Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(760))\).
|
Total |
New |
Old |
Modular forms
| 18144 |
9064 |
9080 |
Cusp forms
| 16417 |
8656 |
7761 |
Eisenstein series
| 1727 |
408 |
1319 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)
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 |
760.2.a |
\(\chi_{760}(1, \cdot)\) |
760.2.a.a |
1 |
1 |
760.2.a.b |
1 |
760.2.a.c |
1 |
760.2.a.d |
1 |
760.2.a.e |
1 |
760.2.a.f |
2 |
760.2.a.g |
2 |
760.2.a.h |
3 |
760.2.a.i |
3 |
760.2.a.j |
3 |
760.2.d |
\(\chi_{760}(609, \cdot)\) |
760.2.d.a |
2 |
1 |
760.2.d.b |
4 |
760.2.d.c |
4 |
760.2.d.d |
4 |
760.2.d.e |
12 |
760.2.e |
\(\chi_{760}(531, \cdot)\) |
760.2.e.a |
80 |
1 |
760.2.f |
\(\chi_{760}(381, \cdot)\) |
760.2.f.a |
28 |
1 |
760.2.f.b |
44 |
760.2.g |
\(\chi_{760}(759, \cdot)\) |
None |
0 |
1 |
760.2.j |
\(\chi_{760}(151, \cdot)\) |
None |
0 |
1 |
760.2.k |
\(\chi_{760}(229, \cdot)\) |
760.2.k.a |
108 |
1 |
760.2.p |
\(\chi_{760}(379, \cdot)\) |
760.2.p.a |
4 |
1 |
760.2.p.b |
4 |
760.2.p.c |
4 |
760.2.p.d |
8 |
760.2.p.e |
8 |
760.2.p.f |
8 |
760.2.p.g |
8 |
760.2.p.h |
16 |
760.2.p.i |
56 |
760.2.q |
\(\chi_{760}(121, \cdot)\) |
760.2.q.a |
2 |
2 |
760.2.q.b |
2 |
760.2.q.c |
2 |
760.2.q.d |
8 |
760.2.q.e |
8 |
760.2.q.f |
8 |
760.2.q.g |
10 |
760.2.t |
\(\chi_{760}(37, \cdot)\) |
760.2.t.a |
232 |
2 |
760.2.u |
\(\chi_{760}(343, \cdot)\) |
None |
0 |
2 |
760.2.v |
\(\chi_{760}(113, \cdot)\) |
760.2.v.a |
12 |
2 |
760.2.v.b |
48 |
760.2.w |
\(\chi_{760}(267, \cdot)\) |
760.2.w.a |
2 |
2 |
760.2.w.b |
2 |
760.2.w.c |
104 |
760.2.w.d |
108 |
760.2.z |
\(\chi_{760}(349, \cdot)\) |
760.2.z.a |
232 |
2 |
760.2.ba |
\(\chi_{760}(31, \cdot)\) |
None |
0 |
2 |
760.2.bf |
\(\chi_{760}(179, \cdot)\) |
760.2.bf.a |
8 |
2 |
760.2.bf.b |
224 |
760.2.bi |
\(\chi_{760}(331, \cdot)\) |
760.2.bi.a |
160 |
2 |
760.2.bj |
\(\chi_{760}(49, \cdot)\) |
760.2.bj.a |
4 |
2 |
760.2.bj.b |
56 |
760.2.bk |
\(\chi_{760}(559, \cdot)\) |
None |
0 |
2 |
760.2.bl |
\(\chi_{760}(501, \cdot)\) |
760.2.bl.a |
4 |
2 |
760.2.bl.b |
4 |
760.2.bl.c |
152 |
760.2.bo |
\(\chi_{760}(81, \cdot)\) |
760.2.bo.a |
24 |
6 |
760.2.bo.b |
30 |
760.2.bo.c |
30 |
760.2.bo.d |
36 |
760.2.bp |
\(\chi_{760}(293, \cdot)\) |
760.2.bp.a |
464 |
4 |
760.2.bq |
\(\chi_{760}(7, \cdot)\) |
None |
0 |
4 |
760.2.bv |
\(\chi_{760}(217, \cdot)\) |
760.2.bv.a |
120 |
4 |
760.2.bw |
\(\chi_{760}(83, \cdot)\) |
760.2.bw.a |
8 |
4 |
760.2.bw.b |
456 |
760.2.bx |
\(\chi_{760}(59, \cdot)\) |
760.2.bx.a |
24 |
6 |
760.2.bx.b |
672 |
760.2.cc |
\(\chi_{760}(61, \cdot)\) |
760.2.cc.a |
480 |
6 |
760.2.cd |
\(\chi_{760}(79, \cdot)\) |
None |
0 |
6 |
760.2.cg |
\(\chi_{760}(9, \cdot)\) |
760.2.cg.a |
180 |
6 |
760.2.ch |
\(\chi_{760}(51, \cdot)\) |
760.2.ch.a |
480 |
6 |
760.2.ci |
\(\chi_{760}(71, \cdot)\) |
None |
0 |
6 |
760.2.cj |
\(\chi_{760}(149, \cdot)\) |
760.2.cj.a |
696 |
6 |
760.2.co |
\(\chi_{760}(33, \cdot)\) |
760.2.co.a |
360 |
12 |
760.2.cp |
\(\chi_{760}(43, \cdot)\) |
760.2.cp.a |
1392 |
12 |
760.2.cs |
\(\chi_{760}(13, \cdot)\) |
760.2.cs.a |
1392 |
12 |
760.2.ct |
\(\chi_{760}(23, \cdot)\) |
None |
0 |
12 |