Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(511))\).
|
Total |
New |
Old |
| Modular forms
| 438 |
360 |
78 |
| Cusp forms
| 6 |
6 |
0 |
| Eisenstein series
| 432 |
354 |
78 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(511))\)
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 |
| 511.1.b |
\(\chi_{511}(293, \cdot)\) |
None |
0 |
1 |
| 511.1.c |
\(\chi_{511}(510, \cdot)\) |
511.1.c.a |
3 |
1 |
| 511.1.c.b |
3 |
| 511.1.j |
\(\chi_{511}(27, \cdot)\) |
None |
0 |
2 |
| 511.1.k |
\(\chi_{511}(447, \cdot)\) |
None |
0 |
2 |
| 511.1.l |
\(\chi_{511}(300, \cdot)\) |
None |
0 |
2 |
| 511.1.o |
\(\chi_{511}(283, \cdot)\) |
None |
0 |
2 |
| 511.1.p |
\(\chi_{511}(145, \cdot)\) |
None |
0 |
2 |
| 511.1.q |
\(\chi_{511}(220, \cdot)\) |
None |
0 |
2 |
| 511.1.r |
\(\chi_{511}(138, \cdot)\) |
None |
0 |
2 |
| 511.1.u |
\(\chi_{511}(82, \cdot)\) |
None |
0 |
2 |
| 511.1.v |
\(\chi_{511}(227, \cdot)\) |
None |
0 |
2 |
| 511.1.w |
\(\chi_{511}(22, \cdot)\) |
None |
0 |
4 |
| 511.1.bc |
\(\chi_{511}(24, \cdot)\) |
None |
0 |
4 |
| 511.1.bd |
\(\chi_{511}(173, \cdot)\) |
None |
0 |
4 |
| 511.1.bg |
\(\chi_{511}(76, \cdot)\) |
None |
0 |
4 |
| 511.1.bh |
\(\chi_{511}(3, \cdot)\) |
None |
0 |
4 |
| 511.1.bj |
\(\chi_{511}(255, \cdot)\) |
None |
0 |
6 |
| 511.1.bk |
\(\chi_{511}(75, \cdot)\) |
None |
0 |
6 |
| 511.1.bn |
\(\chi_{511}(55, \cdot)\) |
None |
0 |
6 |
| 511.1.bo |
\(\chi_{511}(164, \cdot)\) |
None |
0 |
6 |
| 511.1.bp |
\(\chi_{511}(110, \cdot)\) |
None |
0 |
6 |
| 511.1.bq |
\(\chi_{511}(41, \cdot)\) |
None |
0 |
6 |
| 511.1.bt |
\(\chi_{511}(43, \cdot)\) |
None |
0 |
8 |
| 511.1.bv |
\(\chi_{511}(30, \cdot)\) |
None |
0 |
8 |
| 511.1.bw |
\(\chi_{511}(51, \cdot)\) |
None |
0 |
8 |
| 511.1.bz |
\(\chi_{511}(116, \cdot)\) |
None |
0 |
8 |
| 511.1.cb |
\(\chi_{511}(6, \cdot)\) |
None |
0 |
12 |
| 511.1.cc |
\(\chi_{511}(12, \cdot)\) |
None |
0 |
12 |
| 511.1.cf |
\(\chi_{511}(19, \cdot)\) |
None |
0 |
12 |
| 511.1.cg |
\(\chi_{511}(11, \cdot)\) |
None |
0 |
24 |
| 511.1.cj |
\(\chi_{511}(39, \cdot)\) |
None |
0 |
24 |
| 511.1.cl |
\(\chi_{511}(15, \cdot)\) |
None |
0 |
24 |
