Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1512))\).
|
Total |
New |
Old |
Modular forms
| 2422 |
388 |
2034 |
Cusp forms
| 262 |
68 |
194 |
Eisenstein series
| 2160 |
320 |
1840 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1512))\)
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 |
1512.1.d |
\(\chi_{1512}(1457, \cdot)\) |
None |
0 |
1 |
1512.1.e |
\(\chi_{1512}(755, \cdot)\) |
1512.1.e.a |
1 |
1 |
1512.1.e.b |
1 |
1512.1.e.c |
1 |
1512.1.e.d |
1 |
1512.1.f |
\(\chi_{1512}(433, \cdot)\) |
None |
0 |
1 |
1512.1.g |
\(\chi_{1512}(379, \cdot)\) |
None |
0 |
1 |
1512.1.l |
\(\chi_{1512}(1189, \cdot)\) |
1512.1.l.a |
4 |
1 |
1512.1.m |
\(\chi_{1512}(1135, \cdot)\) |
None |
0 |
1 |
1512.1.n |
\(\chi_{1512}(701, \cdot)\) |
None |
0 |
1 |
1512.1.o |
\(\chi_{1512}(1511, \cdot)\) |
None |
0 |
1 |
1512.1.u |
\(\chi_{1512}(395, \cdot)\) |
None |
0 |
2 |
1512.1.v |
\(\chi_{1512}(737, \cdot)\) |
None |
0 |
2 |
1512.1.ba |
\(\chi_{1512}(667, \cdot)\) |
1512.1.ba.a |
4 |
2 |
1512.1.bb |
\(\chi_{1512}(577, \cdot)\) |
None |
0 |
2 |
1512.1.bc |
\(\chi_{1512}(215, \cdot)\) |
None |
0 |
2 |
1512.1.bd |
\(\chi_{1512}(53, \cdot)\) |
1512.1.bd.a |
2 |
2 |
1512.1.bd.b |
2 |
1512.1.bd.c |
2 |
1512.1.bd.d |
2 |
1512.1.bg |
\(\chi_{1512}(197, \cdot)\) |
None |
0 |
2 |
1512.1.bh |
\(\chi_{1512}(143, \cdot)\) |
None |
0 |
2 |
1512.1.bi |
\(\chi_{1512}(989, \cdot)\) |
None |
0 |
2 |
1512.1.bj |
\(\chi_{1512}(503, \cdot)\) |
None |
0 |
2 |
1512.1.bn |
\(\chi_{1512}(181, \cdot)\) |
1512.1.bn.a |
2 |
2 |
1512.1.bn.b |
2 |
1512.1.bn.c |
4 |
1512.1.bo |
\(\chi_{1512}(415, \cdot)\) |
None |
0 |
2 |
1512.1.bp |
\(\chi_{1512}(829, \cdot)\) |
None |
0 |
2 |
1512.1.bq |
\(\chi_{1512}(127, \cdot)\) |
None |
0 |
2 |
1512.1.bv |
\(\chi_{1512}(487, \cdot)\) |
None |
0 |
2 |
1512.1.bw |
\(\chi_{1512}(325, \cdot)\) |
1512.1.bw.a |
4 |
2 |
1512.1.bw.b |
4 |
1512.1.bx |
\(\chi_{1512}(163, \cdot)\) |
None |
0 |
2 |
1512.1.by |
\(\chi_{1512}(649, \cdot)\) |
None |
0 |
2 |
1512.1.cd |
\(\chi_{1512}(937, \cdot)\) |
None |
0 |
2 |
1512.1.ce |
\(\chi_{1512}(235, \cdot)\) |
1512.1.ce.a |
4 |
2 |
1512.1.cf |
\(\chi_{1512}(73, \cdot)\) |
None |
0 |
2 |
1512.1.cg |
\(\chi_{1512}(883, \cdot)\) |
None |
0 |
2 |
1512.1.cl |
\(\chi_{1512}(449, \cdot)\) |
None |
0 |
2 |
1512.1.cm |
\(\chi_{1512}(899, \cdot)\) |
None |
0 |
2 |
1512.1.cn |
\(\chi_{1512}(233, \cdot)\) |
None |
0 |
2 |
1512.1.co |
\(\chi_{1512}(251, \cdot)\) |
None |
0 |
2 |
1512.1.ct |
\(\chi_{1512}(971, \cdot)\) |
None |
0 |
2 |
1512.1.cu |
\(\chi_{1512}(809, \cdot)\) |
1512.1.cu.a |
4 |
2 |
1512.1.cv |
\(\chi_{1512}(1423, \cdot)\) |
None |
0 |
2 |
1512.1.cw |
\(\chi_{1512}(397, \cdot)\) |
None |
0 |
2 |
1512.1.da |
\(\chi_{1512}(1151, \cdot)\) |
None |
0 |
2 |
1512.1.db |
\(\chi_{1512}(557, \cdot)\) |
None |
0 |
2 |
1512.1.df |
\(\chi_{1512}(241, \cdot)\) |
None |
0 |
6 |
1512.1.dh |
\(\chi_{1512}(149, \cdot)\) |
None |
0 |
6 |
1512.1.dk |
\(\chi_{1512}(137, \cdot)\) |
None |
0 |
6 |
1512.1.dm |
\(\chi_{1512}(229, \cdot)\) |
None |
0 |
6 |
1512.1.do |
\(\chi_{1512}(67, \cdot)\) |
None |
0 |
6 |
1512.1.dp |
\(\chi_{1512}(167, \cdot)\) |
None |
0 |
6 |
1512.1.dq |
\(\chi_{1512}(43, \cdot)\) |
None |
0 |
6 |
1512.1.ds |
\(\chi_{1512}(47, \cdot)\) |
None |
0 |
6 |
1512.1.dt |
\(\chi_{1512}(59, \cdot)\) |
None |
0 |
6 |
1512.1.dw |
\(\chi_{1512}(295, \cdot)\) |
None |
0 |
6 |
1512.1.dy |
\(\chi_{1512}(83, \cdot)\) |
None |
0 |
6 |
1512.1.dz |
\(\chi_{1512}(79, \cdot)\) |
None |
0 |
6 |
1512.1.ec |
\(\chi_{1512}(61, \cdot)\) |
None |
0 |
6 |
1512.1.ed |
\(\chi_{1512}(113, \cdot)\) |
None |
0 |
6 |
1512.1.ef |
\(\chi_{1512}(13, \cdot)\) |
1512.1.ef.a |
6 |
6 |
1512.1.ef.b |
6 |
1512.1.ef.c |
12 |
1512.1.ei |
\(\chi_{1512}(65, \cdot)\) |
None |
0 |
6 |
1512.1.ej |
\(\chi_{1512}(221, \cdot)\) |
None |
0 |
6 |
1512.1.em |
\(\chi_{1512}(97, \cdot)\) |
None |
0 |
6 |
1512.1.eo |
\(\chi_{1512}(29, \cdot)\) |
None |
0 |
6 |
1512.1.ep |
\(\chi_{1512}(313, \cdot)\) |
None |
0 |
6 |
1512.1.er |
\(\chi_{1512}(151, \cdot)\) |
None |
0 |
6 |
1512.1.et |
\(\chi_{1512}(131, \cdot)\) |
None |
0 |
6 |
1512.1.ev |
\(\chi_{1512}(383, \cdot)\) |
None |
0 |
6 |
1512.1.ex |
\(\chi_{1512}(403, \cdot)\) |
None |
0 |
6 |