Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1519))\).
|
Total |
New |
Old |
Modular forms
| 1886 |
1478 |
408 |
Cusp forms
| 86 |
71 |
15 |
Eisenstein series
| 1800 |
1407 |
393 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1519))\)
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 |
1519.1.b |
\(\chi_{1519}(342, \cdot)\) |
None |
0 |
1 |
1519.1.c |
\(\chi_{1519}(1177, \cdot)\) |
1519.1.c.a |
1 |
1 |
1519.1.c.b |
3 |
1519.1.c.c |
3 |
1519.1.j |
\(\chi_{1519}(521, \cdot)\) |
None |
0 |
2 |
1519.1.k |
\(\chi_{1519}(863, \cdot)\) |
None |
0 |
2 |
1519.1.n |
\(\chi_{1519}(30, \cdot)\) |
1519.1.n.a |
2 |
2 |
1519.1.n.b |
2 |
1519.1.n.c |
6 |
1519.1.o |
\(\chi_{1519}(471, \cdot)\) |
None |
0 |
2 |
1519.1.p |
\(\chi_{1519}(962, \cdot)\) |
None |
0 |
2 |
1519.1.q |
\(\chi_{1519}(129, \cdot)\) |
None |
0 |
2 |
1519.1.t |
\(\chi_{1519}(99, \cdot)\) |
None |
0 |
2 |
1519.1.u |
\(\chi_{1519}(1028, \cdot)\) |
None |
0 |
2 |
1519.1.x |
\(\chi_{1519}(97, \cdot)\) |
None |
0 |
4 |
1519.1.y |
\(\chi_{1519}(246, \cdot)\) |
None |
0 |
4 |
1519.1.ba |
\(\chi_{1519}(92, \cdot)\) |
1519.1.ba.a |
6 |
6 |
1519.1.ba.b |
12 |
1519.1.bb |
\(\chi_{1519}(125, \cdot)\) |
None |
0 |
6 |
1519.1.bk |
\(\chi_{1519}(148, \cdot)\) |
None |
0 |
8 |
1519.1.bl |
\(\chi_{1519}(195, \cdot)\) |
None |
0 |
8 |
1519.1.bo |
\(\chi_{1519}(116, \cdot)\) |
None |
0 |
8 |
1519.1.bp |
\(\chi_{1519}(79, \cdot)\) |
None |
0 |
8 |
1519.1.bq |
\(\chi_{1519}(264, \cdot)\) |
None |
0 |
8 |
1519.1.br |
\(\chi_{1519}(19, \cdot)\) |
None |
0 |
8 |
1519.1.bu |
\(\chi_{1519}(276, \cdot)\) |
None |
0 |
8 |
1519.1.bv |
\(\chi_{1519}(177, \cdot)\) |
None |
0 |
8 |
1519.1.bx |
\(\chi_{1519}(118, \cdot)\) |
None |
0 |
12 |
1519.1.by |
\(\chi_{1519}(57, \cdot)\) |
None |
0 |
12 |
1519.1.cb |
\(\chi_{1519}(180, \cdot)\) |
None |
0 |
12 |
1519.1.cc |
\(\chi_{1519}(94, \cdot)\) |
None |
0 |
12 |
1519.1.cd |
\(\chi_{1519}(37, \cdot)\) |
None |
0 |
12 |
1519.1.ce |
\(\chi_{1519}(123, \cdot)\) |
1519.1.ce.a |
36 |
12 |
1519.1.ch |
\(\chi_{1519}(130, \cdot)\) |
None |
0 |
12 |
1519.1.ci |
\(\chi_{1519}(5, \cdot)\) |
None |
0 |
12 |
1519.1.cj |
\(\chi_{1519}(15, \cdot)\) |
None |
0 |
24 |
1519.1.ck |
\(\chi_{1519}(132, \cdot)\) |
None |
0 |
24 |
1519.1.cq |
\(\chi_{1519}(44, \cdot)\) |
None |
0 |
48 |
1519.1.cr |
\(\chi_{1519}(38, \cdot)\) |
None |
0 |
48 |
1519.1.cu |
\(\chi_{1519}(10, \cdot)\) |
None |
0 |
48 |
1519.1.cv |
\(\chi_{1519}(33, \cdot)\) |
None |
0 |
48 |
1519.1.cw |
\(\chi_{1519}(11, \cdot)\) |
None |
0 |
48 |
1519.1.cx |
\(\chi_{1519}(23, \cdot)\) |
None |
0 |
48 |
1519.1.da |
\(\chi_{1519}(20, \cdot)\) |
None |
0 |
48 |
1519.1.db |
\(\chi_{1519}(22, \cdot)\) |
None |
0 |
48 |