Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(855))\).
|
Total |
New |
Old |
Modular forms
| 1276 |
519 |
757 |
Cusp forms
| 124 |
61 |
63 |
Eisenstein series
| 1152 |
458 |
694 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(855))\)
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 |
855.1.d |
\(\chi_{855}(476, \cdot)\) |
None |
0 |
1 |
855.1.e |
\(\chi_{855}(721, \cdot)\) |
None |
0 |
1 |
855.1.f |
\(\chi_{855}(134, \cdot)\) |
None |
0 |
1 |
855.1.g |
\(\chi_{855}(379, \cdot)\) |
855.1.g.a |
1 |
1 |
855.1.g.b |
2 |
855.1.g.c |
2 |
855.1.m |
\(\chi_{855}(512, \cdot)\) |
855.1.m.a |
4 |
2 |
855.1.m.b |
4 |
855.1.o |
\(\chi_{855}(172, \cdot)\) |
None |
0 |
2 |
855.1.q |
\(\chi_{855}(601, \cdot)\) |
None |
0 |
2 |
855.1.r |
\(\chi_{855}(581, \cdot)\) |
None |
0 |
2 |
855.1.u |
\(\chi_{855}(539, \cdot)\) |
855.1.u.a |
8 |
2 |
855.1.v |
\(\chi_{855}(559, \cdot)\) |
855.1.v.a |
4 |
2 |
855.1.y |
\(\chi_{855}(544, \cdot)\) |
None |
0 |
2 |
855.1.z |
\(\chi_{855}(94, \cdot)\) |
855.1.z.a |
2 |
2 |
855.1.z.b |
2 |
855.1.z.c |
4 |
855.1.z.d |
8 |
855.1.ba |
\(\chi_{855}(524, \cdot)\) |
None |
0 |
2 |
855.1.bb |
\(\chi_{855}(419, \cdot)\) |
None |
0 |
2 |
855.1.bf |
\(\chi_{855}(31, \cdot)\) |
None |
0 |
2 |
855.1.bg |
\(\chi_{855}(151, \cdot)\) |
None |
0 |
2 |
855.1.bh |
\(\chi_{855}(11, \cdot)\) |
None |
0 |
2 |
855.1.bi |
\(\chi_{855}(191, \cdot)\) |
None |
0 |
2 |
855.1.bn |
\(\chi_{855}(26, \cdot)\) |
None |
0 |
2 |
855.1.bo |
\(\chi_{855}(46, \cdot)\) |
None |
0 |
2 |
855.1.bq |
\(\chi_{855}(259, \cdot)\) |
None |
0 |
2 |
855.1.br |
\(\chi_{855}(239, \cdot)\) |
None |
0 |
2 |
855.1.bw |
\(\chi_{855}(7, \cdot)\) |
None |
0 |
4 |
855.1.by |
\(\chi_{855}(122, \cdot)\) |
None |
0 |
4 |
855.1.ca |
\(\chi_{855}(8, \cdot)\) |
None |
0 |
4 |
855.1.cb |
\(\chi_{855}(277, \cdot)\) |
None |
0 |
4 |
855.1.cd |
\(\chi_{855}(58, \cdot)\) |
None |
0 |
4 |
855.1.cf |
\(\chi_{855}(392, \cdot)\) |
None |
0 |
4 |
855.1.ch |
\(\chi_{855}(113, \cdot)\) |
None |
0 |
4 |
855.1.ck |
\(\chi_{855}(163, \cdot)\) |
855.1.ck.a |
8 |
4 |
855.1.cl |
\(\chi_{855}(79, \cdot)\) |
None |
0 |
6 |
855.1.cm |
\(\chi_{855}(74, \cdot)\) |
None |
0 |
6 |
855.1.cr |
\(\chi_{855}(101, \cdot)\) |
None |
0 |
6 |
855.1.cs |
\(\chi_{855}(91, \cdot)\) |
None |
0 |
6 |
855.1.ct |
\(\chi_{855}(161, \cdot)\) |
None |
0 |
6 |
855.1.cu |
\(\chi_{855}(166, \cdot)\) |
None |
0 |
6 |
855.1.cv |
\(\chi_{855}(149, \cdot)\) |
None |
0 |
6 |
855.1.cw |
\(\chi_{855}(109, \cdot)\) |
855.1.cw.a |
12 |
6 |
855.1.cx |
\(\chi_{855}(44, \cdot)\) |
None |
0 |
6 |
855.1.cy |
\(\chi_{855}(34, \cdot)\) |
None |
0 |
6 |
855.1.de |
\(\chi_{855}(421, \cdot)\) |
None |
0 |
6 |
855.1.df |
\(\chi_{855}(416, \cdot)\) |
None |
0 |
6 |
855.1.dg |
\(\chi_{855}(212, \cdot)\) |
None |
0 |
12 |
855.1.di |
\(\chi_{855}(43, \cdot)\) |
None |
0 |
12 |
855.1.dj |
\(\chi_{855}(28, \cdot)\) |
None |
0 |
12 |
855.1.do |
\(\chi_{855}(2, \cdot)\) |
None |
0 |
12 |
855.1.dp |
\(\chi_{855}(53, \cdot)\) |
None |
0 |
12 |
855.1.dr |
\(\chi_{855}(112, \cdot)\) |
None |
0 |
12 |