Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(656))\).
|
Total |
New |
Old |
Modular forms
| 14000 |
7726 |
6274 |
Cusp forms
| 12881 |
7376 |
5505 |
Eisenstein series
| 1119 |
350 |
769 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(656))\)
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 |
656.2.a |
\(\chi_{656}(1, \cdot)\) |
656.2.a.a |
1 |
1 |
656.2.a.b |
1 |
656.2.a.c |
1 |
656.2.a.d |
2 |
656.2.a.e |
2 |
656.2.a.f |
3 |
656.2.a.g |
3 |
656.2.a.h |
3 |
656.2.a.i |
4 |
656.2.b |
\(\chi_{656}(329, \cdot)\) |
None |
0 |
1 |
656.2.d |
\(\chi_{656}(81, \cdot)\) |
656.2.d.a |
2 |
1 |
656.2.d.b |
2 |
656.2.d.c |
2 |
656.2.d.d |
4 |
656.2.d.e |
4 |
656.2.d.f |
6 |
656.2.g |
\(\chi_{656}(409, \cdot)\) |
None |
0 |
1 |
656.2.i |
\(\chi_{656}(173, \cdot)\) |
656.2.i.a |
2 |
2 |
656.2.i.b |
162 |
656.2.l |
\(\chi_{656}(337, \cdot)\) |
656.2.l.a |
2 |
2 |
656.2.l.b |
2 |
656.2.l.c |
2 |
656.2.l.d |
2 |
656.2.l.e |
2 |
656.2.l.f |
6 |
656.2.l.g |
6 |
656.2.l.h |
8 |
656.2.l.i |
10 |
656.2.n |
\(\chi_{656}(165, \cdot)\) |
656.2.n.a |
2 |
2 |
656.2.n.b |
2 |
656.2.n.c |
2 |
656.2.n.d |
4 |
656.2.n.e |
4 |
656.2.n.f |
66 |
656.2.n.g |
80 |
656.2.o |
\(\chi_{656}(245, \cdot)\) |
656.2.o.a |
164 |
2 |
656.2.r |
\(\chi_{656}(9, \cdot)\) |
None |
0 |
2 |
656.2.t |
\(\chi_{656}(237, \cdot)\) |
656.2.t.a |
2 |
2 |
656.2.t.b |
162 |
656.2.u |
\(\chi_{656}(305, \cdot)\) |
656.2.u.a |
4 |
4 |
656.2.u.b |
4 |
656.2.u.c |
8 |
656.2.u.d |
8 |
656.2.u.e |
8 |
656.2.u.f |
12 |
656.2.u.g |
16 |
656.2.u.h |
20 |
656.2.v |
\(\chi_{656}(331, \cdot)\) |
656.2.v.a |
328 |
4 |
656.2.z |
\(\chi_{656}(55, \cdot)\) |
None |
0 |
4 |
656.2.ba |
\(\chi_{656}(79, \cdot)\) |
656.2.ba.a |
4 |
4 |
656.2.ba.b |
8 |
656.2.ba.c |
24 |
656.2.ba.d |
48 |
656.2.bb |
\(\chi_{656}(3, \cdot)\) |
656.2.bb.a |
328 |
4 |
656.2.be |
\(\chi_{656}(113, \cdot)\) |
656.2.be.a |
8 |
4 |
656.2.be.b |
8 |
656.2.be.c |
8 |
656.2.be.d |
16 |
656.2.be.e |
16 |
656.2.be.f |
24 |
656.2.bg |
\(\chi_{656}(57, \cdot)\) |
None |
0 |
4 |
656.2.bi |
\(\chi_{656}(25, \cdot)\) |
None |
0 |
4 |
656.2.bl |
\(\chi_{656}(197, \cdot)\) |
656.2.bl.a |
656 |
8 |
656.2.bm |
\(\chi_{656}(121, \cdot)\) |
None |
0 |
8 |
656.2.bp |
\(\chi_{656}(45, \cdot)\) |
656.2.bp.a |
656 |
8 |
656.2.bq |
\(\chi_{656}(37, \cdot)\) |
656.2.bq.a |
656 |
8 |
656.2.bs |
\(\chi_{656}(33, \cdot)\) |
656.2.bs.a |
8 |
8 |
656.2.bs.b |
16 |
656.2.bs.c |
24 |
656.2.bs.d |
24 |
656.2.bs.e |
40 |
656.2.bs.f |
48 |
656.2.bu |
\(\chi_{656}(5, \cdot)\) |
656.2.bu.a |
656 |
8 |
656.2.bx |
\(\chi_{656}(259, \cdot)\) |
656.2.bx.a |
1312 |
16 |
656.2.by |
\(\chi_{656}(15, \cdot)\) |
656.2.by.a |
16 |
16 |
656.2.by.b |
96 |
656.2.by.c |
224 |
656.2.bz |
\(\chi_{656}(7, \cdot)\) |
None |
0 |
16 |
656.2.cd |
\(\chi_{656}(11, \cdot)\) |
656.2.cd.a |
1312 |
16 |