Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(560))\).
|
Total |
New |
Old |
Modular forms
| 9888 |
4690 |
5198 |
Cusp forms
| 8545 |
4418 |
4127 |
Eisenstein series
| 1343 |
272 |
1071 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)
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 |
560.2.a |
\(\chi_{560}(1, \cdot)\) |
560.2.a.a |
1 |
1 |
560.2.a.b |
1 |
560.2.a.c |
1 |
560.2.a.d |
1 |
560.2.a.e |
1 |
560.2.a.f |
1 |
560.2.a.g |
2 |
560.2.a.h |
2 |
560.2.a.i |
2 |
560.2.b |
\(\chi_{560}(281, \cdot)\) |
None |
0 |
1 |
560.2.e |
\(\chi_{560}(559, \cdot)\) |
560.2.e.a |
4 |
1 |
560.2.e.b |
4 |
560.2.e.c |
8 |
560.2.e.d |
8 |
560.2.g |
\(\chi_{560}(449, \cdot)\) |
560.2.g.a |
2 |
1 |
560.2.g.b |
2 |
560.2.g.c |
2 |
560.2.g.d |
2 |
560.2.g.e |
4 |
560.2.g.f |
6 |
560.2.h |
\(\chi_{560}(391, \cdot)\) |
None |
0 |
1 |
560.2.k |
\(\chi_{560}(111, \cdot)\) |
560.2.k.a |
8 |
1 |
560.2.k.b |
8 |
560.2.l |
\(\chi_{560}(169, \cdot)\) |
None |
0 |
1 |
560.2.n |
\(\chi_{560}(279, \cdot)\) |
None |
0 |
1 |
560.2.q |
\(\chi_{560}(81, \cdot)\) |
560.2.q.a |
2 |
2 |
560.2.q.b |
2 |
560.2.q.c |
2 |
560.2.q.d |
2 |
560.2.q.e |
2 |
560.2.q.f |
2 |
560.2.q.g |
2 |
560.2.q.h |
2 |
560.2.q.i |
2 |
560.2.q.j |
4 |
560.2.q.k |
4 |
560.2.q.l |
6 |
560.2.r |
\(\chi_{560}(237, \cdot)\) |
560.2.r.a |
184 |
2 |
560.2.t |
\(\chi_{560}(43, \cdot)\) |
560.2.t.a |
144 |
2 |
560.2.w |
\(\chi_{560}(153, \cdot)\) |
None |
0 |
2 |
560.2.x |
\(\chi_{560}(127, \cdot)\) |
560.2.x.a |
12 |
2 |
560.2.x.b |
24 |
560.2.bb |
\(\chi_{560}(29, \cdot)\) |
560.2.bb.a |
2 |
2 |
560.2.bb.b |
2 |
560.2.bb.c |
70 |
560.2.bb.d |
70 |
560.2.bc |
\(\chi_{560}(251, \cdot)\) |
560.2.bc.a |
128 |
2 |
560.2.bd |
\(\chi_{560}(141, \cdot)\) |
560.2.bd.a |
44 |
2 |
560.2.bd.b |
52 |
560.2.be |
\(\chi_{560}(139, \cdot)\) |
560.2.be.a |
184 |
2 |
560.2.bi |
\(\chi_{560}(183, \cdot)\) |
None |
0 |
2 |
560.2.bj |
\(\chi_{560}(97, \cdot)\) |
560.2.bj.a |
4 |
2 |
560.2.bj.b |
8 |
560.2.bj.c |
8 |
560.2.bj.d |
24 |
560.2.bl |
\(\chi_{560}(267, \cdot)\) |
560.2.bl.a |
144 |
2 |
560.2.bn |
\(\chi_{560}(13, \cdot)\) |
560.2.bn.a |
184 |
2 |
560.2.bq |
\(\chi_{560}(199, \cdot)\) |
None |
0 |
2 |
560.2.bs |
\(\chi_{560}(31, \cdot)\) |
560.2.bs.a |
8 |
2 |
560.2.bs.b |
12 |
560.2.bs.c |
12 |
560.2.bv |
\(\chi_{560}(9, \cdot)\) |
None |
0 |
2 |
560.2.bw |
\(\chi_{560}(289, \cdot)\) |
560.2.bw.a |
4 |
2 |
560.2.bw.b |
4 |
560.2.bw.c |
4 |
560.2.bw.d |
4 |
560.2.bw.e |
4 |
560.2.bw.f |
24 |
560.2.bz |
\(\chi_{560}(311, \cdot)\) |
None |
0 |
2 |
560.2.cb |
\(\chi_{560}(121, \cdot)\) |
None |
0 |
2 |
560.2.cc |
\(\chi_{560}(159, \cdot)\) |
560.2.cc.a |
4 |
2 |
560.2.cc.b |
4 |
560.2.cc.c |
4 |
560.2.cc.d |
4 |
560.2.cc.e |
8 |
560.2.cc.f |
8 |
560.2.cc.g |
8 |
560.2.cc.h |
8 |
560.2.cf |
\(\chi_{560}(107, \cdot)\) |
560.2.cf.a |
368 |
4 |
560.2.ch |
\(\chi_{560}(117, \cdot)\) |
560.2.ch.a |
4 |
4 |
560.2.ch.b |
4 |
560.2.ch.c |
360 |
560.2.ci |
\(\chi_{560}(17, \cdot)\) |
560.2.ci.a |
4 |
4 |
560.2.ci.b |
4 |
560.2.ci.c |
16 |
560.2.ci.d |
16 |
560.2.ci.e |
48 |
560.2.cl |
\(\chi_{560}(23, \cdot)\) |
None |
0 |
4 |
560.2.co |
\(\chi_{560}(19, \cdot)\) |
560.2.co.a |
368 |
4 |
560.2.cp |
\(\chi_{560}(221, \cdot)\) |
560.2.cp.a |
256 |
4 |
560.2.cq |
\(\chi_{560}(131, \cdot)\) |
560.2.cq.a |
256 |
4 |
560.2.cr |
\(\chi_{560}(109, \cdot)\) |
560.2.cr.a |
368 |
4 |
560.2.cu |
\(\chi_{560}(207, \cdot)\) |
560.2.cu.a |
8 |
4 |
560.2.cu.b |
24 |
560.2.cu.c |
32 |
560.2.cu.d |
32 |
560.2.cx |
\(\chi_{560}(73, \cdot)\) |
None |
0 |
4 |
560.2.cz |
\(\chi_{560}(157, \cdot)\) |
560.2.cz.a |
4 |
4 |
560.2.cz.b |
4 |
560.2.cz.c |
360 |
560.2.db |
\(\chi_{560}(67, \cdot)\) |
560.2.db.a |
368 |
4 |