Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1856))\).
|
Total |
New |
Old |
Modular forms
| 2154 |
629 |
1525 |
Cusp forms
| 138 |
35 |
103 |
Eisenstein series
| 2016 |
594 |
1422 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1856))\)
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 |
1856.1.b |
\(\chi_{1856}(927, \cdot)\) |
None |
0 |
1 |
1856.1.d |
\(\chi_{1856}(639, \cdot)\) |
None |
0 |
1 |
1856.1.f |
\(\chi_{1856}(1567, \cdot)\) |
None |
0 |
1 |
1856.1.h |
\(\chi_{1856}(1855, \cdot)\) |
1856.1.h.a |
1 |
1 |
1856.1.h.b |
1 |
1856.1.h.c |
1 |
1856.1.h.d |
2 |
1856.1.i |
\(\chi_{1856}(273, \cdot)\) |
None |
0 |
2 |
1856.1.l |
\(\chi_{1856}(1409, \cdot)\) |
1856.1.l.a |
2 |
2 |
1856.1.l.b |
4 |
1856.1.o |
\(\chi_{1856}(175, \cdot)\) |
None |
0 |
2 |
1856.1.p |
\(\chi_{1856}(463, \cdot)\) |
None |
0 |
2 |
1856.1.r |
\(\chi_{1856}(481, \cdot)\) |
None |
0 |
2 |
1856.1.s |
\(\chi_{1856}(17, \cdot)\) |
None |
0 |
2 |
1856.1.w |
\(\chi_{1856}(231, \cdot)\) |
None |
0 |
4 |
1856.1.y |
\(\chi_{1856}(41, \cdot)\) |
None |
0 |
4 |
1856.1.z |
\(\chi_{1856}(505, \cdot)\) |
None |
0 |
4 |
1856.1.bb |
\(\chi_{1856}(407, \cdot)\) |
None |
0 |
4 |
1856.1.bd |
\(\chi_{1856}(63, \cdot)\) |
1856.1.bd.a |
6 |
6 |
1856.1.bf |
\(\chi_{1856}(223, \cdot)\) |
None |
0 |
6 |
1856.1.bh |
\(\chi_{1856}(255, \cdot)\) |
1856.1.bh.a |
6 |
6 |
1856.1.bj |
\(\chi_{1856}(415, \cdot)\) |
None |
0 |
6 |
1856.1.bk |
\(\chi_{1856}(133, \cdot)\) |
None |
0 |
8 |
1856.1.bm |
\(\chi_{1856}(115, \cdot)\) |
None |
0 |
8 |
1856.1.bo |
\(\chi_{1856}(59, \cdot)\) |
None |
0 |
8 |
1856.1.br |
\(\chi_{1856}(365, \cdot)\) |
None |
0 |
8 |
1856.1.bt |
\(\chi_{1856}(113, \cdot)\) |
None |
0 |
12 |
1856.1.bu |
\(\chi_{1856}(97, \cdot)\) |
None |
0 |
12 |
1856.1.bw |
\(\chi_{1856}(207, \cdot)\) |
None |
0 |
12 |
1856.1.bx |
\(\chi_{1856}(111, \cdot)\) |
None |
0 |
12 |
1856.1.ca |
\(\chi_{1856}(193, \cdot)\) |
1856.1.ca.a |
12 |
12 |
1856.1.cd |
\(\chi_{1856}(177, \cdot)\) |
None |
0 |
12 |
1856.1.ce |
\(\chi_{1856}(7, \cdot)\) |
None |
0 |
24 |
1856.1.cg |
\(\chi_{1856}(137, \cdot)\) |
None |
0 |
24 |
1856.1.cj |
\(\chi_{1856}(73, \cdot)\) |
None |
0 |
24 |
1856.1.cl |
\(\chi_{1856}(71, \cdot)\) |
None |
0 |
24 |
1856.1.cn |
\(\chi_{1856}(37, \cdot)\) |
None |
0 |
48 |
1856.1.cp |
\(\chi_{1856}(83, \cdot)\) |
None |
0 |
48 |
1856.1.cr |
\(\chi_{1856}(35, \cdot)\) |
None |
0 |
48 |
1856.1.cs |
\(\chi_{1856}(21, \cdot)\) |
None |
0 |
48 |