Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2205))\).
|
Total |
New |
Old |
Modular forms
| 511872 |
355093 |
156779 |
Cusp forms
| 504192 |
352475 |
151717 |
Eisenstein series
| 7680 |
2618 |
5062 |
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2205))\)
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 |
2205.4.a |
\(\chi_{2205}(1, \cdot)\) |
2205.4.a.a |
1 |
1 |
2205.4.a.b |
1 |
2205.4.a.c |
1 |
2205.4.a.d |
1 |
2205.4.a.e |
1 |
2205.4.a.f |
1 |
2205.4.a.g |
1 |
2205.4.a.h |
1 |
2205.4.a.i |
1 |
2205.4.a.j |
1 |
2205.4.a.k |
1 |
2205.4.a.l |
1 |
2205.4.a.m |
1 |
2205.4.a.n |
1 |
2205.4.a.o |
1 |
2205.4.a.p |
1 |
2205.4.a.q |
1 |
2205.4.a.r |
1 |
2205.4.a.s |
1 |
2205.4.a.t |
1 |
2205.4.a.u |
2 |
2205.4.a.v |
2 |
2205.4.a.w |
2 |
2205.4.a.x |
2 |
2205.4.a.y |
2 |
2205.4.a.z |
2 |
2205.4.a.ba |
2 |
2205.4.a.bb |
2 |
2205.4.a.bc |
2 |
2205.4.a.bd |
2 |
2205.4.a.be |
2 |
2205.4.a.bf |
2 |
2205.4.a.bg |
2 |
2205.4.a.bh |
2 |
2205.4.a.bi |
3 |
2205.4.a.bj |
3 |
2205.4.a.bk |
3 |
2205.4.a.bl |
3 |
2205.4.a.bm |
3 |
2205.4.a.bn |
4 |
2205.4.a.bo |
4 |
2205.4.a.bp |
4 |
2205.4.a.bq |
4 |
2205.4.a.br |
5 |
2205.4.a.bs |
5 |
2205.4.a.bt |
5 |
2205.4.a.bu |
5 |
2205.4.a.bv |
5 |
2205.4.a.bw |
5 |
2205.4.a.bx |
6 |
2205.4.a.by |
6 |
2205.4.a.bz |
6 |
2205.4.a.ca |
6 |
2205.4.a.cb |
8 |
2205.4.a.cc |
8 |
2205.4.a.cd |
8 |
2205.4.a.ce |
8 |
2205.4.a.cf |
8 |
2205.4.a.cg |
8 |
2205.4.a.ch |
12 |
2205.4.a.ci |
12 |
2205.4.b |
\(\chi_{2205}(881, \cdot)\) |
n/a |
160 |
1 |
2205.4.d |
\(\chi_{2205}(1324, \cdot)\) |
n/a |
302 |
1 |
2205.4.g |
\(\chi_{2205}(2204, \cdot)\) |
n/a |
240 |
1 |
2205.4.i |
\(\chi_{2205}(736, \cdot)\) |
n/a |
984 |
2 |
2205.4.j |
\(\chi_{2205}(226, \cdot)\) |
n/a |
400 |
2 |
2205.4.k |
\(\chi_{2205}(961, \cdot)\) |
n/a |
960 |
2 |
2205.4.l |
\(\chi_{2205}(1096, \cdot)\) |
n/a |
960 |
2 |
2205.4.m |
\(\chi_{2205}(197, \cdot)\) |
n/a |
492 |
2 |
2205.4.p |
\(\chi_{2205}(1567, \cdot)\) |
n/a |
592 |
2 |
2205.4.r |
\(\chi_{2205}(214, \cdot)\) |
n/a |
1424 |
2 |
2205.4.t |
\(\chi_{2205}(1391, \cdot)\) |
n/a |
960 |
2 |
2205.4.u |
\(\chi_{2205}(374, \cdot)\) |
n/a |
1424 |
2 |
2205.4.z |
\(\chi_{2205}(734, \cdot)\) |
n/a |
1424 |
2 |
2205.4.bb |
\(\chi_{2205}(1844, \cdot)\) |
n/a |
480 |
2 |
2205.4.be |
\(\chi_{2205}(1256, \cdot)\) |
n/a |
960 |
2 |
2205.4.bf |
\(\chi_{2205}(1549, \cdot)\) |
n/a |
592 |
2 |
2205.4.bh |
\(\chi_{2205}(589, \cdot)\) |
n/a |
1456 |
2 |
2205.4.bj |
\(\chi_{2205}(521, \cdot)\) |
n/a |
320 |
2 |
2205.4.bl |
\(\chi_{2205}(146, \cdot)\) |
n/a |
960 |
2 |
2205.4.bo |
\(\chi_{2205}(79, \cdot)\) |
n/a |
1424 |
2 |
2205.4.bq |
\(\chi_{2205}(509, \cdot)\) |
n/a |
1424 |
2 |
2205.4.bs |
\(\chi_{2205}(316, \cdot)\) |
n/a |
1680 |
6 |
2205.4.bt |
\(\chi_{2205}(178, \cdot)\) |
n/a |
2848 |
4 |
2205.4.bw |
\(\chi_{2205}(263, \cdot)\) |
n/a |
2848 |
4 |
2205.4.by |
\(\chi_{2205}(128, \cdot)\) |
n/a |
2848 |
4 |
2205.4.ca |
\(\chi_{2205}(1207, \cdot)\) |
n/a |
1184 |
4 |
2205.4.cc |
\(\chi_{2205}(97, \cdot)\) |
n/a |
2848 |
4 |
2205.4.cd |
\(\chi_{2205}(932, \cdot)\) |
n/a |
2912 |
4 |
2205.4.cf |
\(\chi_{2205}(422, \cdot)\) |
n/a |
960 |
4 |
2205.4.ch |
\(\chi_{2205}(313, \cdot)\) |
n/a |
2848 |
4 |
2205.4.ck |
\(\chi_{2205}(314, \cdot)\) |
n/a |
2016 |
6 |
2205.4.cn |
\(\chi_{2205}(64, \cdot)\) |
n/a |
2508 |
6 |
2205.4.cp |
\(\chi_{2205}(251, \cdot)\) |
n/a |
1344 |
6 |
2205.4.cq |
\(\chi_{2205}(121, \cdot)\) |
n/a |
8064 |
12 |
2205.4.cr |
\(\chi_{2205}(16, \cdot)\) |
n/a |
8064 |
12 |
2205.4.cs |
\(\chi_{2205}(46, \cdot)\) |
n/a |
3360 |
12 |
2205.4.ct |
\(\chi_{2205}(106, \cdot)\) |
n/a |
8064 |
12 |
2205.4.cv |
\(\chi_{2205}(118, \cdot)\) |
n/a |
5016 |
12 |
2205.4.cw |
\(\chi_{2205}(8, \cdot)\) |
n/a |
4032 |
12 |
2205.4.cz |
\(\chi_{2205}(164, \cdot)\) |
n/a |
12048 |
12 |
2205.4.db |
\(\chi_{2205}(4, \cdot)\) |
n/a |
12048 |
12 |
2205.4.de |
\(\chi_{2205}(41, \cdot)\) |
n/a |
8064 |
12 |
2205.4.dg |
\(\chi_{2205}(26, \cdot)\) |
n/a |
2688 |
12 |
2205.4.di |
\(\chi_{2205}(169, \cdot)\) |
n/a |
12048 |
12 |
2205.4.dk |
\(\chi_{2205}(109, \cdot)\) |
n/a |
5016 |
12 |
2205.4.dl |
\(\chi_{2205}(236, \cdot)\) |
n/a |
8064 |
12 |
2205.4.do |
\(\chi_{2205}(89, \cdot)\) |
n/a |
4032 |
12 |
2205.4.dq |
\(\chi_{2205}(104, \cdot)\) |
n/a |
12048 |
12 |
2205.4.dv |
\(\chi_{2205}(59, \cdot)\) |
n/a |
12048 |
12 |
2205.4.dw |
\(\chi_{2205}(101, \cdot)\) |
n/a |
8064 |
12 |
2205.4.dy |
\(\chi_{2205}(184, \cdot)\) |
n/a |
12048 |
12 |
2205.4.ea |
\(\chi_{2205}(157, \cdot)\) |
n/a |
24096 |
24 |
2205.4.ec |
\(\chi_{2205}(92, \cdot)\) |
n/a |
24096 |
24 |
2205.4.ee |
\(\chi_{2205}(53, \cdot)\) |
n/a |
8064 |
24 |
2205.4.eh |
\(\chi_{2205}(73, \cdot)\) |
n/a |
10032 |
24 |
2205.4.ej |
\(\chi_{2205}(13, \cdot)\) |
n/a |
24096 |
24 |
2205.4.el |
\(\chi_{2205}(2, \cdot)\) |
n/a |
24096 |
24 |
2205.4.en |
\(\chi_{2205}(23, \cdot)\) |
n/a |
24096 |
24 |
2205.4.eo |
\(\chi_{2205}(52, \cdot)\) |
n/a |
24096 |
24 |
"n/a" means that newforms for that character have not been added to the database yet