Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(585))\).
|
Total |
New |
Old |
Modular forms
| 792 |
304 |
488 |
Cusp forms
| 24 |
8 |
16 |
Eisenstein series
| 768 |
296 |
472 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(585))\)
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 |
585.1.d |
\(\chi_{585}(521, \cdot)\) |
None |
0 |
1 |
585.1.e |
\(\chi_{585}(584, \cdot)\) |
None |
0 |
1 |
585.1.f |
\(\chi_{585}(404, \cdot)\) |
None |
0 |
1 |
585.1.g |
\(\chi_{585}(116, \cdot)\) |
None |
0 |
1 |
585.1.m |
\(\chi_{585}(8, \cdot)\) |
None |
0 |
2 |
585.1.o |
\(\chi_{585}(298, \cdot)\) |
585.1.o.a |
8 |
2 |
585.1.s |
\(\chi_{585}(226, \cdot)\) |
None |
0 |
2 |
585.1.t |
\(\chi_{585}(109, \cdot)\) |
None |
0 |
2 |
585.1.u |
\(\chi_{585}(118, \cdot)\) |
None |
0 |
2 |
585.1.x |
\(\chi_{585}(242, \cdot)\) |
None |
0 |
2 |
585.1.y |
\(\chi_{585}(146, \cdot)\) |
None |
0 |
2 |
585.1.z |
\(\chi_{585}(329, \cdot)\) |
None |
0 |
2 |
585.1.bc |
\(\chi_{585}(56, \cdot)\) |
None |
0 |
2 |
585.1.bd |
\(\chi_{585}(74, \cdot)\) |
None |
0 |
2 |
585.1.bg |
\(\chi_{585}(251, \cdot)\) |
None |
0 |
2 |
585.1.bh |
\(\chi_{585}(311, \cdot)\) |
None |
0 |
2 |
585.1.bi |
\(\chi_{585}(224, \cdot)\) |
None |
0 |
2 |
585.1.bj |
\(\chi_{585}(14, \cdot)\) |
None |
0 |
2 |
585.1.bn |
\(\chi_{585}(134, \cdot)\) |
None |
0 |
2 |
585.1.bo |
\(\chi_{585}(194, \cdot)\) |
None |
0 |
2 |
585.1.bp |
\(\chi_{585}(341, \cdot)\) |
None |
0 |
2 |
585.1.bq |
\(\chi_{585}(131, \cdot)\) |
None |
0 |
2 |
585.1.bv |
\(\chi_{585}(374, \cdot)\) |
None |
0 |
2 |
585.1.bw |
\(\chi_{585}(191, \cdot)\) |
None |
0 |
2 |
585.1.by |
\(\chi_{585}(29, \cdot)\) |
None |
0 |
2 |
585.1.bz |
\(\chi_{585}(101, \cdot)\) |
None |
0 |
2 |
585.1.cb |
\(\chi_{585}(2, \cdot)\) |
None |
0 |
4 |
585.1.cd |
\(\chi_{585}(47, \cdot)\) |
None |
0 |
4 |
585.1.ce |
\(\chi_{585}(188, \cdot)\) |
None |
0 |
4 |
585.1.ch |
\(\chi_{585}(137, \cdot)\) |
None |
0 |
4 |
585.1.cj |
\(\chi_{585}(88, \cdot)\) |
None |
0 |
4 |
585.1.ck |
\(\chi_{585}(319, \cdot)\) |
None |
0 |
4 |
585.1.cl |
\(\chi_{585}(106, \cdot)\) |
None |
0 |
4 |
585.1.cp |
\(\chi_{585}(22, \cdot)\) |
None |
0 |
4 |
585.1.cq |
\(\chi_{585}(172, \cdot)\) |
None |
0 |
4 |
585.1.ct |
\(\chi_{585}(157, \cdot)\) |
None |
0 |
4 |
585.1.cu |
\(\chi_{585}(178, \cdot)\) |
None |
0 |
4 |
585.1.cy |
\(\chi_{585}(31, \cdot)\) |
None |
0 |
4 |
585.1.cz |
\(\chi_{585}(124, \cdot)\) |
None |
0 |
4 |
585.1.da |
\(\chi_{585}(76, \cdot)\) |
None |
0 |
4 |
585.1.db |
\(\chi_{585}(34, \cdot)\) |
None |
0 |
4 |
585.1.dg |
\(\chi_{585}(19, \cdot)\) |
None |
0 |
4 |
585.1.dh |
\(\chi_{585}(46, \cdot)\) |
None |
0 |
4 |
585.1.di |
\(\chi_{585}(82, \cdot)\) |
None |
0 |
4 |
585.1.dl |
\(\chi_{585}(43, \cdot)\) |
None |
0 |
4 |
585.1.dm |
\(\chi_{585}(103, \cdot)\) |
None |
0 |
4 |
585.1.do |
\(\chi_{585}(227, \cdot)\) |
None |
0 |
4 |
585.1.dr |
\(\chi_{585}(122, \cdot)\) |
None |
0 |
4 |
585.1.ds |
\(\chi_{585}(98, \cdot)\) |
None |
0 |
4 |
585.1.du |
\(\chi_{585}(353, \cdot)\) |
None |
0 |
4 |