Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(931))\).
|
Total |
New |
Old |
Modular forms
| 36360 |
34492 |
1868 |
Cusp forms
| 34201 |
32844 |
1357 |
Eisenstein series
| 2159 |
1648 |
511 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(931))\)
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 |
931.2.a |
\(\chi_{931}(1, \cdot)\) |
931.2.a.a |
1 |
1 |
931.2.a.b |
1 |
931.2.a.c |
1 |
931.2.a.d |
2 |
931.2.a.e |
2 |
931.2.a.f |
2 |
931.2.a.g |
2 |
931.2.a.h |
2 |
931.2.a.i |
2 |
931.2.a.j |
2 |
931.2.a.k |
3 |
931.2.a.l |
4 |
931.2.a.m |
4 |
931.2.a.n |
7 |
931.2.a.o |
7 |
931.2.a.p |
10 |
931.2.a.q |
10 |
931.2.c |
\(\chi_{931}(930, \cdot)\) |
931.2.c.a |
4 |
1 |
931.2.c.b |
4 |
931.2.c.c |
4 |
931.2.c.d |
6 |
931.2.c.e |
6 |
931.2.c.f |
40 |
931.2.e |
\(\chi_{931}(197, \cdot)\) |
931.2.e.a |
4 |
2 |
931.2.e.b |
6 |
931.2.e.c |
10 |
931.2.e.d |
20 |
931.2.e.e |
24 |
931.2.e.f |
24 |
931.2.e.g |
40 |
931.2.f |
\(\chi_{931}(324, \cdot)\) |
931.2.f.a |
2 |
2 |
931.2.f.b |
2 |
931.2.f.c |
2 |
931.2.f.d |
4 |
931.2.f.e |
4 |
931.2.f.f |
4 |
931.2.f.g |
4 |
931.2.f.h |
4 |
931.2.f.i |
4 |
931.2.f.j |
4 |
931.2.f.k |
4 |
931.2.f.l |
6 |
931.2.f.m |
6 |
931.2.f.n |
8 |
931.2.f.o |
8 |
931.2.f.p |
14 |
931.2.f.q |
20 |
931.2.f.r |
20 |
931.2.g |
\(\chi_{931}(30, \cdot)\) |
931.2.g.a |
4 |
2 |
931.2.g.b |
4 |
931.2.g.c |
6 |
931.2.g.d |
6 |
931.2.g.e |
10 |
931.2.g.f |
10 |
931.2.g.g |
20 |
931.2.g.h |
24 |
931.2.g.i |
40 |
931.2.h |
\(\chi_{931}(410, \cdot)\) |
931.2.h.a |
4 |
2 |
931.2.h.b |
4 |
931.2.h.c |
6 |
931.2.h.d |
6 |
931.2.h.e |
10 |
931.2.h.f |
10 |
931.2.h.g |
20 |
931.2.h.h |
24 |
931.2.h.i |
40 |
931.2.i |
\(\chi_{931}(411, \cdot)\) |
931.2.i.a |
2 |
2 |
931.2.i.b |
2 |
931.2.i.c |
4 |
931.2.i.d |
4 |
931.2.i.e |
4 |
931.2.i.f |
12 |
931.2.i.g |
16 |
931.2.i.h |
80 |
931.2.o |
\(\chi_{931}(227, \cdot)\) |
931.2.o.a |
4 |
2 |
931.2.o.b |
4 |
931.2.o.c |
4 |
931.2.o.d |
4 |
931.2.o.e |
6 |
931.2.o.f |
6 |
931.2.o.g |
8 |
931.2.o.h |
8 |
931.2.o.i |
80 |
931.2.p |
\(\chi_{931}(293, \cdot)\) |
931.2.p.a |
2 |
2 |
931.2.p.b |
2 |
931.2.p.c |
2 |
931.2.p.d |
2 |
931.2.p.e |
4 |
931.2.p.f |
4 |
931.2.p.g |
16 |
931.2.p.h |
16 |
931.2.p.i |
80 |
931.2.s |
\(\chi_{931}(31, \cdot)\) |
931.2.s.a |
2 |
2 |
931.2.s.b |
2 |
931.2.s.c |
4 |
931.2.s.d |
4 |
931.2.s.e |
4 |
931.2.s.f |
12 |
931.2.s.g |
16 |
931.2.s.h |
80 |
931.2.u |
\(\chi_{931}(134, \cdot)\) |
931.2.u.a |
240 |
6 |
931.2.u.b |
264 |
931.2.v |
\(\chi_{931}(177, \cdot)\) |
931.2.v.a |
6 |
6 |
931.2.v.b |
6 |
931.2.v.c |
30 |
931.2.v.d |
30 |
931.2.v.e |
30 |
931.2.v.f |
30 |
931.2.v.g |
60 |
931.2.v.h |
66 |
931.2.v.i |
120 |
931.2.w |
\(\chi_{931}(99, \cdot)\) |
931.2.w.a |
6 |
6 |
931.2.w.b |
30 |
931.2.w.c |
30 |
931.2.w.d |
60 |
931.2.w.e |
66 |
931.2.w.f |
66 |
931.2.w.g |
120 |
931.2.x |
\(\chi_{931}(226, \cdot)\) |
931.2.x.a |
6 |
6 |
931.2.x.b |
6 |
931.2.x.c |
30 |
931.2.x.d |
30 |
931.2.x.e |
30 |
931.2.x.f |
30 |
931.2.x.g |
60 |
931.2.x.h |
66 |
931.2.x.i |
120 |
931.2.z |
\(\chi_{931}(132, \cdot)\) |
931.2.z.a |
12 |
6 |
931.2.z.b |
528 |
931.2.be |
\(\chi_{931}(48, \cdot)\) |
931.2.be.a |
66 |
6 |
931.2.be.b |
66 |
931.2.be.c |
240 |
931.2.bf |
\(\chi_{931}(325, \cdot)\) |
931.2.bf.a |
66 |
6 |
931.2.bf.b |
72 |
931.2.bf.c |
240 |
931.2.bj |
\(\chi_{931}(117, \cdot)\) |
931.2.bj.a |
66 |
6 |
931.2.bj.b |
72 |
931.2.bj.c |
240 |
931.2.bk |
\(\chi_{931}(11, \cdot)\) |
931.2.bk.a |
1104 |
12 |
931.2.bl |
\(\chi_{931}(102, \cdot)\) |
931.2.bl.a |
1104 |
12 |
931.2.bm |
\(\chi_{931}(39, \cdot)\) |
931.2.bm.a |
480 |
12 |
931.2.bm.b |
528 |
931.2.bn |
\(\chi_{931}(64, \cdot)\) |
931.2.bn.a |
1080 |
12 |
931.2.bp |
\(\chi_{931}(103, \cdot)\) |
931.2.bp.a |
1104 |
12 |
931.2.bs |
\(\chi_{931}(27, \cdot)\) |
931.2.bs.a |
1080 |
12 |
931.2.bt |
\(\chi_{931}(75, \cdot)\) |
931.2.bt.a |
24 |
12 |
931.2.bt.b |
1080 |
931.2.bz |
\(\chi_{931}(12, \cdot)\) |
931.2.bz.a |
1104 |
12 |
931.2.ca |
\(\chi_{931}(4, \cdot)\) |
931.2.ca.a |
3276 |
36 |
931.2.cb |
\(\chi_{931}(9, \cdot)\) |
931.2.cb.a |
3276 |
36 |
931.2.cc |
\(\chi_{931}(36, \cdot)\) |
931.2.cc.a |
3312 |
36 |
931.2.cd |
\(\chi_{931}(10, \cdot)\) |
931.2.cd.a |
3276 |
36 |
931.2.ch |
\(\chi_{931}(13, \cdot)\) |
931.2.ch.a |
3312 |
36 |
931.2.ci |
\(\chi_{931}(3, \cdot)\) |
931.2.ci.a |
3276 |
36 |