Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6050))\).
|
Total |
New |
Old |
Modular forms
| 1097960 |
329059 |
768901 |
Cusp forms
| 1080041 |
329059 |
750982 |
Eisenstein series
| 17919 |
0 |
17919 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6050))\)
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 |
6050.2.a |
\(\chi_{6050}(1, \cdot)\) |
6050.2.a.a |
1 |
1 |
6050.2.a.b |
1 |
6050.2.a.c |
1 |
6050.2.a.d |
1 |
6050.2.a.e |
1 |
6050.2.a.f |
1 |
6050.2.a.g |
1 |
6050.2.a.h |
1 |
6050.2.a.i |
1 |
6050.2.a.j |
1 |
6050.2.a.k |
1 |
6050.2.a.l |
1 |
6050.2.a.m |
1 |
6050.2.a.n |
1 |
6050.2.a.o |
1 |
6050.2.a.p |
1 |
6050.2.a.q |
1 |
6050.2.a.r |
1 |
6050.2.a.s |
1 |
6050.2.a.t |
1 |
6050.2.a.u |
1 |
6050.2.a.v |
1 |
6050.2.a.w |
1 |
6050.2.a.x |
1 |
6050.2.a.y |
1 |
6050.2.a.z |
1 |
6050.2.a.ba |
1 |
6050.2.a.bb |
1 |
6050.2.a.bc |
1 |
6050.2.a.bd |
1 |
6050.2.a.be |
1 |
6050.2.a.bf |
1 |
6050.2.a.bg |
1 |
6050.2.a.bh |
1 |
6050.2.a.bi |
1 |
6050.2.a.bj |
1 |
6050.2.a.bk |
1 |
6050.2.a.bl |
1 |
6050.2.a.bm |
1 |
6050.2.a.bn |
1 |
6050.2.a.bo |
1 |
6050.2.a.bp |
1 |
6050.2.a.bq |
1 |
6050.2.a.br |
2 |
6050.2.a.bs |
2 |
6050.2.a.bt |
2 |
6050.2.a.bu |
2 |
6050.2.a.bv |
2 |
6050.2.a.bw |
2 |
6050.2.a.bx |
2 |
6050.2.a.by |
2 |
6050.2.a.bz |
2 |
6050.2.a.ca |
2 |
6050.2.a.cb |
2 |
6050.2.a.cc |
2 |
6050.2.a.cd |
2 |
6050.2.a.ce |
2 |
6050.2.a.cf |
2 |
6050.2.a.cg |
2 |
6050.2.a.ch |
2 |
6050.2.a.ci |
2 |
6050.2.a.cj |
2 |
6050.2.a.ck |
2 |
6050.2.a.cl |
2 |
6050.2.a.cm |
2 |
6050.2.a.cn |
2 |
6050.2.a.co |
2 |
6050.2.a.cp |
2 |
6050.2.a.cq |
2 |
6050.2.a.cr |
2 |
6050.2.a.cs |
2 |
6050.2.a.ct |
2 |
6050.2.a.cu |
2 |
6050.2.a.cv |
2 |
6050.2.a.cw |
2 |
6050.2.a.cx |
2 |
6050.2.a.cy |
4 |
6050.2.a.cz |
4 |
6050.2.a.da |
4 |
6050.2.a.db |
4 |
6050.2.a.dc |
4 |
6050.2.a.dd |
4 |
6050.2.a.de |
4 |
6050.2.a.df |
4 |
6050.2.a.dg |
4 |
6050.2.a.dh |
4 |
6050.2.a.di |
4 |
6050.2.a.dj |
4 |
6050.2.a.dk |
4 |
6050.2.a.dl |
4 |
6050.2.a.dm |
4 |
6050.2.a.dn |
4 |
6050.2.b |
\(\chi_{6050}(4599, \cdot)\) |
n/a |
164 |
1 |
6050.2.f |
\(\chi_{6050}(1693, \cdot)\) |
n/a |
324 |
2 |
6050.2.g |
\(\chi_{6050}(1461, \cdot)\) |
n/a |
1080 |
4 |
6050.2.h |
\(\chi_{6050}(251, \cdot)\) |
n/a |
684 |
4 |
6050.2.i |
\(\chi_{6050}(1721, \cdot)\) |
n/a |
1080 |
4 |
6050.2.j |
\(\chi_{6050}(81, \cdot)\) |
n/a |
1080 |
4 |
6050.2.k |
\(\chi_{6050}(1211, \cdot)\) |
n/a |
1092 |
4 |
6050.2.l |
\(\chi_{6050}(1291, \cdot)\) |
n/a |
1080 |
4 |
6050.2.n |
\(\chi_{6050}(269, \cdot)\) |
n/a |
1080 |
4 |
6050.2.t |
\(\chi_{6050}(969, \cdot)\) |
n/a |
1088 |
4 |
6050.2.y |
\(\chi_{6050}(9, \cdot)\) |
n/a |
1080 |
4 |
6050.2.z |
\(\chi_{6050}(3639, \cdot)\) |
n/a |
1080 |
4 |
6050.2.ba |
\(\chi_{6050}(1049, \cdot)\) |
n/a |
648 |
4 |
6050.2.bb |
\(\chi_{6050}(1219, \cdot)\) |
n/a |
1080 |
4 |
6050.2.be |
\(\chi_{6050}(551, \cdot)\) |
n/a |
2090 |
10 |
6050.2.bf |
\(\chi_{6050}(723, \cdot)\) |
n/a |
2160 |
8 |
6050.2.bi |
\(\chi_{6050}(457, \cdot)\) |
n/a |
1296 |
8 |
6050.2.bj |
\(\chi_{6050}(483, \cdot)\) |
n/a |
2160 |
8 |
6050.2.bk |
\(\chi_{6050}(2877, \cdot)\) |
n/a |
2160 |
8 |
6050.2.bl |
\(\chi_{6050}(403, \cdot)\) |
n/a |
2160 |
8 |
6050.2.bq |
\(\chi_{6050}(233, \cdot)\) |
n/a |
2160 |
8 |
6050.2.bs |
\(\chi_{6050}(199, \cdot)\) |
n/a |
1980 |
10 |
6050.2.bu |
\(\chi_{6050}(43, \cdot)\) |
n/a |
3960 |
20 |
6050.2.bw |
\(\chi_{6050}(111, \cdot)\) |
n/a |
13200 |
40 |
6050.2.bx |
\(\chi_{6050}(141, \cdot)\) |
n/a |
13200 |
40 |
6050.2.by |
\(\chi_{6050}(31, \cdot)\) |
n/a |
13200 |
40 |
6050.2.bz |
\(\chi_{6050}(201, \cdot)\) |
n/a |
8360 |
40 |
6050.2.ca |
\(\chi_{6050}(291, \cdot)\) |
n/a |
13200 |
40 |
6050.2.cb |
\(\chi_{6050}(181, \cdot)\) |
n/a |
13200 |
40 |
6050.2.cc |
\(\chi_{6050}(59, \cdot)\) |
n/a |
13200 |
40 |
6050.2.ck |
\(\chi_{6050}(119, \cdot)\) |
n/a |
13200 |
40 |
6050.2.cl |
\(\chi_{6050}(49, \cdot)\) |
n/a |
7920 |
40 |
6050.2.cm |
\(\chi_{6050}(69, \cdot)\) |
n/a |
13200 |
40 |
6050.2.cn |
\(\chi_{6050}(169, \cdot)\) |
n/a |
13200 |
40 |
6050.2.cs |
\(\chi_{6050}(89, \cdot)\) |
n/a |
13200 |
40 |
6050.2.cv |
\(\chi_{6050}(17, \cdot)\) |
n/a |
26400 |
80 |
6050.2.cw |
\(\chi_{6050}(63, \cdot)\) |
n/a |
26400 |
80 |
6050.2.db |
\(\chi_{6050}(123, \cdot)\) |
n/a |
26400 |
80 |
6050.2.dc |
\(\chi_{6050}(13, \cdot)\) |
n/a |
26400 |
80 |
6050.2.dd |
\(\chi_{6050}(87, \cdot)\) |
n/a |
26400 |
80 |
6050.2.de |
\(\chi_{6050}(7, \cdot)\) |
n/a |
15840 |
80 |
"n/a" means that newforms for that character have not been added to the database yet