, \cdot)\) |
None |
0 |
4 |
775.1.z |
\(\chi_{775}(154, \cdot)\) |
775.1.z.a |
4 |
4 |
775.1.z.b |
8 |
775.1.ba |
\(\chi_{775}(89, \cdot)\) |
None |
0 |
4 |
775.1.bb |
\(\chi_{775}(54, \cdot)\) |
None |
0 |
4 |
775.1.bg |
\(\chi_{775}(29, \cdot)\) |
None |
0 |
4 |
775.1.bh |
\(\chi_{775}(581, \cdot)\) |
None |
0 |
4 |
775.1.bi |
\(\chi_{775}(118, \cdot)\) |
None |
0 |
4 |
775.1.bq |
\(\chi_{775}(2, \cdot)\) |
None |
0 |
8 |
775.1.bt |
\(\chi_{775}(233, \cdot)\) |
None |
0 |
8 |
775.1.bu |
\(\chi_{775}(33, \cdot)\) |
None |
0 |
8 |
775.1.bv |
\(\chi_{775}(63, \cdot)\) |
None |
0 |
8 |
775.1.bw |
\(\chi_{775}(188, \cdot)\) |
None |
0 |
8 |
775.1.cb |
\(\chi_{775}(132, \cdot)\) |
None |
0 |
8 |
775.1.cd |
\(\chi_{775}(34, \cdot)\) |
None |
0 |
8 |
775.1.ce |
\(\chi_{775}(6, \cdot)\) |
None |
0 |
8 |
775.1.cf |
\(\chi_{775}(11, \cdot)\) |
None |
0 |
8 |
775.1.cg |
\(\chi_{775}(146, \cdot)\) |
None |
0 |
8 |
775.1.ch |
\(\chi_{775}(176, \cdot)\) |
None |
0 |
8 |
775.1.ci |
\(\chi_{775}(21, \cdot)\) |
None |
0 |
8 |
775.1.cj |
\(\chi_{775}(44, \cdot)\) |
None |
0 |
8 |
775.1.co |
\(\chi_{775}(79, \cdot)\) |
None |
0 |
8 |
775.1.cp |
\(\chi_{775}(84, \cdot)\) |
None |
0 |
8 |
775.1.cq |
\(\chi_{775}(119, \cdot)\) |
None |
0 |
8 |
775.1.cr |
\(\chi_{775}(24, \cdot)\) |
None |
0 |
8 |
775.1.ct |
\(\chi_{775}(136, \cdot)\) |
None |
0 |
8 |
775.1.cv |
\(\chi_{775}(133, \cdot)\) |
None |
0 |
16 |
775.1.cw |
\(\chi_{775}(7, \cdot)\) |
None |
0 |
16 |
775.1.db |
\(\chi_{775}(112, \cdot)\) |
None |
0 |
16 |
775.1.dc |
\(\chi_{775}(67, \cdot)\) |
None |
0 |
16 |
775.1.dd |
\(\chi_{775}(28, \cdot)\) |
None |
0 |
16 |
775.1.de |
\(\chi_{775}(38, \cdot)\) |
None |
0 |
16 |