Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3969))\).
|
Total |
New |
Old |
| Modular forms
| 6840 |
2880 |
3960 |
| Cusp forms
| 360 |
164 |
196 |
| Eisenstein series
| 6480 |
2716 |
3764 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3969))\)
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 |
| 3969.1.b |
\(\chi_{3969}(3725, \cdot)\) |
3969.1.b.a |
4 |
1 |
| 3969.1.d |
\(\chi_{3969}(244, \cdot)\) |
None |
0 |
1 |
| 3969.1.j |
\(\chi_{3969}(863, \cdot)\) |
3969.1.j.a |
2 |
2 |
| 3969.1.j.b |
4 |
| 3969.1.j.c |
8 |
| 3969.1.k |
\(\chi_{3969}(460, \cdot)\) |
3969.1.k.a |
2 |
2 |
| 3969.1.k.b |
2 |
| 3969.1.k.c |
2 |
| 3969.1.k.d |
2 |
| 3969.1.k.e |
4 |
| 3969.1.l |
\(\chi_{3969}(1567, \cdot)\) |
3969.1.l.a |
2 |
2 |
| 3969.1.l.b |
2 |
| 3969.1.m |
\(\chi_{3969}(325, \cdot)\) |
3969.1.m.a |
2 |
2 |
| 3969.1.m.b |
2 |
| 3969.1.m.c |
4 |
| 3969.1.n |
\(\chi_{3969}(2321, \cdot)\) |
3969.1.n.a |
2 |
2 |
| 3969.1.n.b |
4 |
| 3969.1.n.c |
8 |
| 3969.1.q |
\(\chi_{3969}(2186, \cdot)\) |
3969.1.q.a |
8 |
2 |
| 3969.1.r |
\(\chi_{3969}(1079, \cdot)\) |
3969.1.r.a |
2 |
2 |
| 3969.1.r.b |
2 |
| 3969.1.r.c |
4 |
| 3969.1.r.d |
8 |
| 3969.1.t |
\(\chi_{3969}(2971, \cdot)\) |
3969.1.t.a |
2 |
2 |
| 3969.1.t.b |
2 |
| 3969.1.t.c |
2 |
| 3969.1.t.d |
2 |
| 3969.1.t.e |
4 |
| 3969.1.y |
\(\chi_{3969}(811, \cdot)\) |
None |
0 |
6 |
| 3969.1.ba |
\(\chi_{3969}(323, \cdot)\) |
None |
0 |
6 |
| 3969.1.bb |
\(\chi_{3969}(901, \cdot)\) |
None |
0 |
6 |
| 3969.1.bc |
\(\chi_{3969}(685, \cdot)\) |
None |
0 |
6 |
| 3969.1.bd |
\(\chi_{3969}(19, \cdot)\) |
None |
0 |
6 |
| 3969.1.bf |
\(\chi_{3969}(197, \cdot)\) |
None |
0 |
6 |
| 3969.1.bg |
\(\chi_{3969}(557, \cdot)\) |
None |
0 |
6 |
| 3969.1.bj |
\(\chi_{3969}(116, \cdot)\) |
None |
0 |
6 |
| 3969.1.br |
\(\chi_{3969}(136, \cdot)\) |
3969.1.br.a |
12 |
12 |
| 3969.1.bt |
\(\chi_{3969}(134, \cdot)\) |
3969.1.bt.a |
12 |
12 |
| 3969.1.bu |
\(\chi_{3969}(242, \cdot)\) |
None |
0 |
12 |
| 3969.1.bx |
\(\chi_{3969}(53, \cdot)\) |
3969.1.bx.a |
12 |
12 |
| 3969.1.by |
\(\chi_{3969}(82, \cdot)\) |
None |
0 |
12 |
| 3969.1.bz |
\(\chi_{3969}(55, \cdot)\) |
3969.1.bz.a |
12 |
12 |
| 3969.1.ca |
\(\chi_{3969}(514, \cdot)\) |
3969.1.ca.a |
12 |
12 |
| 3969.1.cb |
\(\chi_{3969}(296, \cdot)\) |
3969.1.cb.a |
12 |
12 |
| 3969.1.cd |
\(\chi_{3969}(263, \cdot)\) |
None |
0 |
18 |
| 3969.1.ce |
\(\chi_{3969}(166, \cdot)\) |
None |
0 |
18 |
| 3969.1.ch |
\(\chi_{3969}(97, \cdot)\) |
None |
0 |
18 |
| 3969.1.ci |
\(\chi_{3969}(31, \cdot)\) |
None |
0 |
18 |
| 3969.1.cj |
\(\chi_{3969}(50, \cdot)\) |
None |
0 |
18 |
| 3969.1.ck |
\(\chi_{3969}(128, \cdot)\) |
None |
0 |
18 |
| 3969.1.cp |
\(\chi_{3969}(44, \cdot)\) |
None |
0 |
36 |
| 3969.1.cs |
\(\chi_{3969}(170, \cdot)\) |
None |
0 |
36 |
| 3969.1.ct |
\(\chi_{3969}(8, \cdot)\) |
None |
0 |
36 |
| 3969.1.cv |
\(\chi_{3969}(10, \cdot)\) |
None |
0 |
36 |
| 3969.1.cw |
\(\chi_{3969}(118, \cdot)\) |
None |
0 |
36 |
| 3969.1.cx |
\(\chi_{3969}(73, \cdot)\) |
None |
0 |
36 |
| 3969.1.dc |
\(\chi_{3969}(29, \cdot)\) |
None |
0 |
108 |
| 3969.1.dd |
\(\chi_{3969}(2, \cdot)\) |
None |
0 |
108 |
| 3969.1.de |
\(\chi_{3969}(13, \cdot)\) |
None |
0 |
108 |
| 3969.1.df |
\(\chi_{3969}(61, \cdot)\) |
None |
0 |
108 |
| 3969.1.di |
\(\chi_{3969}(40, \cdot)\) |
None |
0 |
108 |
| 3969.1.dj |
\(\chi_{3969}(11, \cdot)\) |
None |
0 |
108 |
