Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(567))\).
|
Total |
New |
Old |
Modular forms
| 12312 |
9112 |
3200 |
Cusp forms
| 11017 |
8552 |
2465 |
Eisenstein series
| 1295 |
560 |
735 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(567))\)
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 |
567.2.a |
\(\chi_{567}(1, \cdot)\) |
567.2.a.a |
1 |
1 |
567.2.a.b |
1 |
567.2.a.c |
3 |
567.2.a.d |
3 |
567.2.a.e |
3 |
567.2.a.f |
3 |
567.2.a.g |
3 |
567.2.a.h |
3 |
567.2.a.i |
4 |
567.2.c |
\(\chi_{567}(566, \cdot)\) |
567.2.c.a |
8 |
1 |
567.2.c.b |
8 |
567.2.c.c |
12 |
567.2.e |
\(\chi_{567}(163, \cdot)\) |
567.2.e.a |
2 |
2 |
567.2.e.b |
2 |
567.2.e.c |
8 |
567.2.e.d |
8 |
567.2.e.e |
10 |
567.2.e.f |
10 |
567.2.e.g |
16 |
567.2.f |
\(\chi_{567}(190, \cdot)\) |
567.2.f.a |
2 |
2 |
567.2.f.b |
2 |
567.2.f.c |
2 |
567.2.f.d |
2 |
567.2.f.e |
2 |
567.2.f.f |
2 |
567.2.f.g |
2 |
567.2.f.h |
2 |
567.2.f.i |
4 |
567.2.f.j |
4 |
567.2.f.k |
4 |
567.2.f.l |
6 |
567.2.f.m |
6 |
567.2.f.n |
8 |
567.2.g |
\(\chi_{567}(109, \cdot)\) |
567.2.g.a |
2 |
2 |
567.2.g.b |
2 |
567.2.g.c |
2 |
567.2.g.d |
2 |
567.2.g.e |
2 |
567.2.g.f |
2 |
567.2.g.g |
4 |
567.2.g.h |
6 |
567.2.g.i |
6 |
567.2.g.j |
8 |
567.2.g.k |
8 |
567.2.g.l |
16 |
567.2.h |
\(\chi_{567}(298, \cdot)\) |
567.2.h.a |
2 |
2 |
567.2.h.b |
2 |
567.2.h.c |
2 |
567.2.h.d |
2 |
567.2.h.e |
2 |
567.2.h.f |
2 |
567.2.h.g |
4 |
567.2.h.h |
6 |
567.2.h.i |
6 |
567.2.h.j |
8 |
567.2.h.k |
8 |
567.2.h.l |
16 |
567.2.i |
\(\chi_{567}(215, \cdot)\) |
567.2.i.a |
2 |
2 |
567.2.i.b |
2 |
567.2.i.c |
4 |
567.2.i.d |
4 |
567.2.i.e |
4 |
567.2.i.f |
12 |
567.2.i.g |
32 |
567.2.o |
\(\chi_{567}(188, \cdot)\) |
567.2.o.a |
2 |
2 |
567.2.o.b |
2 |
567.2.o.c |
4 |
567.2.o.d |
4 |
567.2.o.e |
8 |
567.2.o.f |
8 |
567.2.o.g |
16 |
567.2.o.h |
16 |
567.2.p |
\(\chi_{567}(80, \cdot)\) |
567.2.p.a |
2 |
2 |
567.2.p.b |
2 |
567.2.p.c |
10 |
567.2.p.d |
10 |
567.2.p.e |
32 |
567.2.s |
\(\chi_{567}(26, \cdot)\) |
567.2.s.a |
2 |
2 |
567.2.s.b |
2 |
567.2.s.c |
4 |
567.2.s.d |
4 |
567.2.s.e |
4 |
567.2.s.f |
12 |
567.2.s.g |
32 |
567.2.u |
\(\chi_{567}(100, \cdot)\) |
567.2.u.a |
132 |
6 |
567.2.v |
\(\chi_{567}(64, \cdot)\) |
567.2.v.a |
54 |
6 |
567.2.v.b |
54 |
567.2.w |
\(\chi_{567}(37, \cdot)\) |
567.2.w.a |
132 |
6 |
567.2.ba |
\(\chi_{567}(143, \cdot)\) |
567.2.ba.a |
132 |
6 |
567.2.bd |
\(\chi_{567}(17, \cdot)\) |
567.2.bd.a |
132 |
6 |
567.2.be |
\(\chi_{567}(62, \cdot)\) |
567.2.be.a |
132 |
6 |
567.2.bg |
\(\chi_{567}(4, \cdot)\) |
567.2.bg.a |
1260 |
18 |
567.2.bh |
\(\chi_{567}(22, \cdot)\) |
567.2.bh.a |
486 |
18 |
567.2.bh.b |
486 |
567.2.bi |
\(\chi_{567}(25, \cdot)\) |
567.2.bi.a |
1260 |
18 |
567.2.bl |
\(\chi_{567}(47, \cdot)\) |
567.2.bl.a |
1260 |
18 |
567.2.bm |
\(\chi_{567}(20, \cdot)\) |
567.2.bm.a |
1260 |
18 |
567.2.br |
\(\chi_{567}(5, \cdot)\) |
567.2.br.a |
1260 |
18 |