Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3762))\).
|
Total |
New |
Old |
Modular forms
| 394560 |
100328 |
294232 |
Cusp forms
| 383041 |
100328 |
282713 |
Eisenstein series
| 11519 |
0 |
11519 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3762))\)
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 the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
3762.2.a |
\(\chi_{3762}(1, \cdot)\) |
3762.2.a.a |
1 |
1 |
3762.2.a.b |
1 |
3762.2.a.c |
1 |
3762.2.a.d |
1 |
3762.2.a.e |
1 |
3762.2.a.f |
1 |
3762.2.a.g |
1 |
3762.2.a.h |
1 |
3762.2.a.i |
1 |
3762.2.a.j |
1 |
3762.2.a.k |
1 |
3762.2.a.l |
1 |
3762.2.a.m |
1 |
3762.2.a.n |
1 |
3762.2.a.o |
1 |
3762.2.a.p |
1 |
3762.2.a.q |
1 |
3762.2.a.r |
1 |
3762.2.a.s |
2 |
3762.2.a.t |
2 |
3762.2.a.u |
2 |
3762.2.a.v |
2 |
3762.2.a.w |
2 |
3762.2.a.x |
2 |
3762.2.a.y |
2 |
3762.2.a.z |
2 |
3762.2.a.ba |
2 |
3762.2.a.bb |
2 |
3762.2.a.bc |
2 |
3762.2.a.bd |
3 |
3762.2.a.be |
3 |
3762.2.a.bf |
3 |
3762.2.a.bg |
3 |
3762.2.a.bh |
4 |
3762.2.a.bi |
5 |
3762.2.a.bj |
5 |
3762.2.a.bk |
5 |
3762.2.a.bl |
5 |
3762.2.b |
\(\chi_{3762}(989, \cdot)\) |
3762.2.b.a |
36 |
1 |
3762.2.b.b |
36 |
3762.2.d |
\(\chi_{3762}(683, \cdot)\) |
3762.2.d.a |
36 |
1 |
3762.2.d.b |
36 |
3762.2.g |
\(\chi_{3762}(2089, \cdot)\) |
3762.2.g.a |
2 |
1 |
3762.2.g.b |
2 |
3762.2.g.c |
2 |
3762.2.g.d |
2 |
3762.2.g.e |
2 |
3762.2.g.f |
2 |
3762.2.g.g |
8 |
3762.2.g.h |
8 |
3762.2.g.i |
16 |
3762.2.g.j |
16 |
3762.2.g.k |
20 |
3762.2.g.l |
20 |
3762.2.i |
\(\chi_{3762}(1255, \cdot)\) |
n/a |
360 |
2 |
3762.2.j |
\(\chi_{3762}(1717, \cdot)\) |
n/a |
400 |
2 |
3762.2.k |
\(\chi_{3762}(1189, \cdot)\) |
n/a |
172 |
2 |
3762.2.l |
\(\chi_{3762}(463, \cdot)\) |
n/a |
400 |
2 |
3762.2.m |
\(\chi_{3762}(685, \cdot)\) |
n/a |
360 |
4 |
3762.2.o |
\(\chi_{3762}(221, \cdot)\) |
n/a |
400 |
2 |
3762.2.q |
\(\chi_{3762}(2705, \cdot)\) |
n/a |
480 |
2 |
3762.2.r |
\(\chi_{3762}(901, \cdot)\) |
n/a |
200 |
2 |
3762.2.w |
\(\chi_{3762}(835, \cdot)\) |
n/a |
480 |
2 |
3762.2.y |
\(\chi_{3762}(1627, \cdot)\) |
n/a |
480 |
2 |
3762.2.bb |
\(\chi_{3762}(197, \cdot)\) |
n/a |
160 |
2 |
3762.2.bc |
\(\chi_{3762}(2003, \cdot)\) |
n/a |
400 |
2 |
3762.2.be |
\(\chi_{3762}(1937, \cdot)\) |
n/a |
400 |
2 |
3762.2.bg |
\(\chi_{3762}(923, \cdot)\) |
n/a |
480 |
2 |
3762.2.bi |
\(\chi_{3762}(2243, \cdot)\) |
n/a |
432 |
2 |
3762.2.bl |
\(\chi_{3762}(1475, \cdot)\) |
n/a |
144 |
2 |
3762.2.bn |
\(\chi_{3762}(373, \cdot)\) |
n/a |
480 |
2 |
3762.2.bp |
\(\chi_{3762}(199, \cdot)\) |
n/a |
492 |
6 |
3762.2.bq |
\(\chi_{3762}(1651, \cdot)\) |
n/a |
1200 |
6 |
3762.2.br |
\(\chi_{3762}(529, \cdot)\) |
n/a |
1200 |
6 |
3762.2.bt |
\(\chi_{3762}(721, \cdot)\) |
n/a |
400 |
4 |
3762.2.bw |
\(\chi_{3762}(1367, \cdot)\) |
n/a |
320 |
4 |
3762.2.by |
\(\chi_{3762}(305, \cdot)\) |
n/a |
288 |
4 |
3762.2.bz |
\(\chi_{3762}(619, \cdot)\) |
n/a |
1920 |
8 |
3762.2.ca |
\(\chi_{3762}(163, \cdot)\) |
n/a |
800 |
8 |
3762.2.cb |
\(\chi_{3762}(49, \cdot)\) |
n/a |
1920 |
8 |
3762.2.cc |
\(\chi_{3762}(115, \cdot)\) |
n/a |
1728 |
8 |
3762.2.cd |
\(\chi_{3762}(263, \cdot)\) |
n/a |
1440 |
6 |
3762.2.cf |
\(\chi_{3762}(439, \cdot)\) |
n/a |
1440 |
6 |
3762.2.ci |
\(\chi_{3762}(1211, \cdot)\) |
n/a |
1200 |
6 |
3762.2.ck |
\(\chi_{3762}(89, \cdot)\) |
n/a |
384 |
6 |
3762.2.co |
\(\chi_{3762}(241, \cdot)\) |
n/a |
1440 |
6 |
3762.2.cp |
\(\chi_{3762}(593, \cdot)\) |
n/a |
480 |
6 |
3762.2.cr |
\(\chi_{3762}(109, \cdot)\) |
n/a |
600 |
6 |
3762.2.cu |
\(\chi_{3762}(131, \cdot)\) |
n/a |
1440 |
6 |
3762.2.cw |
\(\chi_{3762}(155, \cdot)\) |
n/a |
1200 |
6 |
3762.2.cz |
\(\chi_{3762}(673, \cdot)\) |
n/a |
1920 |
8 |
3762.2.db |
\(\chi_{3762}(179, \cdot)\) |
n/a |
640 |
8 |
3762.2.de |
\(\chi_{3762}(761, \cdot)\) |
n/a |
1728 |
8 |
3762.2.dg |
\(\chi_{3762}(83, \cdot)\) |
n/a |
1920 |
8 |
3762.2.di |
\(\chi_{3762}(113, \cdot)\) |
n/a |
1920 |
8 |
3762.2.dk |
\(\chi_{3762}(335, \cdot)\) |
n/a |
1920 |
8 |
3762.2.dl |
\(\chi_{3762}(809, \cdot)\) |
n/a |
640 |
8 |
3762.2.do |
\(\chi_{3762}(259, \cdot)\) |
n/a |
1920 |
8 |
3762.2.dq |
\(\chi_{3762}(151, \cdot)\) |
n/a |
1920 |
8 |
3762.2.dv |
\(\chi_{3762}(145, \cdot)\) |
n/a |
800 |
8 |
3762.2.dw |
\(\chi_{3762}(695, \cdot)\) |
n/a |
1920 |
8 |
3762.2.dy |
\(\chi_{3762}(905, \cdot)\) |
n/a |
1920 |
8 |
3762.2.ea |
\(\chi_{3762}(169, \cdot)\) |
n/a |
5760 |
24 |
3762.2.eb |
\(\chi_{3762}(25, \cdot)\) |
n/a |
5760 |
24 |
3762.2.ec |
\(\chi_{3762}(289, \cdot)\) |
n/a |
2400 |
24 |
3762.2.ed |
\(\chi_{3762}(203, \cdot)\) |
n/a |
5760 |
24 |
3762.2.eh |
\(\chi_{3762}(101, \cdot)\) |
n/a |
5760 |
24 |
3762.2.ei |
\(\chi_{3762}(127, \cdot)\) |
n/a |
2400 |
24 |
3762.2.ek |
\(\chi_{3762}(17, \cdot)\) |
n/a |
1920 |
24 |
3762.2.en |
\(\chi_{3762}(193, \cdot)\) |
n/a |
5760 |
24 |
3762.2.ep |
\(\chi_{3762}(53, \cdot)\) |
n/a |
1920 |
24 |
3762.2.et |
\(\chi_{3762}(59, \cdot)\) |
n/a |
5760 |
24 |
3762.2.eu |
\(\chi_{3762}(13, \cdot)\) |
n/a |
5760 |
24 |
3762.2.ew |
\(\chi_{3762}(365, \cdot)\) |
n/a |
5760 |
24 |
"n/a" means that newforms for that character have not been added to the database yet