Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(935))\).
|
Total |
New |
Old |
Modular forms
| 35840 |
31747 |
4093 |
Cusp forms
| 33281 |
30131 |
3150 |
Eisenstein series
| 2559 |
1616 |
943 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(935))\)
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 |
935.2.a |
\(\chi_{935}(1, \cdot)\) |
935.2.a.a |
1 |
1 |
935.2.a.b |
1 |
935.2.a.c |
3 |
935.2.a.d |
3 |
935.2.a.e |
3 |
935.2.a.f |
3 |
935.2.a.g |
4 |
935.2.a.h |
6 |
935.2.a.i |
9 |
935.2.a.j |
11 |
935.2.a.k |
11 |
935.2.b |
\(\chi_{935}(749, \cdot)\) |
935.2.b.a |
36 |
1 |
935.2.b.b |
44 |
935.2.e |
\(\chi_{935}(254, \cdot)\) |
935.2.e.a |
88 |
1 |
935.2.f |
\(\chi_{935}(441, \cdot)\) |
935.2.f.a |
26 |
1 |
935.2.f.b |
34 |
935.2.i |
\(\chi_{935}(166, \cdot)\) |
935.2.i.a |
52 |
2 |
935.2.i.b |
68 |
935.2.l |
\(\chi_{935}(98, \cdot)\) |
935.2.l.a |
208 |
2 |
935.2.m |
\(\chi_{935}(307, \cdot)\) |
935.2.m.a |
192 |
2 |
935.2.p |
\(\chi_{935}(373, \cdot)\) |
935.2.p.a |
208 |
2 |
935.2.q |
\(\chi_{935}(208, \cdot)\) |
935.2.q.a |
208 |
2 |
935.2.s |
\(\chi_{935}(89, \cdot)\) |
935.2.s.a |
176 |
2 |
935.2.u |
\(\chi_{935}(86, \cdot)\) |
935.2.u.a |
4 |
4 |
935.2.u.b |
4 |
935.2.u.c |
8 |
935.2.u.d |
52 |
935.2.u.e |
60 |
935.2.u.f |
60 |
935.2.u.g |
68 |
935.2.w |
\(\chi_{935}(417, \cdot)\) |
935.2.w.a |
416 |
4 |
935.2.x |
\(\chi_{935}(111, \cdot)\) |
935.2.x.a |
104 |
4 |
935.2.x.b |
136 |
935.2.z |
\(\chi_{935}(144, \cdot)\) |
935.2.z.a |
368 |
4 |
935.2.bc |
\(\chi_{935}(32, \cdot)\) |
935.2.bc.a |
416 |
4 |
935.2.bf |
\(\chi_{935}(16, \cdot)\) |
935.2.bf.a |
288 |
4 |
935.2.bg |
\(\chi_{935}(169, \cdot)\) |
935.2.bg.a |
416 |
4 |
935.2.bj |
\(\chi_{935}(69, \cdot)\) |
935.2.bj.a |
384 |
4 |
935.2.bl |
\(\chi_{935}(133, \cdot)\) |
935.2.bl.a |
720 |
8 |
935.2.bm |
\(\chi_{935}(131, \cdot)\) |
935.2.bm.a |
576 |
8 |
935.2.bp |
\(\chi_{935}(54, \cdot)\) |
935.2.bp.a |
64 |
8 |
935.2.bp.b |
768 |
935.2.bq |
\(\chi_{935}(12, \cdot)\) |
935.2.bq.a |
720 |
8 |
935.2.bt |
\(\chi_{935}(4, \cdot)\) |
935.2.bt.a |
832 |
8 |
935.2.bv |
\(\chi_{935}(123, \cdot)\) |
935.2.bv.a |
832 |
8 |
935.2.bw |
\(\chi_{935}(118, \cdot)\) |
935.2.bw.a |
832 |
8 |
935.2.bz |
\(\chi_{935}(18, \cdot)\) |
935.2.bz.a |
768 |
8 |
935.2.ca |
\(\chi_{935}(13, \cdot)\) |
935.2.ca.a |
832 |
8 |
935.2.cd |
\(\chi_{935}(81, \cdot)\) |
935.2.cd.a |
576 |
8 |
935.2.cf |
\(\chi_{935}(2, \cdot)\) |
935.2.cf.a |
1664 |
16 |
935.2.cg |
\(\chi_{935}(9, \cdot)\) |
935.2.cg.a |
1664 |
16 |
935.2.ci |
\(\chi_{935}(26, \cdot)\) |
935.2.ci.a |
1152 |
16 |
935.2.cl |
\(\chi_{935}(83, \cdot)\) |
935.2.cl.a |
1664 |
16 |
935.2.cn |
\(\chi_{935}(37, \cdot)\) |
935.2.cn.a |
3328 |
32 |
935.2.cp |
\(\chi_{935}(24, \cdot)\) |
935.2.cp.a |
3328 |
32 |
935.2.cq |
\(\chi_{935}(6, \cdot)\) |
935.2.cq.a |
2304 |
32 |
935.2.cs |
\(\chi_{935}(3, \cdot)\) |
935.2.cs.a |
3328 |
32 |