Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4034))\).
|
Total |
New |
Old |
| Modular forms
| 510552 |
169511 |
341041 |
| Cusp forms
| 506521 |
169511 |
337010 |
| Eisenstein series
| 4031 |
0 |
4031 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4034))\)
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 |
| 4034.2.a |
\(\chi_{4034}(1, \cdot)\) |
4034.2.a.a |
33 |
1 |
| 4034.2.a.b |
35 |
| 4034.2.a.c |
49 |
| 4034.2.a.d |
52 |
| 4034.2.b |
\(\chi_{4034}(4033, \cdot)\) |
n/a |
170 |
1 |
| 4034.2.c |
\(\chi_{4034}(2311, \cdot)\) |
n/a |
340 |
2 |
| 4034.2.d |
\(\chi_{4034}(229, \cdot)\) |
n/a |
340 |
2 |
| 4034.2.e |
\(\chi_{4034}(295, \cdot)\) |
n/a |
340 |
2 |
| 4034.2.f |
\(\chi_{4034}(79, \cdot)\) |
n/a |
1020 |
6 |
| 4034.2.g |
\(\chi_{4034}(1469, \cdot)\) |
n/a |
680 |
4 |
| 4034.2.h |
\(\chi_{4034}(1005, \cdot)\) |
n/a |
1008 |
6 |
| 4034.2.i |
\(\chi_{4034}(765, \cdot)\) |
n/a |
680 |
4 |
| 4034.2.j |
\(\chi_{4034}(817, \cdot)\) |
n/a |
1020 |
6 |
| 4034.2.k |
\(\chi_{4034}(691, \cdot)\) |
n/a |
1352 |
8 |
| 4034.2.l |
\(\chi_{4034}(1029, \cdot)\) |
n/a |
1008 |
6 |
| 4034.2.m |
\(\chi_{4034}(899, \cdot)\) |
n/a |
2040 |
12 |
| 4034.2.n |
\(\chi_{4034}(1701, \cdot)\) |
n/a |
1360 |
8 |
| 4034.2.o |
\(\chi_{4034}(783, \cdot)\) |
n/a |
2040 |
12 |
| 4034.2.q |
\(\chi_{4034}(207, \cdot)\) |
n/a |
2016 |
12 |
| 4034.2.r |
\(\chi_{4034}(175, \cdot)\) |
n/a |
2040 |
12 |
| 4034.2.s |
\(\chi_{4034}(77, \cdot)\) |
n/a |
2704 |
16 |
| 4034.2.t |
\(\chi_{4034}(313, \cdot)\) |
n/a |
4080 |
24 |
| 4034.2.u |
\(\chi_{4034}(139, \cdot)\) |
n/a |
6048 |
36 |
| 4034.2.v |
\(\chi_{4034}(99, \cdot)\) |
n/a |
4032 |
24 |
| 4034.2.w |
\(\chi_{4034}(75, \cdot)\) |
n/a |
4080 |
24 |
| 4034.2.y |
\(\chi_{4034}(61, \cdot)\) |
n/a |
8112 |
48 |
| 4034.2.z |
\(\chi_{4034}(93, \cdot)\) |
n/a |
6048 |
36 |
| 4034.2.ba |
\(\chi_{4034}(169, \cdot)\) |
n/a |
8016 |
48 |
| 4034.2.bb |
\(\chi_{4034}(65, \cdot)\) |
n/a |
8160 |
48 |
| 4034.2.bd |
\(\chi_{4034}(11, \cdot)\) |
n/a |
12096 |
72 |
| 4034.2.bf |
\(\chi_{4034}(27, \cdot)\) |
n/a |
16224 |
96 |
| 4034.2.bg |
\(\chi_{4034}(9, \cdot)\) |
n/a |
24192 |
144 |
| 4034.2.bi |
\(\chi_{4034}(3, \cdot)\) |
n/a |
48096 |
288 |
"n/a" means that newforms for that character have not been added to the database yet
