Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(549))\).
|
Total |
New |
Old |
Modular forms
| 11640 |
9095 |
2545 |
Cusp forms
| 10681 |
8565 |
2116 |
Eisenstein series
| 959 |
530 |
429 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(549))\)
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 |
549.2.a |
\(\chi_{549}(1, \cdot)\) |
549.2.a.a |
1 |
1 |
549.2.a.b |
1 |
549.2.a.c |
1 |
549.2.a.d |
2 |
549.2.a.e |
2 |
549.2.a.f |
3 |
549.2.a.g |
3 |
549.2.a.h |
6 |
549.2.a.i |
6 |
549.2.c |
\(\chi_{549}(487, \cdot)\) |
549.2.c.a |
2 |
1 |
549.2.c.b |
2 |
549.2.c.c |
4 |
549.2.c.d |
4 |
549.2.c.e |
6 |
549.2.c.f |
8 |
549.2.e |
\(\chi_{549}(352, \cdot)\) |
549.2.e.a |
2 |
2 |
549.2.e.b |
2 |
549.2.e.c |
4 |
549.2.e.d |
4 |
549.2.e.e |
6 |
549.2.e.f |
6 |
549.2.e.g |
8 |
549.2.e.h |
16 |
549.2.f |
\(\chi_{549}(184, \cdot)\) |
549.2.f.a |
2 |
2 |
549.2.f.b |
2 |
549.2.f.c |
4 |
549.2.f.d |
54 |
549.2.f.e |
58 |
549.2.g |
\(\chi_{549}(196, \cdot)\) |
549.2.g.a |
10 |
2 |
549.2.g.b |
110 |
549.2.h |
\(\chi_{549}(13, \cdot)\) |
549.2.h.a |
10 |
2 |
549.2.h.b |
110 |
549.2.j |
\(\chi_{549}(233, \cdot)\) |
549.2.j.a |
44 |
2 |
549.2.k |
\(\chi_{549}(217, \cdot)\) |
549.2.k.a |
12 |
4 |
549.2.k.b |
20 |
549.2.k.c |
28 |
549.2.k.d |
40 |
549.2.l |
\(\chi_{549}(292, \cdot)\) |
549.2.l.a |
2 |
2 |
549.2.l.b |
4 |
549.2.l.c |
114 |
549.2.r |
\(\chi_{549}(121, \cdot)\) |
549.2.r.a |
4 |
2 |
549.2.r.b |
116 |
549.2.s |
\(\chi_{549}(109, \cdot)\) |
549.2.s.a |
2 |
2 |
549.2.s.b |
2 |
549.2.s.c |
2 |
549.2.s.d |
4 |
549.2.s.e |
4 |
549.2.s.f |
4 |
549.2.s.g |
8 |
549.2.s.h |
8 |
549.2.s.i |
8 |
549.2.s.j |
8 |
549.2.v |
\(\chi_{549}(319, \cdot)\) |
549.2.v.a |
2 |
2 |
549.2.v.b |
4 |
549.2.v.c |
114 |
549.2.y |
\(\chi_{549}(64, \cdot)\) |
549.2.y.a |
16 |
4 |
549.2.y.b |
16 |
549.2.y.c |
24 |
549.2.y.d |
48 |
549.2.ba |
\(\chi_{549}(29, \cdot)\) |
549.2.ba.a |
240 |
4 |
549.2.bd |
\(\chi_{549}(11, \cdot)\) |
549.2.bd.a |
4 |
4 |
549.2.bd.b |
236 |
549.2.be |
\(\chi_{549}(143, \cdot)\) |
549.2.be.a |
80 |
4 |
549.2.bh |
\(\chi_{549}(32, \cdot)\) |
549.2.bh.a |
240 |
4 |
549.2.bi |
\(\chi_{549}(22, \cdot)\) |
549.2.bi.a |
480 |
8 |
549.2.bj |
\(\chi_{549}(16, \cdot)\) |
549.2.bj.a |
480 |
8 |
549.2.bk |
\(\chi_{549}(34, \cdot)\) |
549.2.bk.a |
480 |
8 |
549.2.bl |
\(\chi_{549}(73, \cdot)\) |
549.2.bl.a |
8 |
8 |
549.2.bl.b |
32 |
549.2.bl.c |
40 |
549.2.bl.d |
48 |
549.2.bl.e |
64 |
549.2.bm |
\(\chi_{549}(8, \cdot)\) |
549.2.bm.a |
176 |
8 |
549.2.bp |
\(\chi_{549}(4, \cdot)\) |
549.2.bp.a |
480 |
8 |
549.2.bs |
\(\chi_{549}(19, \cdot)\) |
549.2.bs.a |
8 |
8 |
549.2.bs.b |
16 |
549.2.bs.c |
16 |
549.2.bs.d |
40 |
549.2.bs.e |
40 |
549.2.bs.f |
80 |
549.2.bt |
\(\chi_{549}(52, \cdot)\) |
549.2.bt.a |
480 |
8 |
549.2.bz |
\(\chi_{549}(97, \cdot)\) |
549.2.bz.a |
480 |
8 |
549.2.ca |
\(\chi_{549}(2, \cdot)\) |
549.2.ca.a |
960 |
16 |
549.2.cd |
\(\chi_{549}(17, \cdot)\) |
549.2.cd.a |
320 |
16 |
549.2.ce |
\(\chi_{549}(23, \cdot)\) |
549.2.ce.a |
960 |
16 |
549.2.ch |
\(\chi_{549}(59, \cdot)\) |
549.2.ch.a |
960 |
16 |