Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2009))\).
|
Total |
New |
Old |
Modular forms
| 2424 |
1904 |
520 |
Cusp forms
| 24 |
12 |
12 |
Eisenstein series
| 2400 |
1892 |
508 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2009))\)
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 |
2009.1.b |
\(\chi_{2009}(1518, \cdot)\) |
None |
0 |
1 |
2009.1.d |
\(\chi_{2009}(2008, \cdot)\) |
None |
0 |
1 |
2009.1.g |
\(\chi_{2009}(1567, \cdot)\) |
None |
0 |
2 |
2009.1.i |
\(\chi_{2009}(901, \cdot)\) |
2009.1.i.a |
6 |
2 |
2009.1.i.b |
6 |
2009.1.k |
\(\chi_{2009}(411, \cdot)\) |
None |
0 |
2 |
2009.1.n |
\(\chi_{2009}(834, \cdot)\) |
None |
0 |
4 |
2009.1.p |
\(\chi_{2009}(734, \cdot)\) |
None |
0 |
4 |
2009.1.q |
\(\chi_{2009}(146, \cdot)\) |
None |
0 |
4 |
2009.1.r |
\(\chi_{2009}(460, \cdot)\) |
None |
0 |
4 |
2009.1.t |
\(\chi_{2009}(286, \cdot)\) |
None |
0 |
6 |
2009.1.v |
\(\chi_{2009}(83, \cdot)\) |
None |
0 |
6 |
2009.1.x |
\(\chi_{2009}(244, \cdot)\) |
None |
0 |
8 |
2009.1.ba |
\(\chi_{2009}(79, \cdot)\) |
None |
0 |
8 |
2009.1.bc |
\(\chi_{2009}(132, \cdot)\) |
None |
0 |
12 |
2009.1.be |
\(\chi_{2009}(31, \cdot)\) |
None |
0 |
8 |
2009.1.bf |
\(\chi_{2009}(215, \cdot)\) |
None |
0 |
8 |
2009.1.bi |
\(\chi_{2009}(99, \cdot)\) |
None |
0 |
16 |
2009.1.bk |
\(\chi_{2009}(124, \cdot)\) |
None |
0 |
12 |
2009.1.bm |
\(\chi_{2009}(40, \cdot)\) |
None |
0 |
12 |
2009.1.bn |
\(\chi_{2009}(85, \cdot)\) |
None |
0 |
24 |
2009.1.bq |
\(\chi_{2009}(80, \cdot)\) |
None |
0 |
16 |
2009.1.br |
\(\chi_{2009}(209, \cdot)\) |
None |
0 |
24 |
2009.1.bs |
\(\chi_{2009}(139, \cdot)\) |
None |
0 |
24 |
2009.1.bv |
\(\chi_{2009}(73, \cdot)\) |
None |
0 |
24 |
2009.1.by |
\(\chi_{2009}(30, \cdot)\) |
None |
0 |
32 |
2009.1.ca |
\(\chi_{2009}(20, \cdot)\) |
None |
0 |
48 |
2009.1.cc |
\(\chi_{2009}(44, \cdot)\) |
None |
0 |
48 |
2009.1.ce |
\(\chi_{2009}(10, \cdot)\) |
None |
0 |
48 |
2009.1.cf |
\(\chi_{2009}(45, \cdot)\) |
None |
0 |
48 |
2009.1.ch |
\(\chi_{2009}(15, \cdot)\) |
None |
0 |
96 |
2009.1.ci |
\(\chi_{2009}(5, \cdot)\) |
None |
0 |
96 |
2009.1.ck |
\(\chi_{2009}(11, \cdot)\) |
None |
0 |
192 |