Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3344))\).
|
Total |
New |
Old |
| Modular forms
| 350640 |
191476 |
159164 |
| Cusp forms
| 340561 |
188720 |
151841 |
| Eisenstein series
| 10079 |
2756 |
7323 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3344))\)
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 |
| 3344.2.a |
\(\chi_{3344}(1, \cdot)\) |
3344.2.a.a |
1 |
1 |
| 3344.2.a.b |
1 |
| 3344.2.a.c |
1 |
| 3344.2.a.d |
1 |
| 3344.2.a.e |
1 |
| 3344.2.a.f |
1 |
| 3344.2.a.g |
1 |
| 3344.2.a.h |
1 |
| 3344.2.a.i |
1 |
| 3344.2.a.j |
2 |
| 3344.2.a.k |
2 |
| 3344.2.a.l |
2 |
| 3344.2.a.m |
2 |
| 3344.2.a.n |
2 |
| 3344.2.a.o |
2 |
| 3344.2.a.p |
3 |
| 3344.2.a.q |
3 |
| 3344.2.a.r |
3 |
| 3344.2.a.s |
4 |
| 3344.2.a.t |
5 |
| 3344.2.a.u |
5 |
| 3344.2.a.v |
6 |
| 3344.2.a.w |
6 |
| 3344.2.a.x |
6 |
| 3344.2.a.y |
6 |
| 3344.2.a.z |
6 |
| 3344.2.a.ba |
7 |
| 3344.2.a.bb |
9 |
| 3344.2.c |
\(\chi_{3344}(3191, \cdot)\) |
None |
0 |
1 |
| 3344.2.e |
\(\chi_{3344}(1673, \cdot)\) |
None |
0 |
1 |
| 3344.2.f |
\(\chi_{3344}(417, \cdot)\) |
n/a |
118 |
1 |
| 3344.2.h |
\(\chi_{3344}(1407, \cdot)\) |
n/a |
108 |
1 |
| 3344.2.j |
\(\chi_{3344}(2089, \cdot)\) |
None |
0 |
1 |
| 3344.2.l |
\(\chi_{3344}(3079, \cdot)\) |
None |
0 |
1 |
| 3344.2.o |
\(\chi_{3344}(1519, \cdot)\) |
3344.2.o.a |
36 |
1 |
| 3344.2.o.b |
64 |
| 3344.2.q |
\(\chi_{3344}(353, \cdot)\) |
n/a |
200 |
2 |
| 3344.2.r |
\(\chi_{3344}(571, \cdot)\) |
n/a |
864 |
2 |
| 3344.2.u |
\(\chi_{3344}(837, \cdot)\) |
n/a |
720 |
2 |
| 3344.2.v |
\(\chi_{3344}(1253, \cdot)\) |
n/a |
952 |
2 |
| 3344.2.y |
\(\chi_{3344}(683, \cdot)\) |
n/a |
800 |
2 |
| 3344.2.z |
\(\chi_{3344}(609, \cdot)\) |
n/a |
432 |
4 |
| 3344.2.ba |
\(\chi_{3344}(639, \cdot)\) |
n/a |
200 |
2 |
| 3344.2.be |
\(\chi_{3344}(1209, \cdot)\) |
None |
0 |
2 |
| 3344.2.bg |
\(\chi_{3344}(87, \cdot)\) |
None |
0 |
2 |
| 3344.2.bi |
\(\chi_{3344}(65, \cdot)\) |
n/a |
236 |
2 |
| 3344.2.bk |
\(\chi_{3344}(1759, \cdot)\) |
n/a |
240 |
2 |
| 3344.2.bl |
\(\chi_{3344}(2311, \cdot)\) |
None |
0 |
2 |
| 3344.2.bn |
\(\chi_{3344}(2025, \cdot)\) |
None |
0 |
2 |
| 3344.2.bp |
\(\chi_{3344}(177, \cdot)\) |
n/a |
600 |
6 |
| 3344.2.br |
\(\chi_{3344}(911, \cdot)\) |
n/a |
480 |
4 |
| 3344.2.bu |
\(\chi_{3344}(39, \cdot)\) |
None |
0 |
4 |
| 3344.2.bw |
\(\chi_{3344}(569, \cdot)\) |
None |
0 |
4 |
| 3344.2.by |
\(\chi_{3344}(799, \cdot)\) |
n/a |
432 |
4 |
| 3344.2.ca |
\(\chi_{3344}(721, \cdot)\) |
n/a |
472 |
4 |
| 3344.2.cb |
\(\chi_{3344}(1065, \cdot)\) |
None |
0 |
4 |
| 3344.2.cd |
\(\chi_{3344}(455, \cdot)\) |
None |
0 |
4 |
| 3344.2.cf |
\(\chi_{3344}(45, \cdot)\) |
n/a |
1600 |
4 |
| 3344.2.ci |
\(\chi_{3344}(923, \cdot)\) |
n/a |
1904 |
4 |
| 3344.2.cj |
\(\chi_{3344}(331, \cdot)\) |
n/a |
1600 |
4 |
| 3344.2.cm |
\(\chi_{3344}(373, \cdot)\) |
n/a |
1904 |
4 |
| 3344.2.cn |
\(\chi_{3344}(49, \cdot)\) |
n/a |
944 |
8 |
| 3344.2.cp |
\(\chi_{3344}(263, \cdot)\) |
None |
0 |
6 |
| 3344.2.cr |
\(\chi_{3344}(441, \cdot)\) |
None |
0 |
6 |
| 3344.2.cu |
\(\chi_{3344}(175, \cdot)\) |
n/a |
720 |
6 |
| 3344.2.cv |
\(\chi_{3344}(287, \cdot)\) |
n/a |
600 |
6 |
| 3344.2.cy |
\(\chi_{3344}(857, \cdot)\) |
None |
0 |
6 |
| 3344.2.da |
\(\chi_{3344}(375, \cdot)\) |
None |
0 |
6 |
| 3344.2.db |
\(\chi_{3344}(241, \cdot)\) |
n/a |
708 |
6 |
| 3344.2.dd |
\(\chi_{3344}(75, \cdot)\) |
n/a |
3808 |
8 |
| 3344.2.dg |
\(\chi_{3344}(189, \cdot)\) |
n/a |
3808 |
8 |
| 3344.2.dh |
\(\chi_{3344}(229, \cdot)\) |
n/a |
3456 |
8 |
| 3344.2.dk |
\(\chi_{3344}(723, \cdot)\) |
n/a |
3456 |
8 |
| 3344.2.dm |
\(\chi_{3344}(201, \cdot)\) |
None |
0 |
8 |
| 3344.2.do |
\(\chi_{3344}(103, \cdot)\) |
None |
0 |
8 |
| 3344.2.dp |
\(\chi_{3344}(239, \cdot)\) |
n/a |
960 |
8 |
| 3344.2.dr |
\(\chi_{3344}(145, \cdot)\) |
n/a |
944 |
8 |
| 3344.2.dt |
\(\chi_{3344}(7, \cdot)\) |
None |
0 |
8 |
| 3344.2.dv |
\(\chi_{3344}(217, \cdot)\) |
None |
0 |
8 |
| 3344.2.dz |
\(\chi_{3344}(31, \cdot)\) |
n/a |
960 |
8 |
| 3344.2.ea |
\(\chi_{3344}(67, \cdot)\) |
n/a |
4800 |
12 |
| 3344.2.ec |
\(\chi_{3344}(21, \cdot)\) |
n/a |
5712 |
12 |
| 3344.2.ef |
\(\chi_{3344}(309, \cdot)\) |
n/a |
4800 |
12 |
| 3344.2.eh |
\(\chi_{3344}(43, \cdot)\) |
n/a |
5712 |
12 |
| 3344.2.ei |
\(\chi_{3344}(81, \cdot)\) |
n/a |
2832 |
24 |
| 3344.2.ej |
\(\chi_{3344}(293, \cdot)\) |
n/a |
7616 |
16 |
| 3344.2.em |
\(\chi_{3344}(27, \cdot)\) |
n/a |
7616 |
16 |
| 3344.2.en |
\(\chi_{3344}(83, \cdot)\) |
n/a |
7616 |
16 |
| 3344.2.eq |
\(\chi_{3344}(125, \cdot)\) |
n/a |
7616 |
16 |
| 3344.2.es |
\(\chi_{3344}(129, \cdot)\) |
n/a |
2832 |
24 |
| 3344.2.et |
\(\chi_{3344}(71, \cdot)\) |
None |
0 |
24 |
| 3344.2.ev |
\(\chi_{3344}(41, \cdot)\) |
None |
0 |
24 |
| 3344.2.ey |
\(\chi_{3344}(15, \cdot)\) |
n/a |
2880 |
24 |
| 3344.2.ez |
\(\chi_{3344}(63, \cdot)\) |
n/a |
2880 |
24 |
| 3344.2.fc |
\(\chi_{3344}(9, \cdot)\) |
None |
0 |
24 |
| 3344.2.fe |
\(\chi_{3344}(215, \cdot)\) |
None |
0 |
24 |
| 3344.2.fg |
\(\chi_{3344}(35, \cdot)\) |
n/a |
22848 |
48 |
| 3344.2.fi |
\(\chi_{3344}(5, \cdot)\) |
n/a |
22848 |
48 |
| 3344.2.fl |
\(\chi_{3344}(13, \cdot)\) |
n/a |
22848 |
48 |
| 3344.2.fn |
\(\chi_{3344}(3, \cdot)\) |
n/a |
22848 |
48 |
"n/a" means that newforms for that character have not been added to the database yet
