Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1025))\).
|
Total |
New |
Old |
Modular forms
| 43120 |
39464 |
3656 |
Cusp forms
| 40881 |
37866 |
3015 |
Eisenstein series
| 2239 |
1598 |
641 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1025))\)
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 |
1025.2.a |
\(\chi_{1025}(1, \cdot)\) |
1025.2.a.a |
1 |
1 |
1025.2.a.b |
1 |
1025.2.a.c |
1 |
1025.2.a.d |
2 |
1025.2.a.e |
2 |
1025.2.a.f |
2 |
1025.2.a.g |
2 |
1025.2.a.h |
3 |
1025.2.a.i |
3 |
1025.2.a.j |
3 |
1025.2.a.k |
5 |
1025.2.a.l |
5 |
1025.2.a.m |
6 |
1025.2.a.n |
7 |
1025.2.a.o |
7 |
1025.2.a.p |
14 |
1025.2.b |
\(\chi_{1025}(124, \cdot)\) |
1025.2.b.a |
2 |
1 |
1025.2.b.b |
2 |
1025.2.b.c |
2 |
1025.2.b.d |
4 |
1025.2.b.e |
4 |
1025.2.b.f |
4 |
1025.2.b.g |
6 |
1025.2.b.h |
6 |
1025.2.b.i |
6 |
1025.2.b.j |
10 |
1025.2.b.k |
14 |
1025.2.c |
\(\chi_{1025}(1024, \cdot)\) |
1025.2.c.a |
4 |
1 |
1025.2.c.b |
4 |
1025.2.c.c |
12 |
1025.2.c.d |
12 |
1025.2.c.e |
28 |
1025.2.d |
\(\chi_{1025}(901, \cdot)\) |
1025.2.d.a |
2 |
1 |
1025.2.d.b |
2 |
1025.2.d.c |
6 |
1025.2.d.d |
6 |
1025.2.d.e |
14 |
1025.2.d.f |
14 |
1025.2.d.g |
20 |
1025.2.e |
\(\chi_{1025}(401, \cdot)\) |
n/a |
126 |
2 |
1025.2.j |
\(\chi_{1025}(524, \cdot)\) |
n/a |
124 |
2 |
1025.2.k |
\(\chi_{1025}(221, \cdot)\) |
n/a |
408 |
4 |
1025.2.l |
\(\chi_{1025}(16, \cdot)\) |
n/a |
408 |
4 |
1025.2.m |
\(\chi_{1025}(206, \cdot)\) |
n/a |
400 |
4 |
1025.2.n |
\(\chi_{1025}(141, \cdot)\) |
n/a |
408 |
4 |
1025.2.o |
\(\chi_{1025}(51, \cdot)\) |
n/a |
256 |
4 |
1025.2.p |
\(\chi_{1025}(346, \cdot)\) |
n/a |
408 |
4 |
1025.2.q |
\(\chi_{1025}(232, \cdot)\) |
n/a |
244 |
4 |
1025.2.t |
\(\chi_{1025}(68, \cdot)\) |
n/a |
244 |
4 |
1025.2.u |
\(\chi_{1025}(209, \cdot)\) |
n/a |
416 |
4 |
1025.2.v |
\(\chi_{1025}(344, \cdot)\) |
n/a |
416 |
4 |
1025.2.w |
\(\chi_{1025}(351, \cdot)\) |
n/a |
256 |
4 |
1025.2.x |
\(\chi_{1025}(646, \cdot)\) |
n/a |
408 |
4 |
1025.2.y |
\(\chi_{1025}(81, \cdot)\) |
n/a |
408 |
4 |
1025.2.z |
\(\chi_{1025}(31, \cdot)\) |
n/a |
408 |
4 |
1025.2.ba |
\(\chi_{1025}(86, \cdot)\) |
n/a |
408 |
4 |
1025.2.bb |
\(\chi_{1025}(174, \cdot)\) |
n/a |
240 |
4 |
1025.2.bc |
\(\chi_{1025}(154, \cdot)\) |
n/a |
416 |
4 |
1025.2.bd |
\(\chi_{1025}(4, \cdot)\) |
n/a |
416 |
4 |
1025.2.be |
\(\chi_{1025}(269, \cdot)\) |
n/a |
416 |
4 |
1025.2.bf |
\(\chi_{1025}(204, \cdot)\) |
n/a |
416 |
4 |
1025.2.bg |
\(\chi_{1025}(329, \cdot)\) |
n/a |
400 |
4 |
1025.2.bh |
\(\chi_{1025}(469, \cdot)\) |
n/a |
416 |
4 |
1025.2.bi |
\(\chi_{1025}(264, \cdot)\) |
n/a |
416 |
4 |
1025.2.bj |
\(\chi_{1025}(59, \cdot)\) |
n/a |
416 |
4 |
1025.2.bk |
\(\chi_{1025}(474, \cdot)\) |
n/a |
240 |
4 |
1025.2.bl |
\(\chi_{1025}(146, \cdot)\) |
n/a |
408 |
4 |
1025.2.bm |
\(\chi_{1025}(121, \cdot)\) |
n/a |
832 |
8 |
1025.2.bn |
\(\chi_{1025}(49, \cdot)\) |
n/a |
496 |
8 |
1025.2.bo |
\(\chi_{1025}(9, \cdot)\) |
n/a |
816 |
8 |
1025.2.bp |
\(\chi_{1025}(84, \cdot)\) |
n/a |
816 |
8 |
1025.2.bq |
\(\chi_{1025}(39, \cdot)\) |
n/a |
816 |
8 |
1025.2.br |
\(\chi_{1025}(244, \cdot)\) |
n/a |
816 |
8 |
1025.2.cq |
\(\chi_{1025}(226, \cdot)\) |
n/a |
504 |
8 |
1025.2.cr |
\(\chi_{1025}(61, \cdot)\) |
n/a |
832 |
8 |
1025.2.cs |
\(\chi_{1025}(21, \cdot)\) |
n/a |
832 |
8 |
1025.2.ct |
\(\chi_{1025}(46, \cdot)\) |
n/a |
832 |
8 |
1025.2.cu |
\(\chi_{1025}(91, \cdot)\) |
n/a |
832 |
8 |
1025.2.cv |
\(\chi_{1025}(144, \cdot)\) |
n/a |
816 |
8 |
1025.2.cw |
\(\chi_{1025}(28, \cdot)\) |
n/a |
1648 |
16 |
1025.2.cx |
\(\chi_{1025}(167, \cdot)\) |
n/a |
1648 |
16 |
1025.2.cy |
\(\chi_{1025}(112, \cdot)\) |
n/a |
1648 |
16 |
1025.2.cz |
\(\chi_{1025}(7, \cdot)\) |
n/a |
976 |
16 |
1025.2.da |
\(\chi_{1025}(58, \cdot)\) |
n/a |
1648 |
16 |
1025.2.db |
\(\chi_{1025}(88, \cdot)\) |
n/a |
1648 |
16 |
1025.2.do |
\(\chi_{1025}(22, \cdot)\) |
n/a |
1648 |
16 |
1025.2.dp |
\(\chi_{1025}(13, \cdot)\) |
n/a |
1648 |
16 |
1025.2.dq |
\(\chi_{1025}(17, \cdot)\) |
n/a |
1648 |
16 |
1025.2.dr |
\(\chi_{1025}(93, \cdot)\) |
n/a |
976 |
16 |
1025.2.ds |
\(\chi_{1025}(3, \cdot)\) |
n/a |
1648 |
16 |
1025.2.dt |
\(\chi_{1025}(12, \cdot)\) |
n/a |
1648 |
16 |
"n/a" means that newforms for that character have not been added to the database yet