Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2132))\).
|
Total |
New |
Old |
Modular forms
| 2670 |
1104 |
1566 |
Cusp forms
| 270 |
244 |
26 |
Eisenstein series
| 2400 |
860 |
1540 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2132))\)
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 |
2132.1.c |
\(\chi_{2132}(1559, \cdot)\) |
None |
0 |
1 |
2132.1.e |
\(\chi_{2132}(1067, \cdot)\) |
None |
0 |
1 |
2132.1.f |
\(\chi_{2132}(2131, \cdot)\) |
2132.1.f.a |
1 |
1 |
2132.1.f.b |
1 |
2132.1.f.c |
1 |
2132.1.f.d |
1 |
2132.1.h |
\(\chi_{2132}(1639, \cdot)\) |
None |
0 |
1 |
2132.1.k |
\(\chi_{2132}(1721, \cdot)\) |
None |
0 |
2 |
2132.1.l |
\(\chi_{2132}(911, \cdot)\) |
None |
0 |
2 |
2132.1.n |
\(\chi_{2132}(73, \cdot)\) |
None |
0 |
2 |
2132.1.p |
\(\chi_{2132}(1321, \cdot)\) |
None |
0 |
2 |
2132.1.r |
\(\chi_{2132}(155, \cdot)\) |
2132.1.r.a |
2 |
2 |
2132.1.r.b |
2 |
2132.1.r.c |
4 |
2132.1.r.d |
4 |
2132.1.t |
\(\chi_{2132}(1149, \cdot)\) |
None |
0 |
2 |
2132.1.x |
\(\chi_{2132}(491, \cdot)\) |
None |
0 |
2 |
2132.1.y |
\(\chi_{2132}(1147, \cdot)\) |
2132.1.y.a |
2 |
2 |
2132.1.y.b |
2 |
2132.1.z |
\(\chi_{2132}(1395, \cdot)\) |
None |
0 |
2 |
2132.1.bb |
\(\chi_{2132}(575, \cdot)\) |
None |
0 |
2 |
2132.1.bd |
\(\chi_{2132}(1175, \cdot)\) |
2132.1.bd.a |
4 |
4 |
2132.1.bf |
\(\chi_{2132}(1093, \cdot)\) |
None |
0 |
4 |
2132.1.bg |
\(\chi_{2132}(1585, \cdot)\) |
None |
0 |
4 |
2132.1.bj |
\(\chi_{2132}(1227, \cdot)\) |
2132.1.bj.a |
4 |
4 |
2132.1.bl |
\(\chi_{2132}(1431, \cdot)\) |
None |
0 |
4 |
2132.1.bn |
\(\chi_{2132}(51, \cdot)\) |
None |
0 |
4 |
2132.1.bp |
\(\chi_{2132}(599, \cdot)\) |
None |
0 |
4 |
2132.1.br |
\(\chi_{2132}(1091, \cdot)\) |
None |
0 |
4 |
2132.1.bt |
\(\chi_{2132}(657, \cdot)\) |
None |
0 |
4 |
2132.1.bv |
\(\chi_{2132}(419, \cdot)\) |
None |
0 |
4 |
2132.1.bx |
\(\chi_{2132}(501, \cdot)\) |
None |
0 |
4 |
2132.1.bz |
\(\chi_{2132}(401, \cdot)\) |
None |
0 |
4 |
2132.1.cb |
\(\chi_{2132}(647, \cdot)\) |
2132.1.cb.a |
4 |
4 |
2132.1.cb.b |
4 |
2132.1.cc |
\(\chi_{2132}(245, \cdot)\) |
None |
0 |
4 |
2132.1.cf |
\(\chi_{2132}(681, \cdot)\) |
None |
0 |
8 |
2132.1.ci |
\(\chi_{2132}(103, \cdot)\) |
2132.1.ci.a |
8 |
8 |
2132.1.ci.b |
8 |
2132.1.ck |
\(\chi_{2132}(21, \cdot)\) |
None |
0 |
8 |
2132.1.cm |
\(\chi_{2132}(5, \cdot)\) |
None |
0 |
8 |
2132.1.co |
\(\chi_{2132}(131, \cdot)\) |
None |
0 |
8 |
2132.1.cq |
\(\chi_{2132}(57, \cdot)\) |
None |
0 |
8 |
2132.1.cs |
\(\chi_{2132}(167, \cdot)\) |
2132.1.cs.a |
8 |
8 |
2132.1.cv |
\(\chi_{2132}(601, \cdot)\) |
None |
0 |
8 |
2132.1.cw |
\(\chi_{2132}(413, \cdot)\) |
None |
0 |
8 |
2132.1.cy |
\(\chi_{2132}(219, \cdot)\) |
2132.1.cy.a |
8 |
8 |
2132.1.cz |
\(\chi_{2132}(107, \cdot)\) |
2132.1.cz.a |
8 |
8 |
2132.1.cz.b |
8 |
2132.1.da |
\(\chi_{2132}(23, \cdot)\) |
None |
0 |
8 |
2132.1.dd |
\(\chi_{2132}(139, \cdot)\) |
2132.1.dd.a |
8 |
8 |
2132.1.dd.b |
8 |
2132.1.dd.c |
16 |
2132.1.df |
\(\chi_{2132}(283, \cdot)\) |
None |
0 |
8 |
2132.1.dh |
\(\chi_{2132}(47, \cdot)\) |
2132.1.dh.a |
16 |
16 |
2132.1.dk |
\(\chi_{2132}(129, \cdot)\) |
None |
0 |
16 |
2132.1.dl |
\(\chi_{2132}(53, \cdot)\) |
None |
0 |
16 |
2132.1.dn |
\(\chi_{2132}(151, \cdot)\) |
2132.1.dn.a |
16 |
16 |
2132.1.do |
\(\chi_{2132}(37, \cdot)\) |
None |
0 |
16 |
2132.1.dq |
\(\chi_{2132}(43, \cdot)\) |
2132.1.dq.a |
16 |
16 |
2132.1.dq.b |
16 |
2132.1.ds |
\(\chi_{2132}(33, \cdot)\) |
None |
0 |
16 |
2132.1.du |
\(\chi_{2132}(197, \cdot)\) |
None |
0 |
16 |
2132.1.dw |
\(\chi_{2132}(87, \cdot)\) |
None |
0 |
16 |
2132.1.dz |
\(\chi_{2132}(45, \cdot)\) |
None |
0 |
16 |
2132.1.ea |
\(\chi_{2132}(63, \cdot)\) |
2132.1.ea.a |
32 |
32 |
2132.1.ec |
\(\chi_{2132}(17, \cdot)\) |
None |
0 |
32 |
2132.1.ed |
\(\chi_{2132}(29, \cdot)\) |
None |
0 |
32 |
2132.1.eg |
\(\chi_{2132}(7, \cdot)\) |
2132.1.eg.a |
32 |
32 |