Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(981))\).
|
Total |
New |
Old |
Modular forms
| 938 |
514 |
424 |
Cusp forms
| 74 |
32 |
42 |
Eisenstein series
| 864 |
482 |
382 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(981))\)
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 |
981.1.b |
\(\chi_{981}(764, \cdot)\) |
None |
0 |
1 |
981.1.d |
\(\chi_{981}(980, \cdot)\) |
981.1.d.a |
2 |
1 |
981.1.d.b |
2 |
981.1.j |
\(\chi_{981}(469, \cdot)\) |
981.1.j.a |
2 |
2 |
981.1.l |
\(\chi_{981}(917, \cdot)\) |
981.1.l.a |
4 |
2 |
981.1.m |
\(\chi_{981}(173, \cdot)\) |
None |
0 |
2 |
981.1.n |
\(\chi_{981}(326, \cdot)\) |
981.1.n.a |
2 |
2 |
981.1.o |
\(\chi_{981}(155, \cdot)\) |
None |
0 |
2 |
981.1.p |
\(\chi_{981}(263, \cdot)\) |
None |
0 |
2 |
981.1.s |
\(\chi_{981}(110, \cdot)\) |
None |
0 |
2 |
981.1.t |
\(\chi_{981}(281, \cdot)\) |
None |
0 |
2 |
981.1.v |
\(\chi_{981}(809, \cdot)\) |
None |
0 |
2 |
981.1.z |
\(\chi_{981}(226, \cdot)\) |
981.1.z.a |
4 |
4 |
981.1.bc |
\(\chi_{981}(76, \cdot)\) |
981.1.bc.a |
4 |
4 |
981.1.bd |
\(\chi_{981}(646, \cdot)\) |
None |
0 |
4 |
981.1.bg |
\(\chi_{981}(259, \cdot)\) |
None |
0 |
4 |
981.1.bh |
\(\chi_{981}(245, \cdot)\) |
None |
0 |
6 |
981.1.bj |
\(\chi_{981}(71, \cdot)\) |
None |
0 |
6 |
981.1.bk |
\(\chi_{981}(311, \cdot)\) |
None |
0 |
6 |
981.1.bl |
\(\chi_{981}(125, \cdot)\) |
None |
0 |
6 |
981.1.bm |
\(\chi_{981}(38, \cdot)\) |
None |
0 |
6 |
981.1.bp |
\(\chi_{981}(113, \cdot)\) |
None |
0 |
6 |
981.1.bt |
\(\chi_{981}(382, \cdot)\) |
None |
0 |
12 |
981.1.bw |
\(\chi_{981}(220, \cdot)\) |
None |
0 |
12 |
981.1.bx |
\(\chi_{981}(19, \cdot)\) |
981.1.bx.a |
12 |
12 |
981.1.bz |
\(\chi_{981}(170, \cdot)\) |
None |
0 |
18 |
981.1.ca |
\(\chi_{981}(74, \cdot)\) |
None |
0 |
18 |
981.1.cb |
\(\chi_{981}(20, \cdot)\) |
None |
0 |
18 |
981.1.cc |
\(\chi_{981}(131, \cdot)\) |
None |
0 |
18 |
981.1.cf |
\(\chi_{981}(5, \cdot)\) |
None |
0 |
18 |
981.1.ch |
\(\chi_{981}(26, \cdot)\) |
None |
0 |
18 |
981.1.cj |
\(\chi_{981}(52, \cdot)\) |
None |
0 |
36 |
981.1.ck |
\(\chi_{981}(13, \cdot)\) |
None |
0 |
36 |
981.1.cn |
\(\chi_{981}(10, \cdot)\) |
None |
0 |
36 |