Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(546))\).
|
Total |
New |
Old |
Modular forms
| 8640 |
1905 |
6735 |
Cusp forms
| 7489 |
1905 |
5584 |
Eisenstein series
| 1151 |
0 |
1151 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)
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 |
546.2.a |
\(\chi_{546}(1, \cdot)\) |
546.2.a.a |
1 |
1 |
546.2.a.b |
1 |
546.2.a.c |
1 |
546.2.a.d |
1 |
546.2.a.e |
1 |
546.2.a.f |
1 |
546.2.a.g |
1 |
546.2.a.h |
2 |
546.2.a.i |
2 |
546.2.a.j |
2 |
546.2.c |
\(\chi_{546}(337, \cdot)\) |
546.2.c.a |
2 |
1 |
546.2.c.b |
2 |
546.2.c.c |
2 |
546.2.c.d |
2 |
546.2.c.e |
4 |
546.2.e |
\(\chi_{546}(545, \cdot)\) |
546.2.e.a |
2 |
1 |
546.2.e.b |
2 |
546.2.e.c |
2 |
546.2.e.d |
2 |
546.2.e.e |
8 |
546.2.e.f |
8 |
546.2.e.g |
8 |
546.2.e.h |
8 |
546.2.g |
\(\chi_{546}(209, \cdot)\) |
546.2.g.a |
4 |
1 |
546.2.g.b |
4 |
546.2.g.c |
12 |
546.2.g.d |
12 |
546.2.i |
\(\chi_{546}(79, \cdot)\) |
546.2.i.a |
2 |
2 |
546.2.i.b |
2 |
546.2.i.c |
2 |
546.2.i.d |
2 |
546.2.i.e |
2 |
546.2.i.f |
2 |
546.2.i.g |
2 |
546.2.i.h |
4 |
546.2.i.i |
4 |
546.2.i.j |
4 |
546.2.i.k |
6 |
546.2.j |
\(\chi_{546}(289, \cdot)\) |
546.2.j.a |
2 |
2 |
546.2.j.b |
8 |
546.2.j.c |
8 |
546.2.j.d |
8 |
546.2.j.e |
10 |
546.2.k |
\(\chi_{546}(373, \cdot)\) |
546.2.k.a |
2 |
2 |
546.2.k.b |
8 |
546.2.k.c |
8 |
546.2.k.d |
8 |
546.2.k.e |
10 |
546.2.l |
\(\chi_{546}(211, \cdot)\) |
546.2.l.a |
2 |
2 |
546.2.l.b |
2 |
546.2.l.c |
2 |
546.2.l.d |
2 |
546.2.l.e |
2 |
546.2.l.f |
2 |
546.2.l.g |
2 |
546.2.l.h |
2 |
546.2.l.i |
4 |
546.2.l.j |
4 |
546.2.l.k |
4 |
546.2.l.l |
4 |
546.2.o |
\(\chi_{546}(265, \cdot)\) |
546.2.o.a |
8 |
2 |
546.2.o.b |
8 |
546.2.o.c |
8 |
546.2.o.d |
8 |
546.2.p |
\(\chi_{546}(239, \cdot)\) |
546.2.p.a |
8 |
2 |
546.2.p.b |
8 |
546.2.p.c |
20 |
546.2.p.d |
20 |
546.2.q |
\(\chi_{546}(251, \cdot)\) |
546.2.q.a |
2 |
2 |
546.2.q.b |
2 |
546.2.q.c |
2 |
546.2.q.d |
2 |
546.2.q.e |
4 |
546.2.q.f |
4 |
546.2.q.g |
4 |
546.2.q.h |
4 |
546.2.q.i |
24 |
546.2.q.j |
24 |
546.2.s |
\(\chi_{546}(43, \cdot)\) |
546.2.s.a |
4 |
2 |
546.2.s.b |
4 |
546.2.s.c |
4 |
546.2.s.d |
4 |
546.2.s.e |
8 |
546.2.u |
\(\chi_{546}(185, \cdot)\) |
546.2.u.a |
76 |
2 |
546.2.z |
\(\chi_{546}(131, \cdot)\) |
546.2.z.a |
32 |
2 |
546.2.z.b |
32 |
546.2.bb |
\(\chi_{546}(269, \cdot)\) |
546.2.bb.a |
76 |
2 |
546.2.bd |
\(\chi_{546}(121, \cdot)\) |
546.2.bd.a |
16 |
2 |
546.2.bd.b |
20 |
546.2.bg |
\(\chi_{546}(311, \cdot)\) |
546.2.bg.a |
36 |
2 |
546.2.bg.b |
36 |
546.2.bi |
\(\chi_{546}(17, \cdot)\) |
546.2.bi.a |
2 |
2 |
546.2.bi.b |
2 |
546.2.bi.c |
2 |
546.2.bi.d |
2 |
546.2.bi.e |
34 |
546.2.bi.f |
34 |
546.2.bk |
\(\chi_{546}(25, \cdot)\) |
546.2.bk.a |
8 |
2 |
546.2.bk.b |
12 |
546.2.bk.c |
20 |
546.2.bm |
\(\chi_{546}(205, \cdot)\) |
546.2.bm.a |
16 |
2 |
546.2.bm.b |
20 |
546.2.bn |
\(\chi_{546}(101, \cdot)\) |
546.2.bn.a |
2 |
2 |
546.2.bn.b |
2 |
546.2.bn.c |
2 |
546.2.bn.d |
2 |
546.2.bn.e |
34 |
546.2.bn.f |
34 |
546.2.bq |
\(\chi_{546}(419, \cdot)\) |
546.2.bq.a |
4 |
2 |
546.2.bq.b |
4 |
546.2.bq.c |
64 |
546.2.bu |
\(\chi_{546}(71, \cdot)\) |
546.2.bu.a |
56 |
4 |
546.2.bu.b |
56 |
546.2.bv |
\(\chi_{546}(317, \cdot)\) |
546.2.bv.a |
144 |
4 |
546.2.bw |
\(\chi_{546}(11, \cdot)\) |
546.2.bw.a |
152 |
4 |
546.2.bx |
\(\chi_{546}(97, \cdot)\) |
546.2.bx.a |
40 |
4 |
546.2.bx.b |
40 |
546.2.by |
\(\chi_{546}(19, \cdot)\) |
546.2.by.a |
32 |
4 |
546.2.by.b |
40 |
546.2.bz |
\(\chi_{546}(31, \cdot)\) |
546.2.bz.a |
40 |
4 |
546.2.bz.b |
40 |
546.2.cg |
\(\chi_{546}(145, \cdot)\) |
546.2.cg.a |
32 |
4 |
546.2.cg.b |
40 |
546.2.ch |
\(\chi_{546}(137, \cdot)\) |
546.2.ch.a |
152 |
4 |