Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(513))\).
|
Total |
New |
Old |
| Modular forms
| 10260 |
7910 |
2350 |
| Cusp forms
| 9181 |
7366 |
1815 |
| Eisenstein series
| 1079 |
544 |
535 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(513))\)
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 |
| 513.2.a |
\(\chi_{513}(1, \cdot)\) |
513.2.a.a |
1 |
1 |
| 513.2.a.b |
1 |
| 513.2.a.c |
2 |
| 513.2.a.d |
3 |
| 513.2.a.e |
3 |
| 513.2.a.f |
3 |
| 513.2.a.g |
3 |
| 513.2.a.h |
4 |
| 513.2.a.i |
4 |
| 513.2.d |
\(\chi_{513}(512, \cdot)\) |
513.2.d.a |
2 |
1 |
| 513.2.d.b |
12 |
| 513.2.d.c |
12 |
| 513.2.e |
\(\chi_{513}(172, \cdot)\) |
513.2.e.a |
18 |
2 |
| 513.2.e.b |
18 |
| 513.2.f |
\(\chi_{513}(163, \cdot)\) |
513.2.f.a |
2 |
2 |
| 513.2.f.b |
2 |
| 513.2.f.c |
2 |
| 513.2.f.d |
2 |
| 513.2.f.e |
8 |
| 513.2.f.f |
12 |
| 513.2.f.g |
12 |
| 513.2.f.h |
12 |
| 513.2.g |
\(\chi_{513}(64, \cdot)\) |
513.2.g.a |
2 |
2 |
| 513.2.g.b |
2 |
| 513.2.g.c |
32 |
| 513.2.h |
\(\chi_{513}(235, \cdot)\) |
513.2.h.a |
2 |
2 |
| 513.2.h.b |
2 |
| 513.2.h.c |
32 |
| 513.2.k |
\(\chi_{513}(8, \cdot)\) |
513.2.k.a |
36 |
2 |
| 513.2.l |
\(\chi_{513}(170, \cdot)\) |
513.2.l.a |
36 |
2 |
| 513.2.m |
\(\chi_{513}(107, \cdot)\) |
513.2.m.a |
2 |
2 |
| 513.2.m.b |
2 |
| 513.2.m.c |
4 |
| 513.2.m.d |
4 |
| 513.2.m.e |
8 |
| 513.2.m.f |
8 |
| 513.2.m.g |
24 |
| 513.2.t |
\(\chi_{513}(179, \cdot)\) |
513.2.t.a |
36 |
2 |
| 513.2.u |
\(\chi_{513}(25, \cdot)\) |
513.2.u.a |
348 |
6 |
| 513.2.v |
\(\chi_{513}(196, \cdot)\) |
513.2.v.a |
348 |
6 |
| 513.2.w |
\(\chi_{513}(4, \cdot)\) |
513.2.w.a |
348 |
6 |
| 513.2.x |
\(\chi_{513}(43, \cdot)\) |
513.2.x.a |
348 |
6 |
| 513.2.y |
\(\chi_{513}(28, \cdot)\) |
513.2.y.a |
6 |
6 |
| 513.2.y.b |
6 |
| 513.2.y.c |
6 |
| 513.2.y.d |
24 |
| 513.2.y.e |
36 |
| 513.2.y.f |
36 |
| 513.2.y.g |
48 |
| 513.2.z |
\(\chi_{513}(226, \cdot)\) |
513.2.z.a |
108 |
6 |
| 513.2.ba |
\(\chi_{513}(58, \cdot)\) |
513.2.ba.a |
162 |
6 |
| 513.2.ba.b |
162 |
| 513.2.bb |
\(\chi_{513}(106, \cdot)\) |
513.2.bb.a |
348 |
6 |
| 513.2.bc |
\(\chi_{513}(7, \cdot)\) |
513.2.bc.a |
348 |
6 |
| 513.2.bd |
\(\chi_{513}(73, \cdot)\) |
513.2.bd.a |
108 |
6 |
| 513.2.be |
\(\chi_{513}(139, \cdot)\) |
513.2.be.a |
348 |
6 |
| 513.2.bf |
\(\chi_{513}(61, \cdot)\) |
513.2.bf.a |
348 |
6 |
| 513.2.bi |
\(\chi_{513}(14, \cdot)\) |
513.2.bi.a |
348 |
6 |
| 513.2.bj |
\(\chi_{513}(41, \cdot)\) |
513.2.bj.a |
348 |
6 |
| 513.2.bk |
\(\chi_{513}(86, \cdot)\) |
513.2.bk.a |
348 |
6 |
| 513.2.bo |
\(\chi_{513}(71, \cdot)\) |
513.2.bo.a |
108 |
6 |
| 513.2.bp |
\(\chi_{513}(53, \cdot)\) |
513.2.bp.a |
6 |
6 |
| 513.2.bp.b |
36 |
| 513.2.bp.c |
36 |
| 513.2.bp.d |
84 |
| 513.2.bu |
\(\chi_{513}(122, \cdot)\) |
513.2.bu.a |
348 |
6 |
| 513.2.bv |
\(\chi_{513}(50, \cdot)\) |
513.2.bv.a |
348 |
6 |
| 513.2.bw |
\(\chi_{513}(56, \cdot)\) |
513.2.bw.a |
348 |
6 |
| 513.2.cd |
\(\chi_{513}(116, \cdot)\) |
513.2.cd.a |
108 |
6 |
| 513.2.cg |
\(\chi_{513}(2, \cdot)\) |
513.2.cg.a |
348 |
6 |
| 513.2.ch |
\(\chi_{513}(167, \cdot)\) |
513.2.ch.a |
348 |
6 |
| 513.2.cp |
\(\chi_{513}(29, \cdot)\) |
513.2.cp.a |
348 |
6 |
