Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(833))\).
|
Total |
New |
Old |
| Modular forms
| 29184 |
27624 |
1560 |
| Cusp forms
| 27265 |
26170 |
1095 |
| Eisenstein series
| 1919 |
1454 |
465 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(833))\)
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 |
| 833.2.a |
\(\chi_{833}(1, \cdot)\) |
833.2.a.a |
1 |
1 |
| 833.2.a.b |
3 |
| 833.2.a.c |
3 |
| 833.2.a.d |
4 |
| 833.2.a.e |
4 |
| 833.2.a.f |
4 |
| 833.2.a.g |
5 |
| 833.2.a.h |
7 |
| 833.2.a.i |
7 |
| 833.2.a.j |
8 |
| 833.2.a.k |
8 |
| 833.2.b |
\(\chi_{833}(50, \cdot)\) |
833.2.b.a |
10 |
1 |
| 833.2.b.b |
10 |
| 833.2.b.c |
10 |
| 833.2.b.d |
10 |
| 833.2.b.e |
16 |
| 833.2.e |
\(\chi_{833}(18, \cdot)\) |
833.2.e.a |
2 |
2 |
| 833.2.e.b |
2 |
| 833.2.e.c |
6 |
| 833.2.e.d |
8 |
| 833.2.e.e |
8 |
| 833.2.e.f |
8 |
| 833.2.e.g |
8 |
| 833.2.e.h |
10 |
| 833.2.e.i |
10 |
| 833.2.e.j |
14 |
| 833.2.e.k |
16 |
| 833.2.e.l |
16 |
| 833.2.g |
\(\chi_{833}(344, \cdot)\) |
833.2.g.a |
2 |
2 |
| 833.2.g.b |
2 |
| 833.2.g.c |
4 |
| 833.2.g.d |
4 |
| 833.2.g.e |
16 |
| 833.2.g.f |
16 |
| 833.2.g.g |
16 |
| 833.2.g.h |
20 |
| 833.2.g.i |
32 |
| 833.2.j |
\(\chi_{833}(67, \cdot)\) |
833.2.j.a |
20 |
2 |
| 833.2.j.b |
20 |
| 833.2.j.c |
20 |
| 833.2.j.d |
20 |
| 833.2.j.e |
32 |
| 833.2.k |
\(\chi_{833}(120, \cdot)\) |
833.2.k.a |
6 |
6 |
| 833.2.k.b |
216 |
| 833.2.k.c |
234 |
| 833.2.l |
\(\chi_{833}(246, \cdot)\) |
833.2.l.a |
4 |
4 |
| 833.2.l.b |
32 |
| 833.2.l.c |
32 |
| 833.2.l.d |
40 |
| 833.2.l.e |
40 |
| 833.2.l.f |
40 |
| 833.2.l.g |
40 |
| 833.2.o |
\(\chi_{833}(30, \cdot)\) |
833.2.o.a |
4 |
4 |
| 833.2.o.b |
4 |
| 833.2.o.c |
8 |
| 833.2.o.d |
32 |
| 833.2.o.e |
32 |
| 833.2.o.f |
40 |
| 833.2.o.g |
40 |
| 833.2.o.h |
64 |
| 833.2.r |
\(\chi_{833}(169, \cdot)\) |
833.2.r.a |
492 |
6 |
| 833.2.t |
\(\chi_{833}(48, \cdot)\) |
833.2.t.a |
72 |
8 |
| 833.2.t.b |
72 |
| 833.2.t.c |
72 |
| 833.2.t.d |
72 |
| 833.2.t.e |
160 |
| 833.2.u |
\(\chi_{833}(86, \cdot)\) |
833.2.u.a |
420 |
12 |
| 833.2.u.b |
468 |
| 833.2.v |
\(\chi_{833}(128, \cdot)\) |
833.2.v.a |
8 |
8 |
| 833.2.v.b |
8 |
| 833.2.v.c |
64 |
| 833.2.v.d |
64 |
| 833.2.v.e |
64 |
| 833.2.v.f |
80 |
| 833.2.v.g |
80 |
| 833.2.v.h |
80 |
| 833.2.x |
\(\chi_{833}(64, \cdot)\) |
833.2.x.a |
984 |
12 |
| 833.2.z |
\(\chi_{833}(16, \cdot)\) |
833.2.z.a |
984 |
12 |
| 833.2.bc |
\(\chi_{833}(31, \cdot)\) |
833.2.bc.a |
144 |
16 |
| 833.2.bc.b |
144 |
| 833.2.bc.c |
144 |
| 833.2.bc.d |
144 |
| 833.2.bc.e |
160 |
| 833.2.bc.f |
160 |
| 833.2.bf |
\(\chi_{833}(8, \cdot)\) |
833.2.bf.a |
1968 |
24 |
| 833.2.bg |
\(\chi_{833}(4, \cdot)\) |
833.2.bg.a |
1968 |
24 |
| 833.2.bi |
\(\chi_{833}(6, \cdot)\) |
833.2.bi.a |
3936 |
48 |
| 833.2.bl |
\(\chi_{833}(2, \cdot)\) |
833.2.bl.a |
3936 |
48 |
| 833.2.bn |
\(\chi_{833}(3, \cdot)\) |
833.2.bn.a |
7872 |
96 |
