Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(273))\).
|
Total |
New |
Old |
| Modular forms
| 2976 |
2019 |
957 |
| Cusp forms
| 2401 |
1803 |
598 |
| Eisenstein series
| 575 |
216 |
359 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)
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 |
| 273.2.a |
\(\chi_{273}(1, \cdot)\) |
273.2.a.a |
1 |
1 |
| 273.2.a.b |
1 |
| 273.2.a.c |
2 |
| 273.2.a.d |
3 |
| 273.2.a.e |
4 |
| 273.2.c |
\(\chi_{273}(64, \cdot)\) |
273.2.c.a |
2 |
1 |
| 273.2.c.b |
6 |
| 273.2.c.c |
8 |
| 273.2.e |
\(\chi_{273}(209, \cdot)\) |
273.2.e.a |
32 |
1 |
| 273.2.g |
\(\chi_{273}(272, \cdot)\) |
273.2.g.a |
32 |
1 |
| 273.2.i |
\(\chi_{273}(79, \cdot)\) |
273.2.i.a |
2 |
2 |
| 273.2.i.b |
6 |
| 273.2.i.c |
6 |
| 273.2.i.d |
8 |
| 273.2.i.e |
10 |
| 273.2.j |
\(\chi_{273}(100, \cdot)\) |
273.2.j.a |
2 |
2 |
| 273.2.j.b |
16 |
| 273.2.j.c |
20 |
| 273.2.k |
\(\chi_{273}(22, \cdot)\) |
273.2.k.a |
6 |
2 |
| 273.2.k.b |
6 |
| 273.2.k.c |
6 |
| 273.2.k.d |
6 |
| 273.2.l |
\(\chi_{273}(16, \cdot)\) |
273.2.l.a |
2 |
2 |
| 273.2.l.b |
16 |
| 273.2.l.c |
20 |
| 273.2.n |
\(\chi_{273}(8, \cdot)\) |
273.2.n.a |
4 |
2 |
| 273.2.n.b |
4 |
| 273.2.n.c |
48 |
| 273.2.p |
\(\chi_{273}(34, \cdot)\) |
273.2.p.a |
4 |
2 |
| 273.2.p.b |
4 |
| 273.2.p.c |
4 |
| 273.2.p.d |
4 |
| 273.2.p.e |
12 |
| 273.2.p.f |
12 |
| 273.2.r |
\(\chi_{273}(68, \cdot)\) |
273.2.r.a |
2 |
2 |
| 273.2.r.b |
64 |
| 273.2.t |
\(\chi_{273}(4, \cdot)\) |
273.2.t.a |
2 |
2 |
| 273.2.t.b |
4 |
| 273.2.t.c |
12 |
| 273.2.t.d |
20 |
| 273.2.u |
\(\chi_{273}(62, \cdot)\) |
273.2.u.a |
2 |
2 |
| 273.2.u.b |
2 |
| 273.2.u.c |
64 |
| 273.2.y |
\(\chi_{273}(101, \cdot)\) |
273.2.y.a |
2 |
2 |
| 273.2.y.b |
64 |
| 273.2.ba |
\(\chi_{273}(38, \cdot)\) |
273.2.ba.a |
2 |
2 |
| 273.2.ba.b |
2 |
| 273.2.ba.c |
64 |
| 273.2.bd |
\(\chi_{273}(43, \cdot)\) |
273.2.bd.a |
16 |
2 |
| 273.2.bd.b |
16 |
| 273.2.bf |
\(\chi_{273}(152, \cdot)\) |
273.2.bf.a |
2 |
2 |
| 273.2.bf.b |
64 |
| 273.2.bh |
\(\chi_{273}(131, \cdot)\) |
273.2.bh.a |
64 |
2 |
| 273.2.bj |
\(\chi_{273}(25, \cdot)\) |
273.2.bj.a |
2 |
2 |
| 273.2.bj.b |
2 |
| 273.2.bj.c |
16 |
| 273.2.bj.d |
16 |
| 273.2.bl |
\(\chi_{273}(88, \cdot)\) |
273.2.bl.a |
2 |
2 |
| 273.2.bl.b |
4 |
| 273.2.bl.c |
12 |
| 273.2.bl.d |
20 |
| 273.2.bn |
\(\chi_{273}(146, \cdot)\) |
273.2.bn.a |
2 |
2 |
| 273.2.bn.b |
2 |
| 273.2.bn.c |
64 |
| 273.2.br |
\(\chi_{273}(17, \cdot)\) |
273.2.br.a |
2 |
2 |
| 273.2.br.b |
64 |
| 273.2.bt |
\(\chi_{273}(136, \cdot)\) |
273.2.bt.a |
36 |
4 |
| 273.2.bt.b |
40 |
| 273.2.bv |
\(\chi_{273}(2, \cdot)\) |
273.2.bv.a |
4 |
4 |
| 273.2.bv.b |
128 |
| 273.2.bw |
\(\chi_{273}(11, \cdot)\) |
273.2.bw.a |
4 |
4 |
| 273.2.bw.b |
128 |
| 273.2.by |
\(\chi_{273}(76, \cdot)\) |
273.2.by.a |
4 |
4 |
| 273.2.by.b |
4 |
| 273.2.by.c |
32 |
| 273.2.by.d |
32 |
| 273.2.bz |
\(\chi_{273}(31, \cdot)\) |
273.2.bz.a |
36 |
4 |
| 273.2.bz.b |
36 |
| 273.2.cc |
\(\chi_{273}(50, \cdot)\) |
273.2.cc.a |
112 |
4 |
| 273.2.cd |
\(\chi_{273}(44, \cdot)\) |
273.2.cd.a |
4 |
4 |
| 273.2.cd.b |
4 |
| 273.2.cd.c |
8 |
| 273.2.cd.d |
8 |
| 273.2.cd.e |
112 |
| 273.2.cg |
\(\chi_{273}(19, \cdot)\) |
273.2.cg.a |
36 |
4 |
| 273.2.cg.b |
40 |
