Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1911))\).
|
Total |
New |
Old |
Modular forms
| 398016 |
282066 |
115950 |
Cusp forms
| 392256 |
279930 |
112326 |
Eisenstein series
| 5760 |
2136 |
3624 |
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1911))\)
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 |
1911.4.a |
\(\chi_{1911}(1, \cdot)\) |
1911.4.a.a |
1 |
1 |
1911.4.a.b |
1 |
1911.4.a.c |
1 |
1911.4.a.d |
1 |
1911.4.a.e |
1 |
1911.4.a.f |
1 |
1911.4.a.g |
2 |
1911.4.a.h |
2 |
1911.4.a.i |
3 |
1911.4.a.j |
3 |
1911.4.a.k |
3 |
1911.4.a.l |
4 |
1911.4.a.m |
4 |
1911.4.a.n |
5 |
1911.4.a.o |
6 |
1911.4.a.p |
6 |
1911.4.a.q |
6 |
1911.4.a.r |
7 |
1911.4.a.s |
7 |
1911.4.a.t |
7 |
1911.4.a.u |
7 |
1911.4.a.v |
11 |
1911.4.a.w |
11 |
1911.4.a.x |
11 |
1911.4.a.y |
11 |
1911.4.a.z |
13 |
1911.4.a.ba |
13 |
1911.4.a.bb |
13 |
1911.4.a.bc |
13 |
1911.4.a.bd |
14 |
1911.4.a.be |
14 |
1911.4.a.bf |
22 |
1911.4.a.bg |
22 |
1911.4.c |
\(\chi_{1911}(883, \cdot)\) |
n/a |
288 |
1 |
1911.4.e |
\(\chi_{1911}(1028, \cdot)\) |
n/a |
480 |
1 |
1911.4.g |
\(\chi_{1911}(1910, \cdot)\) |
n/a |
552 |
1 |
1911.4.i |
\(\chi_{1911}(79, \cdot)\) |
n/a |
480 |
2 |
1911.4.j |
\(\chi_{1911}(373, \cdot)\) |
n/a |
560 |
2 |
1911.4.k |
\(\chi_{1911}(295, \cdot)\) |
n/a |
572 |
2 |
1911.4.l |
\(\chi_{1911}(802, \cdot)\) |
n/a |
560 |
2 |
1911.4.n |
\(\chi_{1911}(785, \cdot)\) |
n/a |
1128 |
2 |
1911.4.p |
\(\chi_{1911}(538, \cdot)\) |
n/a |
560 |
2 |
1911.4.r |
\(\chi_{1911}(68, \cdot)\) |
n/a |
1104 |
2 |
1911.4.t |
\(\chi_{1911}(1096, \cdot)\) |
n/a |
560 |
2 |
1911.4.u |
\(\chi_{1911}(881, \cdot)\) |
n/a |
1104 |
2 |
1911.4.y |
\(\chi_{1911}(374, \cdot)\) |
n/a |
1104 |
2 |
1911.4.ba |
\(\chi_{1911}(1403, \cdot)\) |
n/a |
1104 |
2 |
1911.4.bd |
\(\chi_{1911}(589, \cdot)\) |
n/a |
576 |
2 |
1911.4.bf |
\(\chi_{1911}(1244, \cdot)\) |
n/a |
1104 |
2 |
1911.4.bh |
\(\chi_{1911}(521, \cdot)\) |
n/a |
960 |
2 |
1911.4.bj |
\(\chi_{1911}(961, \cdot)\) |
n/a |
560 |
2 |
1911.4.bl |
\(\chi_{1911}(361, \cdot)\) |
n/a |
560 |
2 |
1911.4.bn |
\(\chi_{1911}(146, \cdot)\) |
n/a |
1104 |
2 |
1911.4.br |
\(\chi_{1911}(803, \cdot)\) |
n/a |
1104 |
2 |
1911.4.bs |
\(\chi_{1911}(274, \cdot)\) |
n/a |
2016 |
6 |
1911.4.bu |
\(\chi_{1911}(1060, \cdot)\) |
n/a |
1120 |
4 |
1911.4.bw |
\(\chi_{1911}(128, \cdot)\) |
n/a |
2208 |
4 |
1911.4.bx |
\(\chi_{1911}(422, \cdot)\) |
n/a |
2208 |
4 |
1911.4.bz |
\(\chi_{1911}(97, \cdot)\) |
n/a |
1120 |
4 |
1911.4.ca |
\(\chi_{1911}(31, \cdot)\) |
n/a |
1120 |
4 |
1911.4.cd |
\(\chi_{1911}(50, \cdot)\) |
n/a |
2256 |
4 |
1911.4.ce |
\(\chi_{1911}(863, \cdot)\) |
n/a |
2208 |
4 |
1911.4.ch |
\(\chi_{1911}(19, \cdot)\) |
n/a |
1120 |
4 |
1911.4.ck |
\(\chi_{1911}(272, \cdot)\) |
n/a |
4680 |
6 |
1911.4.cm |
\(\chi_{1911}(209, \cdot)\) |
n/a |
4032 |
6 |
1911.4.co |
\(\chi_{1911}(64, \cdot)\) |
n/a |
2352 |
6 |
1911.4.cq |
\(\chi_{1911}(16, \cdot)\) |
n/a |
4704 |
12 |
1911.4.cr |
\(\chi_{1911}(22, \cdot)\) |
n/a |
4704 |
12 |
1911.4.cs |
\(\chi_{1911}(100, \cdot)\) |
n/a |
4704 |
12 |
1911.4.ct |
\(\chi_{1911}(235, \cdot)\) |
n/a |
4032 |
12 |
1911.4.cu |
\(\chi_{1911}(34, \cdot)\) |
n/a |
4704 |
12 |
1911.4.cw |
\(\chi_{1911}(8, \cdot)\) |
n/a |
9360 |
12 |
1911.4.cy |
\(\chi_{1911}(17, \cdot)\) |
n/a |
9360 |
12 |
1911.4.dc |
\(\chi_{1911}(230, \cdot)\) |
n/a |
9360 |
12 |
1911.4.de |
\(\chi_{1911}(88, \cdot)\) |
n/a |
4704 |
12 |
1911.4.dg |
\(\chi_{1911}(25, \cdot)\) |
n/a |
4704 |
12 |
1911.4.di |
\(\chi_{1911}(131, \cdot)\) |
n/a |
8064 |
12 |
1911.4.dk |
\(\chi_{1911}(152, \cdot)\) |
n/a |
9360 |
12 |
1911.4.dm |
\(\chi_{1911}(43, \cdot)\) |
n/a |
4704 |
12 |
1911.4.dp |
\(\chi_{1911}(38, \cdot)\) |
n/a |
9360 |
12 |
1911.4.dr |
\(\chi_{1911}(101, \cdot)\) |
n/a |
9360 |
12 |
1911.4.dv |
\(\chi_{1911}(62, \cdot)\) |
n/a |
9360 |
12 |
1911.4.dw |
\(\chi_{1911}(4, \cdot)\) |
n/a |
4704 |
12 |
1911.4.dy |
\(\chi_{1911}(269, \cdot)\) |
n/a |
9360 |
12 |
1911.4.eb |
\(\chi_{1911}(115, \cdot)\) |
n/a |
9408 |
24 |
1911.4.ee |
\(\chi_{1911}(44, \cdot)\) |
n/a |
18720 |
24 |
1911.4.ef |
\(\chi_{1911}(71, \cdot)\) |
n/a |
18720 |
24 |
1911.4.ei |
\(\chi_{1911}(73, \cdot)\) |
n/a |
9408 |
24 |
1911.4.ej |
\(\chi_{1911}(76, \cdot)\) |
n/a |
9408 |
24 |
1911.4.el |
\(\chi_{1911}(11, \cdot)\) |
n/a |
18720 |
24 |
1911.4.em |
\(\chi_{1911}(2, \cdot)\) |
n/a |
18720 |
24 |
1911.4.eo |
\(\chi_{1911}(136, \cdot)\) |
n/a |
9408 |
24 |
"n/a" means that newforms for that character have not been added to the database yet