Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(592))\).
|
Total |
New |
Old |
Modular forms
| 11448 |
6304 |
5144 |
Cusp forms
| 10441 |
5990 |
4451 |
Eisenstein series
| 1007 |
314 |
693 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(592))\)
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 |
592.2.a |
\(\chi_{592}(1, \cdot)\) |
592.2.a.a |
1 |
1 |
592.2.a.b |
1 |
592.2.a.c |
1 |
592.2.a.d |
1 |
592.2.a.e |
1 |
592.2.a.f |
2 |
592.2.a.g |
2 |
592.2.a.h |
2 |
592.2.a.i |
3 |
592.2.a.j |
4 |
592.2.c |
\(\chi_{592}(297, \cdot)\) |
None |
0 |
1 |
592.2.e |
\(\chi_{592}(73, \cdot)\) |
None |
0 |
1 |
592.2.g |
\(\chi_{592}(369, \cdot)\) |
592.2.g.a |
2 |
1 |
592.2.g.b |
2 |
592.2.g.c |
4 |
592.2.g.d |
10 |
592.2.i |
\(\chi_{592}(417, \cdot)\) |
592.2.i.a |
2 |
2 |
592.2.i.b |
2 |
592.2.i.c |
2 |
592.2.i.d |
2 |
592.2.i.e |
6 |
592.2.i.f |
6 |
592.2.i.g |
6 |
592.2.i.h |
10 |
592.2.j |
\(\chi_{592}(327, \cdot)\) |
None |
0 |
2 |
592.2.m |
\(\chi_{592}(43, \cdot)\) |
592.2.m.a |
148 |
2 |
592.2.n |
\(\chi_{592}(221, \cdot)\) |
592.2.n.a |
148 |
2 |
592.2.o |
\(\chi_{592}(149, \cdot)\) |
592.2.o.a |
144 |
2 |
592.2.s |
\(\chi_{592}(339, \cdot)\) |
592.2.s.a |
148 |
2 |
592.2.t |
\(\chi_{592}(31, \cdot)\) |
592.2.t.a |
2 |
2 |
592.2.t.b |
4 |
592.2.t.c |
4 |
592.2.t.d |
28 |
592.2.w |
\(\chi_{592}(529, \cdot)\) |
592.2.w.a |
2 |
2 |
592.2.w.b |
2 |
592.2.w.c |
4 |
592.2.w.d |
4 |
592.2.w.e |
4 |
592.2.w.f |
20 |
592.2.y |
\(\chi_{592}(233, \cdot)\) |
None |
0 |
2 |
592.2.ba |
\(\chi_{592}(121, \cdot)\) |
None |
0 |
2 |
592.2.bc |
\(\chi_{592}(33, \cdot)\) |
592.2.bc.a |
6 |
6 |
592.2.bc.b |
6 |
592.2.bc.c |
6 |
592.2.bc.d |
12 |
592.2.bc.e |
24 |
592.2.bc.f |
24 |
592.2.bc.g |
30 |
592.2.be |
\(\chi_{592}(319, \cdot)\) |
592.2.be.a |
4 |
4 |
592.2.be.b |
8 |
592.2.be.c |
8 |
592.2.be.d |
16 |
592.2.be.e |
20 |
592.2.be.f |
20 |
592.2.bf |
\(\chi_{592}(251, \cdot)\) |
592.2.bf.a |
296 |
4 |
592.2.bj |
\(\chi_{592}(269, \cdot)\) |
592.2.bj.a |
296 |
4 |
592.2.bk |
\(\chi_{592}(85, \cdot)\) |
592.2.bk.a |
296 |
4 |
592.2.bl |
\(\chi_{592}(51, \cdot)\) |
592.2.bl.a |
296 |
4 |
592.2.bo |
\(\chi_{592}(23, \cdot)\) |
None |
0 |
4 |
592.2.bq |
\(\chi_{592}(65, \cdot)\) |
592.2.bq.a |
6 |
6 |
592.2.bq.b |
12 |
592.2.bq.c |
12 |
592.2.bq.d |
18 |
592.2.bq.e |
60 |
592.2.bs |
\(\chi_{592}(9, \cdot)\) |
None |
0 |
6 |
592.2.bv |
\(\chi_{592}(25, \cdot)\) |
None |
0 |
6 |
592.2.bx |
\(\chi_{592}(15, \cdot)\) |
592.2.bx.a |
12 |
12 |
592.2.bx.b |
12 |
592.2.bx.c |
12 |
592.2.bx.d |
60 |
592.2.bx.e |
60 |
592.2.bx.f |
72 |
592.2.by |
\(\chi_{592}(21, \cdot)\) |
592.2.by.a |
888 |
12 |
592.2.ca |
\(\chi_{592}(19, \cdot)\) |
592.2.ca.a |
888 |
12 |
592.2.cd |
\(\chi_{592}(59, \cdot)\) |
592.2.cd.a |
888 |
12 |
592.2.ce |
\(\chi_{592}(53, \cdot)\) |
592.2.ce.a |
888 |
12 |
592.2.ch |
\(\chi_{592}(39, \cdot)\) |
None |
0 |
12 |