Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(399))\).
|
Total |
New |
Old |
| Modular forms
| 6192 |
4287 |
1905 |
| Cusp forms
| 5329 |
3951 |
1378 |
| Eisenstein series
| 863 |
336 |
527 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(399))\)
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 |
| 399.2.a |
\(\chi_{399}(1, \cdot)\) |
399.2.a.a |
1 |
1 |
| 399.2.a.b |
1 |
| 399.2.a.c |
1 |
| 399.2.a.d |
3 |
| 399.2.a.e |
3 |
| 399.2.a.f |
5 |
| 399.2.a.g |
5 |
| 399.2.c |
\(\chi_{399}(265, \cdot)\) |
399.2.c.a |
2 |
1 |
| 399.2.c.b |
2 |
| 399.2.c.c |
12 |
| 399.2.c.d |
12 |
| 399.2.d |
\(\chi_{399}(20, \cdot)\) |
399.2.d.a |
48 |
1 |
| 399.2.f |
\(\chi_{399}(113, \cdot)\) |
399.2.f.a |
4 |
1 |
| 399.2.f.b |
16 |
| 399.2.f.c |
20 |
| 399.2.i |
\(\chi_{399}(163, \cdot)\) |
399.2.i.a |
2 |
2 |
| 399.2.i.b |
22 |
| 399.2.i.c |
28 |
| 399.2.j |
\(\chi_{399}(58, \cdot)\) |
399.2.j.a |
2 |
2 |
| 399.2.j.b |
2 |
| 399.2.j.c |
4 |
| 399.2.j.d |
8 |
| 399.2.j.e |
8 |
| 399.2.j.f |
8 |
| 399.2.j.g |
16 |
| 399.2.k |
\(\chi_{399}(64, \cdot)\) |
399.2.k.a |
8 |
2 |
| 399.2.k.b |
8 |
| 399.2.k.c |
12 |
| 399.2.k.d |
12 |
| 399.2.l |
\(\chi_{399}(121, \cdot)\) |
399.2.l.a |
2 |
2 |
| 399.2.l.b |
22 |
| 399.2.l.c |
28 |
| 399.2.m |
\(\chi_{399}(145, \cdot)\) |
399.2.m.a |
2 |
2 |
| 399.2.m.b |
4 |
| 399.2.m.c |
22 |
| 399.2.m.d |
24 |
| 399.2.p |
\(\chi_{399}(26, \cdot)\) |
399.2.p.a |
2 |
2 |
| 399.2.p.b |
2 |
| 399.2.p.c |
96 |
| 399.2.t |
\(\chi_{399}(8, \cdot)\) |
399.2.t.a |
40 |
2 |
| 399.2.t.b |
40 |
| 399.2.w |
\(\chi_{399}(170, \cdot)\) |
399.2.w.a |
2 |
2 |
| 399.2.w.b |
2 |
| 399.2.w.c |
8 |
| 399.2.w.d |
88 |
| 399.2.x |
\(\chi_{399}(65, \cdot)\) |
399.2.x.a |
2 |
2 |
| 399.2.x.b |
2 |
| 399.2.x.c |
96 |
| 399.2.z |
\(\chi_{399}(83, \cdot)\) |
399.2.z.a |
96 |
2 |
| 399.2.bc |
\(\chi_{399}(248, \cdot)\) |
399.2.bc.a |
96 |
2 |
| 399.2.bd |
\(\chi_{399}(68, \cdot)\) |
399.2.bd.a |
2 |
2 |
| 399.2.bd.b |
2 |
| 399.2.bd.c |
96 |
| 399.2.bg |
\(\chi_{399}(31, \cdot)\) |
399.2.bg.a |
2 |
2 |
| 399.2.bg.b |
4 |
| 399.2.bg.c |
22 |
| 399.2.bg.d |
24 |
| 399.2.bh |
\(\chi_{399}(94, \cdot)\) |
399.2.bh.a |
2 |
2 |
| 399.2.bh.b |
2 |
| 399.2.bh.c |
4 |
| 399.2.bh.d |
4 |
| 399.2.bh.e |
20 |
| 399.2.bh.f |
20 |
| 399.2.bk |
\(\chi_{399}(160, \cdot)\) |
399.2.bk.a |
2 |
2 |
| 399.2.bk.b |
2 |
| 399.2.bk.c |
2 |
| 399.2.bk.d |
2 |
| 399.2.bk.e |
24 |
| 399.2.bk.f |
24 |
| 399.2.bm |
\(\chi_{399}(107, \cdot)\) |
399.2.bm.a |
2 |
2 |
| 399.2.bm.b |
2 |
| 399.2.bm.c |
96 |
| 399.2.bo |
\(\chi_{399}(43, \cdot)\) |
399.2.bo.a |
6 |
6 |
| 399.2.bo.b |
18 |
| 399.2.bo.c |
24 |
| 399.2.bo.d |
36 |
| 399.2.bo.e |
36 |
| 399.2.bp |
\(\chi_{399}(130, \cdot)\) |
399.2.bp.a |
72 |
6 |
| 399.2.bp.b |
90 |
| 399.2.bq |
\(\chi_{399}(4, \cdot)\) |
399.2.bq.a |
72 |
6 |
| 399.2.bq.b |
90 |
| 399.2.br |
\(\chi_{399}(2, \cdot)\) |
399.2.br.a |
6 |
6 |
| 399.2.br.b |
288 |
| 399.2.bv |
\(\chi_{399}(86, \cdot)\) |
399.2.bv.a |
6 |
6 |
| 399.2.bv.b |
288 |
| 399.2.bw |
\(\chi_{399}(29, \cdot)\) |
399.2.bw.a |
120 |
6 |
| 399.2.bw.b |
120 |
| 399.2.cb |
\(\chi_{399}(5, \cdot)\) |
399.2.cb.a |
6 |
6 |
| 399.2.cb.b |
288 |
| 399.2.cc |
\(\chi_{399}(13, \cdot)\) |
399.2.cc.a |
78 |
6 |
| 399.2.cc.b |
78 |
| 399.2.cd |
\(\chi_{399}(52, \cdot)\) |
399.2.cd.a |
78 |
6 |
| 399.2.cd.b |
84 |
| 399.2.ci |
\(\chi_{399}(17, \cdot)\) |
399.2.ci.a |
6 |
6 |
| 399.2.ci.b |
288 |
| 399.2.cj |
\(\chi_{399}(62, \cdot)\) |
399.2.cj.a |
6 |
6 |
| 399.2.cj.b |
6 |
| 399.2.cj.c |
288 |
| 399.2.ck |
\(\chi_{399}(10, \cdot)\) |
399.2.ck.a |
78 |
6 |
| 399.2.ck.b |
84 |
