Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1008))\).
|
Total |
New |
Old |
Modular forms
| 1544 |
252 |
1292 |
Cusp forms
| 200 |
49 |
151 |
Eisenstein series
| 1344 |
203 |
1141 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1008))\)
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 |
1008.1.d |
\(\chi_{1008}(449, \cdot)\) |
None |
0 |
1 |
1008.1.e |
\(\chi_{1008}(503, \cdot)\) |
None |
0 |
1 |
1008.1.f |
\(\chi_{1008}(433, \cdot)\) |
1008.1.f.a |
1 |
1 |
1008.1.g |
\(\chi_{1008}(631, \cdot)\) |
None |
0 |
1 |
1008.1.l |
\(\chi_{1008}(937, \cdot)\) |
None |
0 |
1 |
1008.1.m |
\(\chi_{1008}(127, \cdot)\) |
None |
0 |
1 |
1008.1.n |
\(\chi_{1008}(953, \cdot)\) |
None |
0 |
1 |
1008.1.o |
\(\chi_{1008}(1007, \cdot)\) |
None |
0 |
1 |
1008.1.u |
\(\chi_{1008}(181, \cdot)\) |
1008.1.u.a |
2 |
2 |
1008.1.u.b |
2 |
1008.1.u.c |
2 |
1008.1.w |
\(\chi_{1008}(197, \cdot)\) |
None |
0 |
2 |
1008.1.y |
\(\chi_{1008}(251, \cdot)\) |
1008.1.y.a |
4 |
2 |
1008.1.y.b |
4 |
1008.1.ba |
\(\chi_{1008}(379, \cdot)\) |
None |
0 |
2 |
1008.1.bc |
\(\chi_{1008}(311, \cdot)\) |
None |
0 |
2 |
1008.1.bd |
\(\chi_{1008}(65, \cdot)\) |
None |
0 |
2 |
1008.1.bi |
\(\chi_{1008}(583, \cdot)\) |
None |
0 |
2 |
1008.1.bj |
\(\chi_{1008}(817, \cdot)\) |
None |
0 |
2 |
1008.1.bk |
\(\chi_{1008}(143, \cdot)\) |
None |
0 |
2 |
1008.1.bl |
\(\chi_{1008}(233, \cdot)\) |
None |
0 |
2 |
1008.1.bo |
\(\chi_{1008}(281, \cdot)\) |
None |
0 |
2 |
1008.1.bp |
\(\chi_{1008}(383, \cdot)\) |
None |
0 |
2 |
1008.1.bq |
\(\chi_{1008}(137, \cdot)\) |
None |
0 |
2 |
1008.1.br |
\(\chi_{1008}(335, \cdot)\) |
None |
0 |
2 |
1008.1.bv |
\(\chi_{1008}(265, \cdot)\) |
None |
0 |
2 |
1008.1.bw |
\(\chi_{1008}(655, \cdot)\) |
1008.1.bw.a |
4 |
2 |
1008.1.bx |
\(\chi_{1008}(745, \cdot)\) |
None |
0 |
2 |
1008.1.by |
\(\chi_{1008}(463, \cdot)\) |
None |
0 |
2 |
1008.1.cd |
\(\chi_{1008}(415, \cdot)\) |
1008.1.cd.a |
2 |
2 |
1008.1.cd.b |
2 |
1008.1.ce |
\(\chi_{1008}(73, \cdot)\) |
None |
0 |
2 |
1008.1.cf |
\(\chi_{1008}(487, \cdot)\) |
None |
0 |
2 |
1008.1.cg |
\(\chi_{1008}(145, \cdot)\) |
1008.1.cg.a |
2 |
2 |
1008.1.cl |
\(\chi_{1008}(97, \cdot)\) |
None |
0 |
2 |
1008.1.cm |
\(\chi_{1008}(151, \cdot)\) |
None |
0 |
2 |
1008.1.cn |
\(\chi_{1008}(241, \cdot)\) |
None |
0 |
2 |
1008.1.co |
\(\chi_{1008}(295, \cdot)\) |
None |
0 |
2 |
1008.1.ct |
\(\chi_{1008}(113, \cdot)\) |
None |
0 |
2 |
1008.1.cu |
\(\chi_{1008}(887, \cdot)\) |
None |
0 |
2 |
1008.1.cv |
\(\chi_{1008}(401, \cdot)\) |
None |
0 |
2 |
1008.1.cw |
\(\chi_{1008}(167, \cdot)\) |
None |
0 |
2 |
1008.1.db |
\(\chi_{1008}(215, \cdot)\) |
None |
0 |
2 |
1008.1.dc |
\(\chi_{1008}(305, \cdot)\) |
1008.1.dc.a |
4 |
2 |
1008.1.dd |
\(\chi_{1008}(79, \cdot)\) |
1008.1.dd.a |
4 |
2 |
1008.1.de |
\(\chi_{1008}(313, \cdot)\) |
None |
0 |
2 |
1008.1.di |
\(\chi_{1008}(47, \cdot)\) |
None |
0 |
2 |
1008.1.dj |
\(\chi_{1008}(473, \cdot)\) |
None |
0 |
2 |
1008.1.dl |
\(\chi_{1008}(29, \cdot)\) |
None |
0 |
4 |
1008.1.dn |
\(\chi_{1008}(13, \cdot)\) |
None |
0 |
4 |
1008.1.dp |
\(\chi_{1008}(59, \cdot)\) |
None |
0 |
4 |
1008.1.dq |
\(\chi_{1008}(403, \cdot)\) |
None |
0 |
4 |
1008.1.dt |
\(\chi_{1008}(163, \cdot)\) |
1008.1.dt.a |
8 |
4 |
1008.1.dv |
\(\chi_{1008}(395, \cdot)\) |
None |
0 |
4 |
1008.1.dw |
\(\chi_{1008}(131, \cdot)\) |
None |
0 |
4 |
1008.1.dz |
\(\chi_{1008}(67, \cdot)\) |
None |
0 |
4 |
1008.1.eb |
\(\chi_{1008}(61, \cdot)\) |
None |
0 |
4 |
1008.1.ed |
\(\chi_{1008}(53, \cdot)\) |
1008.1.ed.a |
8 |
4 |
1008.1.ee |
\(\chi_{1008}(149, \cdot)\) |
None |
0 |
4 |
1008.1.eg |
\(\chi_{1008}(229, \cdot)\) |
None |
0 |
4 |
1008.1.ej |
\(\chi_{1008}(325, \cdot)\) |
None |
0 |
4 |
1008.1.el |
\(\chi_{1008}(221, \cdot)\) |
None |
0 |
4 |
1008.1.en |
\(\chi_{1008}(43, \cdot)\) |
None |
0 |
4 |
1008.1.ep |
\(\chi_{1008}(83, \cdot)\) |
None |
0 |
4 |