Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(832))\).
|
Total |
New |
Old |
| Modular forms
| 22368 |
12194 |
10174 |
| Cusp forms
| 20641 |
11710 |
8931 |
| Eisenstein series
| 1727 |
484 |
1243 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(832))\)
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 |
| 832.2.a |
\(\chi_{832}(1, \cdot)\) |
832.2.a.a |
1 |
1 |
| 832.2.a.b |
1 |
| 832.2.a.c |
1 |
| 832.2.a.d |
1 |
| 832.2.a.e |
1 |
| 832.2.a.f |
1 |
| 832.2.a.g |
1 |
| 832.2.a.h |
1 |
| 832.2.a.i |
1 |
| 832.2.a.j |
1 |
| 832.2.a.k |
2 |
| 832.2.a.l |
2 |
| 832.2.a.m |
2 |
| 832.2.a.n |
2 |
| 832.2.a.o |
2 |
| 832.2.a.p |
4 |
| 832.2.b |
\(\chi_{832}(417, \cdot)\) |
832.2.b.a |
4 |
1 |
| 832.2.b.b |
4 |
| 832.2.b.c |
8 |
| 832.2.b.d |
8 |
| 832.2.e |
\(\chi_{832}(545, \cdot)\) |
832.2.e.a |
4 |
1 |
| 832.2.e.b |
4 |
| 832.2.e.c |
8 |
| 832.2.e.d |
12 |
| 832.2.f |
\(\chi_{832}(129, \cdot)\) |
832.2.f.a |
2 |
1 |
| 832.2.f.b |
2 |
| 832.2.f.c |
2 |
| 832.2.f.d |
2 |
| 832.2.f.e |
2 |
| 832.2.f.f |
4 |
| 832.2.f.g |
4 |
| 832.2.f.h |
4 |
| 832.2.f.i |
4 |
| 832.2.i |
\(\chi_{832}(321, \cdot)\) |
832.2.i.a |
2 |
2 |
| 832.2.i.b |
2 |
| 832.2.i.c |
2 |
| 832.2.i.d |
2 |
| 832.2.i.e |
2 |
| 832.2.i.f |
2 |
| 832.2.i.g |
2 |
| 832.2.i.h |
2 |
| 832.2.i.i |
2 |
| 832.2.i.j |
2 |
| 832.2.i.k |
4 |
| 832.2.i.l |
4 |
| 832.2.i.m |
4 |
| 832.2.i.n |
4 |
| 832.2.i.o |
4 |
| 832.2.i.p |
4 |
| 832.2.i.q |
8 |
| 832.2.k |
\(\chi_{832}(255, \cdot)\) |
832.2.k.a |
2 |
2 |
| 832.2.k.b |
2 |
| 832.2.k.c |
2 |
| 832.2.k.d |
2 |
| 832.2.k.e |
4 |
| 832.2.k.f |
4 |
| 832.2.k.g |
8 |
| 832.2.k.h |
8 |
| 832.2.k.i |
8 |
| 832.2.k.j |
12 |
| 832.2.l |
\(\chi_{832}(239, \cdot)\) |
832.2.l.a |
2 |
2 |
| 832.2.l.b |
50 |
| 832.2.n |
\(\chi_{832}(209, \cdot)\) |
832.2.n.a |
48 |
2 |
| 832.2.p |
\(\chi_{832}(337, \cdot)\) |
832.2.p.a |
8 |
2 |
| 832.2.p.b |
44 |
| 832.2.s |
\(\chi_{832}(47, \cdot)\) |
832.2.s.a |
2 |
2 |
| 832.2.s.b |
50 |
| 832.2.u |
\(\chi_{832}(31, \cdot)\) |
832.2.u.a |
6 |
2 |
| 832.2.u.b |
6 |
| 832.2.u.c |
6 |
| 832.2.u.d |
6 |
| 832.2.u.e |
16 |
| 832.2.u.f |
16 |
| 832.2.w |
\(\chi_{832}(257, \cdot)\) |
832.2.w.a |
2 |
2 |
| 832.2.w.b |
2 |
| 832.2.w.c |
2 |
| 832.2.w.d |
2 |
| 832.2.w.e |
4 |
| 832.2.w.f |
4 |
| 832.2.w.g |
8 |
| 832.2.w.h |
8 |
| 832.2.w.i |
8 |
| 832.2.w.j |
12 |
| 832.2.z |
\(\chi_{832}(289, \cdot)\) |
832.2.z.a |
16 |
2 |
| 832.2.z.b |
20 |
| 832.2.z.c |
20 |
| 832.2.ba |
\(\chi_{832}(225, \cdot)\) |
832.2.ba.a |
4 |
2 |
| 832.2.ba.b |
4 |
| 832.2.ba.c |
4 |
| 832.2.ba.d |
4 |
| 832.2.ba.e |
4 |
| 832.2.ba.f |
4 |
| 832.2.ba.g |
8 |
| 832.2.ba.h |
12 |
| 832.2.ba.i |
12 |
| 832.2.bd |
\(\chi_{832}(343, \cdot)\) |
None |
0 |
4 |
| 832.2.bf |
\(\chi_{832}(105, \cdot)\) |
None |
0 |
4 |
| 832.2.bg |
\(\chi_{832}(25, \cdot)\) |
None |
0 |
4 |
| 832.2.bi |
\(\chi_{832}(135, \cdot)\) |
None |
0 |
4 |
| 832.2.bk |
\(\chi_{832}(223, \cdot)\) |
832.2.bk.a |
16 |
4 |
| 832.2.bk.b |
16 |
| 832.2.bk.c |
20 |
| 832.2.bk.d |
20 |
| 832.2.bk.e |
20 |
| 832.2.bk.f |
20 |
| 832.2.bn |
\(\chi_{832}(175, \cdot)\) |
832.2.bn.a |
104 |
4 |
| 832.2.bp |
\(\chi_{832}(17, \cdot)\) |
832.2.bp.a |
104 |
4 |
| 832.2.br |
\(\chi_{832}(81, \cdot)\) |
832.2.br.a |
104 |
4 |
| 832.2.bs |
\(\chi_{832}(15, \cdot)\) |
832.2.bs.a |
104 |
4 |
| 832.2.bu |
\(\chi_{832}(63, \cdot)\) |
832.2.bu.a |
4 |
4 |
| 832.2.bu.b |
4 |
| 832.2.bu.c |
4 |
| 832.2.bu.d |
4 |
| 832.2.bu.e |
4 |
| 832.2.bu.f |
4 |
| 832.2.bu.g |
4 |
| 832.2.bu.h |
4 |
| 832.2.bu.i |
8 |
| 832.2.bu.j |
8 |
| 832.2.bu.k |
8 |
| 832.2.bu.l |
16 |
| 832.2.bu.m |
16 |
| 832.2.bu.n |
16 |
| 832.2.bw |
\(\chi_{832}(99, \cdot)\) |
832.2.bw.a |
880 |
8 |
| 832.2.by |
\(\chi_{832}(53, \cdot)\) |
832.2.by.a |
768 |
8 |
| 832.2.cb |
\(\chi_{832}(77, \cdot)\) |
832.2.cb.a |
880 |
8 |
| 832.2.cc |
\(\chi_{832}(83, \cdot)\) |
832.2.cc.a |
880 |
8 |
| 832.2.cf |
\(\chi_{832}(71, \cdot)\) |
None |
0 |
8 |
| 832.2.ch |
\(\chi_{832}(121, \cdot)\) |
None |
0 |
8 |
| 832.2.ci |
\(\chi_{832}(9, \cdot)\) |
None |
0 |
8 |
| 832.2.ck |
\(\chi_{832}(7, \cdot)\) |
None |
0 |
8 |
| 832.2.cn |
\(\chi_{832}(11, \cdot)\) |
832.2.cn.a |
1760 |
16 |
| 832.2.cp |
\(\chi_{832}(29, \cdot)\) |
832.2.cp.a |
1760 |
16 |
| 832.2.cq |
\(\chi_{832}(69, \cdot)\) |
832.2.cq.a |
1760 |
16 |
| 832.2.ct |
\(\chi_{832}(115, \cdot)\) |
832.2.ct.a |
1760 |
16 |
