Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6422))\).
|
Total |
New |
Old |
Modular forms
| 1285848 |
418515 |
867333 |
Cusp forms
| 1269433 |
418515 |
850918 |
Eisenstein series
| 16415 |
0 |
16415 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6422))\)
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 |
6422.2.a |
\(\chi_{6422}(1, \cdot)\) |
6422.2.a.a |
1 |
1 |
6422.2.a.b |
1 |
6422.2.a.c |
1 |
6422.2.a.d |
1 |
6422.2.a.e |
1 |
6422.2.a.f |
1 |
6422.2.a.g |
1 |
6422.2.a.h |
1 |
6422.2.a.i |
1 |
6422.2.a.j |
1 |
6422.2.a.k |
3 |
6422.2.a.l |
3 |
6422.2.a.m |
3 |
6422.2.a.n |
3 |
6422.2.a.o |
3 |
6422.2.a.p |
3 |
6422.2.a.q |
3 |
6422.2.a.r |
3 |
6422.2.a.s |
3 |
6422.2.a.t |
3 |
6422.2.a.u |
3 |
6422.2.a.v |
3 |
6422.2.a.w |
3 |
6422.2.a.x |
3 |
6422.2.a.y |
3 |
6422.2.a.z |
4 |
6422.2.a.ba |
4 |
6422.2.a.bb |
4 |
6422.2.a.bc |
6 |
6422.2.a.bd |
6 |
6422.2.a.be |
7 |
6422.2.a.bf |
7 |
6422.2.a.bg |
8 |
6422.2.a.bh |
8 |
6422.2.a.bi |
9 |
6422.2.a.bj |
9 |
6422.2.a.bk |
9 |
6422.2.a.bl |
9 |
6422.2.a.bm |
14 |
6422.2.a.bn |
14 |
6422.2.a.bo |
15 |
6422.2.a.bp |
15 |
6422.2.a.bq |
15 |
6422.2.a.br |
15 |
6422.2.d |
\(\chi_{6422}(3041, \cdot)\) |
n/a |
230 |
1 |
6422.2.e |
\(\chi_{6422}(653, \cdot)\) |
n/a |
516 |
2 |
6422.2.f |
\(\chi_{6422}(2367, \cdot)\) |
n/a |
514 |
2 |
6422.2.g |
\(\chi_{6422}(191, \cdot)\) |
n/a |
464 |
2 |
6422.2.h |
\(\chi_{6422}(315, \cdot)\) |
n/a |
516 |
2 |
6422.2.i |
\(\chi_{6422}(1253, \cdot)\) |
n/a |
508 |
2 |
6422.2.m |
\(\chi_{6422}(2851, \cdot)\) |
n/a |
460 |
2 |
6422.2.n |
\(\chi_{6422}(5407, \cdot)\) |
n/a |
508 |
2 |
6422.2.o |
\(\chi_{6422}(1375, \cdot)\) |
n/a |
516 |
2 |
6422.2.v |
\(\chi_{6422}(1037, \cdot)\) |
n/a |
516 |
2 |
6422.2.w |
\(\chi_{6422}(529, \cdot)\) |
n/a |
1536 |
6 |
6422.2.x |
\(\chi_{6422}(339, \cdot)\) |
n/a |
1554 |
6 |
6422.2.y |
\(\chi_{6422}(1543, \cdot)\) |
n/a |
1536 |
6 |
6422.2.z |
\(\chi_{6422}(2117, \cdot)\) |
n/a |
1032 |
4 |
6422.2.bd |
\(\chi_{6422}(1779, \cdot)\) |
n/a |
1032 |
4 |
6422.2.be |
\(\chi_{6422}(1671, \cdot)\) |
n/a |
1032 |
4 |
6422.2.bf |
\(\chi_{6422}(4971, \cdot)\) |
n/a |
1016 |
4 |
6422.2.bh |
\(\chi_{6422}(495, \cdot)\) |
n/a |
3264 |
12 |
6422.2.bi |
\(\chi_{6422}(823, \cdot)\) |
n/a |
1536 |
6 |
6422.2.bm |
\(\chi_{6422}(1013, \cdot)\) |
n/a |
1548 |
6 |
6422.2.bn |
\(\chi_{6422}(23, \cdot)\) |
n/a |
1536 |
6 |
6422.2.br |
\(\chi_{6422}(77, \cdot)\) |
n/a |
3288 |
12 |
6422.2.bx |
\(\chi_{6422}(249, \cdot)\) |
n/a |
3072 |
12 |
6422.2.by |
\(\chi_{6422}(89, \cdot)\) |
n/a |
3072 |
12 |
6422.2.bz |
\(\chi_{6422}(775, \cdot)\) |
n/a |
3096 |
12 |
6422.2.ca |
\(\chi_{6422}(425, \cdot)\) |
n/a |
7248 |
24 |
6422.2.cb |
\(\chi_{6422}(419, \cdot)\) |
n/a |
6528 |
24 |
6422.2.cc |
\(\chi_{6422}(235, \cdot)\) |
n/a |
7344 |
24 |
6422.2.cd |
\(\chi_{6422}(87, \cdot)\) |
n/a |
7248 |
24 |
6422.2.cf |
\(\chi_{6422}(151, \cdot)\) |
n/a |
7344 |
24 |
6422.2.cg |
\(\chi_{6422}(49, \cdot)\) |
n/a |
7248 |
24 |
6422.2.cn |
\(\chi_{6422}(277, \cdot)\) |
n/a |
7248 |
24 |
6422.2.co |
\(\chi_{6422}(311, \cdot)\) |
n/a |
7344 |
24 |
6422.2.cp |
\(\chi_{6422}(153, \cdot)\) |
n/a |
6576 |
24 |
6422.2.cs |
\(\chi_{6422}(9, \cdot)\) |
n/a |
21888 |
72 |
6422.2.ct |
\(\chi_{6422}(131, \cdot)\) |
n/a |
21744 |
72 |
6422.2.cu |
\(\chi_{6422}(35, \cdot)\) |
n/a |
21888 |
72 |
6422.2.cw |
\(\chi_{6422}(31, \cdot)\) |
n/a |
14688 |
48 |
6422.2.cx |
\(\chi_{6422}(37, \cdot)\) |
n/a |
14496 |
48 |
6422.2.cy |
\(\chi_{6422}(145, \cdot)\) |
n/a |
14496 |
48 |
6422.2.dc |
\(\chi_{6422}(141, \cdot)\) |
n/a |
14496 |
48 |
6422.2.dg |
\(\chi_{6422}(17, \cdot)\) |
n/a |
21888 |
72 |
6422.2.dh |
\(\chi_{6422}(25, \cdot)\) |
n/a |
21744 |
72 |
6422.2.dl |
\(\chi_{6422}(199, \cdot)\) |
n/a |
21888 |
72 |
6422.2.dm |
\(\chi_{6422}(21, \cdot)\) |
n/a |
43488 |
144 |
6422.2.dn |
\(\chi_{6422}(15, \cdot)\) |
n/a |
43776 |
144 |
6422.2.do |
\(\chi_{6422}(41, \cdot)\) |
n/a |
43776 |
144 |
"n/a" means that newforms for that character have not been added to the database yet