Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4029))\).
|
Total |
New |
Old |
| Modular forms
| 604032 |
448327 |
155705 |
| Cusp forms
| 594049 |
443711 |
150338 |
| Eisenstein series
| 9983 |
4616 |
5367 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4029))\)
We only show spaces with even 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 |
| 4029.2.a |
\(\chi_{4029}(1, \cdot)\) |
4029.2.a.a |
1 |
1 |
| 4029.2.a.b |
1 |
| 4029.2.a.c |
2 |
| 4029.2.a.d |
3 |
| 4029.2.a.e |
18 |
| 4029.2.a.f |
22 |
| 4029.2.a.g |
22 |
| 4029.2.a.h |
25 |
| 4029.2.a.i |
25 |
| 4029.2.a.j |
25 |
| 4029.2.a.k |
31 |
| 4029.2.a.l |
32 |
| 4029.2.b |
\(\chi_{4029}(3554, \cdot)\) |
n/a |
428 |
1 |
| 4029.2.e |
\(\chi_{4029}(4028, \cdot)\) |
n/a |
476 |
1 |
| 4029.2.f |
\(\chi_{4029}(475, \cdot)\) |
n/a |
232 |
1 |
| 4029.2.i |
\(\chi_{4029}(766, \cdot)\) |
n/a |
428 |
2 |
| 4029.2.k |
\(\chi_{4029}(1186, \cdot)\) |
n/a |
464 |
2 |
| 4029.2.m |
\(\chi_{4029}(710, \cdot)\) |
n/a |
952 |
2 |
| 4029.2.p |
\(\chi_{4029}(1240, \cdot)\) |
n/a |
480 |
2 |
| 4029.2.q |
\(\chi_{4029}(1478, \cdot)\) |
n/a |
952 |
2 |
| 4029.2.t |
\(\chi_{4029}(1004, \cdot)\) |
n/a |
852 |
2 |
| 4029.2.w |
\(\chi_{4029}(712, \cdot)\) |
n/a |
944 |
4 |
| 4029.2.x |
\(\chi_{4029}(236, \cdot)\) |
n/a |
1904 |
4 |
| 4029.2.y |
\(\chi_{4029}(293, \cdot)\) |
n/a |
1904 |
4 |
| 4029.2.ba |
\(\chi_{4029}(55, \cdot)\) |
n/a |
960 |
4 |
| 4029.2.bc |
\(\chi_{4029}(52, \cdot)\) |
n/a |
2544 |
12 |
| 4029.2.bd |
\(\chi_{4029}(394, \cdot)\) |
n/a |
1920 |
8 |
| 4029.2.be |
\(\chi_{4029}(80, \cdot)\) |
n/a |
3744 |
8 |
| 4029.2.bh |
\(\chi_{4029}(529, \cdot)\) |
n/a |
1920 |
8 |
| 4029.2.bi |
\(\chi_{4029}(767, \cdot)\) |
n/a |
3808 |
8 |
| 4029.2.bn |
\(\chi_{4029}(67, \cdot)\) |
n/a |
2880 |
12 |
| 4029.2.bo |
\(\chi_{4029}(254, \cdot)\) |
n/a |
5712 |
12 |
| 4029.2.br |
\(\chi_{4029}(137, \cdot)\) |
n/a |
5136 |
12 |
| 4029.2.bs |
\(\chi_{4029}(256, \cdot)\) |
n/a |
5136 |
24 |
| 4029.2.bv |
\(\chi_{4029}(23, \cdot)\) |
n/a |
7616 |
16 |
| 4029.2.bw |
\(\chi_{4029}(214, \cdot)\) |
n/a |
3840 |
16 |
| 4029.2.bx |
\(\chi_{4029}(140, \cdot)\) |
n/a |
11424 |
24 |
| 4029.2.bz |
\(\chi_{4029}(64, \cdot)\) |
n/a |
5760 |
24 |
| 4029.2.cb |
\(\chi_{4029}(35, \cdot)\) |
n/a |
10224 |
24 |
| 4029.2.ce |
\(\chi_{4029}(305, \cdot)\) |
n/a |
11424 |
24 |
| 4029.2.cf |
\(\chi_{4029}(16, \cdot)\) |
n/a |
5760 |
24 |
| 4029.2.ci |
\(\chi_{4029}(185, \cdot)\) |
n/a |
22848 |
48 |
| 4029.2.cj |
\(\chi_{4029}(100, \cdot)\) |
n/a |
11520 |
48 |
| 4029.2.cn |
\(\chi_{4029}(4, \cdot)\) |
n/a |
11520 |
48 |
| 4029.2.cp |
\(\chi_{4029}(47, \cdot)\) |
n/a |
22848 |
48 |
| 4029.2.cs |
\(\chi_{4029}(62, \cdot)\) |
n/a |
45696 |
96 |
| 4029.2.ct |
\(\chi_{4029}(58, \cdot)\) |
n/a |
23040 |
96 |
| 4029.2.cw |
\(\chi_{4029}(53, \cdot)\) |
n/a |
45696 |
96 |
| 4029.2.cx |
\(\chi_{4029}(19, \cdot)\) |
n/a |
23040 |
96 |
| 4029.2.cy |
\(\chi_{4029}(7, \cdot)\) |
n/a |
46080 |
192 |
| 4029.2.cz |
\(\chi_{4029}(5, \cdot)\) |
n/a |
91392 |
192 |
"n/a" means that newforms for that character have not been added to the database yet
