Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3724))\).
|
Total |
New |
Old |
Modular forms
| 428760 |
237319 |
191441 |
Cusp forms
| 417961 |
234019 |
183942 |
Eisenstein series
| 10799 |
3300 |
7499 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3724))\)
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 |
3724.2.a |
\(\chi_{3724}(1, \cdot)\) |
3724.2.a.a |
1 |
1 |
3724.2.a.b |
1 |
3724.2.a.c |
2 |
3724.2.a.d |
2 |
3724.2.a.e |
2 |
3724.2.a.f |
2 |
3724.2.a.g |
2 |
3724.2.a.h |
3 |
3724.2.a.i |
3 |
3724.2.a.j |
3 |
3724.2.a.k |
5 |
3724.2.a.l |
5 |
3724.2.a.m |
7 |
3724.2.a.n |
7 |
3724.2.a.o |
8 |
3724.2.a.p |
8 |
3724.2.f |
\(\chi_{3724}(2547, \cdot)\) |
n/a |
360 |
1 |
3724.2.g |
\(\chi_{3724}(1861, \cdot)\) |
3724.2.g.a |
2 |
1 |
3724.2.g.b |
2 |
3724.2.g.c |
4 |
3724.2.g.d |
4 |
3724.2.g.e |
8 |
3724.2.g.f |
16 |
3724.2.g.g |
32 |
3724.2.h |
\(\chi_{3724}(3039, \cdot)\) |
n/a |
400 |
1 |
3724.2.i |
\(\chi_{3724}(3117, \cdot)\) |
n/a |
120 |
2 |
3724.2.j |
\(\chi_{3724}(197, \cdot)\) |
n/a |
138 |
2 |
3724.2.k |
\(\chi_{3724}(1341, \cdot)\) |
n/a |
132 |
2 |
3724.2.l |
\(\chi_{3724}(961, \cdot)\) |
n/a |
132 |
2 |
3724.2.q |
\(\chi_{3724}(521, \cdot)\) |
n/a |
132 |
2 |
3724.2.r |
\(\chi_{3724}(619, \cdot)\) |
n/a |
784 |
2 |
3724.2.s |
\(\chi_{3724}(1471, \cdot)\) |
n/a |
800 |
2 |
3724.2.t |
\(\chi_{3724}(2431, \cdot)\) |
n/a |
784 |
2 |
3724.2.u |
\(\chi_{3724}(391, \cdot)\) |
n/a |
784 |
2 |
3724.2.v |
\(\chi_{3724}(2089, \cdot)\) |
n/a |
132 |
2 |
3724.2.w |
\(\chi_{3724}(2775, \cdot)\) |
n/a |
720 |
2 |
3724.2.x |
\(\chi_{3724}(293, \cdot)\) |
n/a |
136 |
2 |
3724.2.y |
\(\chi_{3724}(1243, \cdot)\) |
n/a |
784 |
2 |
3724.2.bl |
\(\chi_{3724}(863, \cdot)\) |
n/a |
784 |
2 |
3724.2.bm |
\(\chi_{3724}(901, \cdot)\) |
n/a |
132 |
2 |
3724.2.bn |
\(\chi_{3724}(999, \cdot)\) |
n/a |
784 |
2 |
3724.2.bo |
\(\chi_{3724}(533, \cdot)\) |
n/a |
504 |
6 |
3724.2.bp |
\(\chi_{3724}(785, \cdot)\) |
n/a |
408 |
6 |
3724.2.bq |
\(\chi_{3724}(177, \cdot)\) |
n/a |
402 |
6 |
3724.2.br |
\(\chi_{3724}(557, \cdot)\) |
n/a |
402 |
6 |
3724.2.bs |
\(\chi_{3724}(379, \cdot)\) |
n/a |
3336 |
6 |
3724.2.bt |
\(\chi_{3724}(265, \cdot)\) |
n/a |
552 |
6 |
3724.2.bu |
\(\chi_{3724}(419, \cdot)\) |
n/a |
3024 |
6 |
3724.2.bz |
\(\chi_{3724}(803, \cdot)\) |
n/a |
2352 |
6 |
3724.2.ca |
\(\chi_{3724}(67, \cdot)\) |
n/a |
2352 |
6 |
3724.2.cd |
\(\chi_{3724}(97, \cdot)\) |
n/a |
396 |
6 |
3724.2.ce |
\(\chi_{3724}(325, \cdot)\) |
n/a |
402 |
6 |
3724.2.cj |
\(\chi_{3724}(295, \cdot)\) |
n/a |
2400 |
6 |
3724.2.ck |
\(\chi_{3724}(195, \cdot)\) |
n/a |
2352 |
6 |
3724.2.cl |
\(\chi_{3724}(215, \cdot)\) |
n/a |
2352 |
6 |
3724.2.cm |
\(\chi_{3724}(459, \cdot)\) |
n/a |
2352 |
6 |
3724.2.cr |
\(\chi_{3724}(117, \cdot)\) |
n/a |
402 |
6 |
3724.2.cu |
\(\chi_{3724}(429, \cdot)\) |
n/a |
1128 |
12 |
3724.2.cv |
\(\chi_{3724}(121, \cdot)\) |
n/a |
1128 |
12 |
3724.2.cw |
\(\chi_{3724}(505, \cdot)\) |
n/a |
1104 |
12 |
3724.2.cx |
\(\chi_{3724}(305, \cdot)\) |
n/a |
1008 |
12 |
3724.2.cy |
\(\chi_{3724}(311, \cdot)\) |
n/a |
6672 |
12 |
3724.2.cz |
\(\chi_{3724}(297, \cdot)\) |
n/a |
1128 |
12 |
3724.2.da |
\(\chi_{3724}(331, \cdot)\) |
n/a |
6672 |
12 |
3724.2.dn |
\(\chi_{3724}(107, \cdot)\) |
n/a |
6672 |
12 |
3724.2.do |
\(\chi_{3724}(69, \cdot)\) |
n/a |
1104 |
12 |
3724.2.dp |
\(\chi_{3724}(115, \cdot)\) |
n/a |
6048 |
12 |
3724.2.dq |
\(\chi_{3724}(341, \cdot)\) |
n/a |
1128 |
12 |
3724.2.dr |
\(\chi_{3724}(83, \cdot)\) |
n/a |
6672 |
12 |
3724.2.ds |
\(\chi_{3724}(151, \cdot)\) |
n/a |
6672 |
12 |
3724.2.dt |
\(\chi_{3724}(183, \cdot)\) |
n/a |
6672 |
12 |
3724.2.du |
\(\chi_{3724}(87, \cdot)\) |
n/a |
6672 |
12 |
3724.2.dv |
\(\chi_{3724}(145, \cdot)\) |
n/a |
1128 |
12 |
3724.2.ea |
\(\chi_{3724}(25, \cdot)\) |
n/a |
3348 |
36 |
3724.2.eb |
\(\chi_{3724}(85, \cdot)\) |
n/a |
3384 |
36 |
3724.2.ec |
\(\chi_{3724}(9, \cdot)\) |
n/a |
3348 |
36 |
3724.2.ef |
\(\chi_{3724}(33, \cdot)\) |
n/a |
3348 |
36 |
3724.2.ek |
\(\chi_{3724}(55, \cdot)\) |
n/a |
20016 |
36 |
3724.2.el |
\(\chi_{3724}(15, \cdot)\) |
n/a |
20016 |
36 |
3724.2.em |
\(\chi_{3724}(51, \cdot)\) |
n/a |
20016 |
36 |
3724.2.en |
\(\chi_{3724}(47, \cdot)\) |
n/a |
20016 |
36 |
3724.2.es |
\(\chi_{3724}(13, \cdot)\) |
n/a |
3384 |
36 |
3724.2.et |
\(\chi_{3724}(89, \cdot)\) |
n/a |
3348 |
36 |
3724.2.ew |
\(\chi_{3724}(135, \cdot)\) |
n/a |
20016 |
36 |
3724.2.ex |
\(\chi_{3724}(131, \cdot)\) |
n/a |
20016 |
36 |
"n/a" means that newforms for that character have not been added to the database yet