Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(525))\).
|
Total |
New |
Old |
Modular forms
| 10272 |
6564 |
3708 |
Cusp forms
| 8929 |
6152 |
2777 |
Eisenstein series
| 1343 |
412 |
931 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)
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 the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
525.2.a |
\(\chi_{525}(1, \cdot)\) |
525.2.a.a |
1 |
1 |
525.2.a.b |
1 |
525.2.a.c |
1 |
525.2.a.d |
1 |
525.2.a.e |
2 |
525.2.a.f |
2 |
525.2.a.g |
2 |
525.2.a.h |
2 |
525.2.a.i |
2 |
525.2.a.j |
3 |
525.2.a.k |
3 |
525.2.b |
\(\chi_{525}(251, \cdot)\) |
525.2.b.a |
2 |
1 |
525.2.b.b |
2 |
525.2.b.c |
2 |
525.2.b.d |
2 |
525.2.b.e |
4 |
525.2.b.f |
4 |
525.2.b.g |
4 |
525.2.b.h |
8 |
525.2.b.i |
8 |
525.2.b.j |
8 |
525.2.d |
\(\chi_{525}(274, \cdot)\) |
525.2.d.a |
2 |
1 |
525.2.d.b |
2 |
525.2.d.c |
4 |
525.2.d.d |
4 |
525.2.d.e |
4 |
525.2.g |
\(\chi_{525}(524, \cdot)\) |
525.2.g.a |
4 |
1 |
525.2.g.b |
4 |
525.2.g.c |
4 |
525.2.g.d |
8 |
525.2.g.e |
8 |
525.2.g.f |
16 |
525.2.i |
\(\chi_{525}(151, \cdot)\) |
525.2.i.a |
2 |
2 |
525.2.i.b |
2 |
525.2.i.c |
2 |
525.2.i.d |
2 |
525.2.i.e |
2 |
525.2.i.f |
4 |
525.2.i.g |
4 |
525.2.i.h |
8 |
525.2.i.i |
8 |
525.2.i.j |
8 |
525.2.i.k |
8 |
525.2.j |
\(\chi_{525}(218, \cdot)\) |
525.2.j.a |
16 |
2 |
525.2.j.b |
24 |
525.2.j.c |
32 |
525.2.m |
\(\chi_{525}(118, \cdot)\) |
525.2.m.a |
8 |
2 |
525.2.m.b |
16 |
525.2.m.c |
24 |
525.2.n |
\(\chi_{525}(106, \cdot)\) |
525.2.n.a |
4 |
4 |
525.2.n.b |
20 |
525.2.n.c |
24 |
525.2.n.d |
32 |
525.2.n.e |
32 |
525.2.q |
\(\chi_{525}(299, \cdot)\) |
525.2.q.a |
4 |
2 |
525.2.q.b |
4 |
525.2.q.c |
4 |
525.2.q.d |
4 |
525.2.q.e |
16 |
525.2.q.f |
16 |
525.2.q.g |
40 |
525.2.r |
\(\chi_{525}(424, \cdot)\) |
525.2.r.a |
4 |
2 |
525.2.r.b |
4 |
525.2.r.c |
4 |
525.2.r.d |
4 |
525.2.r.e |
4 |
525.2.r.f |
4 |
525.2.r.g |
8 |
525.2.r.h |
16 |
525.2.t |
\(\chi_{525}(26, \cdot)\) |
525.2.t.a |
2 |
2 |
525.2.t.b |
2 |
525.2.t.c |
2 |
525.2.t.d |
2 |
525.2.t.e |
2 |
525.2.t.f |
8 |
525.2.t.g |
8 |
525.2.t.h |
20 |
525.2.t.i |
20 |
525.2.t.j |
24 |
525.2.w |
\(\chi_{525}(104, \cdot)\) |
525.2.w.a |
304 |
4 |
525.2.z |
\(\chi_{525}(64, \cdot)\) |
525.2.z.a |
56 |
4 |
525.2.z.b |
72 |
525.2.bb |
\(\chi_{525}(41, \cdot)\) |
525.2.bb.a |
304 |
4 |
525.2.bc |
\(\chi_{525}(82, \cdot)\) |
525.2.bc.a |
8 |
4 |
525.2.bc.b |
8 |
525.2.bc.c |
24 |
525.2.bc.d |
24 |
525.2.bc.e |
32 |
525.2.bf |
\(\chi_{525}(32, \cdot)\) |
525.2.bf.a |
8 |
4 |
525.2.bf.b |
8 |
525.2.bf.c |
8 |
525.2.bf.d |
8 |
525.2.bf.e |
16 |
525.2.bf.f |
48 |
525.2.bf.g |
80 |
525.2.bg |
\(\chi_{525}(16, \cdot)\) |
525.2.bg.a |
160 |
8 |
525.2.bg.b |
160 |
525.2.bh |
\(\chi_{525}(13, \cdot)\) |
525.2.bh.a |
320 |
8 |
525.2.bk |
\(\chi_{525}(8, \cdot)\) |
525.2.bk.a |
480 |
8 |
525.2.bm |
\(\chi_{525}(131, \cdot)\) |
525.2.bm.a |
608 |
8 |
525.2.bo |
\(\chi_{525}(4, \cdot)\) |
525.2.bo.a |
320 |
8 |
525.2.bp |
\(\chi_{525}(59, \cdot)\) |
525.2.bp.a |
608 |
8 |
525.2.bs |
\(\chi_{525}(2, \cdot)\) |
525.2.bs.a |
1216 |
16 |
525.2.bv |
\(\chi_{525}(52, \cdot)\) |
525.2.bv.a |
640 |
16 |