Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(315))\).
|
Total |
New |
Old |
Modular forms
| 3840 |
2540 |
1300 |
Cusp forms
| 3073 |
2268 |
805 |
Eisenstein series
| 767 |
272 |
495 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)
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 |
315.2.a |
\(\chi_{315}(1, \cdot)\) |
315.2.a.a |
1 |
1 |
315.2.a.b |
1 |
315.2.a.c |
2 |
315.2.a.d |
2 |
315.2.a.e |
2 |
315.2.a.f |
2 |
315.2.b |
\(\chi_{315}(251, \cdot)\) |
315.2.b.a |
4 |
1 |
315.2.b.b |
4 |
315.2.d |
\(\chi_{315}(64, \cdot)\) |
315.2.d.a |
2 |
1 |
315.2.d.b |
2 |
315.2.d.c |
2 |
315.2.d.d |
2 |
315.2.d.e |
6 |
315.2.g |
\(\chi_{315}(314, \cdot)\) |
315.2.g.a |
16 |
1 |
315.2.i |
\(\chi_{315}(106, \cdot)\) |
315.2.i.a |
2 |
2 |
315.2.i.b |
2 |
315.2.i.c |
8 |
315.2.i.d |
8 |
315.2.i.e |
12 |
315.2.i.f |
16 |
315.2.j |
\(\chi_{315}(46, \cdot)\) |
315.2.j.a |
2 |
2 |
315.2.j.b |
2 |
315.2.j.c |
4 |
315.2.j.d |
4 |
315.2.j.e |
4 |
315.2.j.f |
6 |
315.2.j.g |
6 |
315.2.k |
\(\chi_{315}(16, \cdot)\) |
315.2.k.a |
4 |
2 |
315.2.k.b |
24 |
315.2.k.c |
36 |
315.2.l |
\(\chi_{315}(121, \cdot)\) |
315.2.l.a |
4 |
2 |
315.2.l.b |
24 |
315.2.l.c |
36 |
315.2.m |
\(\chi_{315}(8, \cdot)\) |
315.2.m.a |
12 |
2 |
315.2.m.b |
12 |
315.2.p |
\(\chi_{315}(118, \cdot)\) |
315.2.p.a |
4 |
2 |
315.2.p.b |
4 |
315.2.p.c |
4 |
315.2.p.d |
8 |
315.2.p.e |
16 |
315.2.r |
\(\chi_{315}(184, \cdot)\) |
315.2.r.a |
4 |
2 |
315.2.r.b |
84 |
315.2.t |
\(\chi_{315}(101, \cdot)\) |
315.2.t.a |
2 |
2 |
315.2.t.b |
30 |
315.2.t.c |
32 |
315.2.u |
\(\chi_{315}(59, \cdot)\) |
315.2.u.a |
88 |
2 |
315.2.z |
\(\chi_{315}(104, \cdot)\) |
315.2.z.a |
8 |
2 |
315.2.z.b |
80 |
315.2.bb |
\(\chi_{315}(89, \cdot)\) |
315.2.bb.a |
8 |
2 |
315.2.bb.b |
24 |
315.2.be |
\(\chi_{315}(236, \cdot)\) |
315.2.be.a |
2 |
2 |
315.2.be.b |
30 |
315.2.be.c |
32 |
315.2.bf |
\(\chi_{315}(109, \cdot)\) |
315.2.bf.a |
4 |
2 |
315.2.bf.b |
16 |
315.2.bf.c |
16 |
315.2.bh |
\(\chi_{315}(169, \cdot)\) |
315.2.bh.a |
4 |
2 |
315.2.bh.b |
4 |
315.2.bh.c |
64 |
315.2.bj |
\(\chi_{315}(26, \cdot)\) |
315.2.bj.a |
12 |
2 |
315.2.bj.b |
12 |
315.2.bl |
\(\chi_{315}(41, \cdot)\) |
315.2.bl.a |
2 |
2 |
315.2.bl.b |
2 |
315.2.bl.c |
2 |
315.2.bl.d |
2 |
315.2.bl.e |
2 |
315.2.bl.f |
2 |
315.2.bl.g |
2 |
315.2.bl.h |
2 |
315.2.bl.i |
24 |
315.2.bl.j |
24 |
315.2.bo |
\(\chi_{315}(4, \cdot)\) |
315.2.bo.a |
4 |
2 |
315.2.bo.b |
84 |
315.2.bq |
\(\chi_{315}(164, \cdot)\) |
315.2.bq.a |
88 |
2 |
315.2.bs |
\(\chi_{315}(52, \cdot)\) |
315.2.bs.a |
4 |
4 |
315.2.bs.b |
4 |
315.2.bs.c |
4 |
315.2.bs.d |
4 |
315.2.bs.e |
160 |
315.2.bv |
\(\chi_{315}(23, \cdot)\) |
315.2.bv.a |
176 |
4 |
315.2.bx |
\(\chi_{315}(2, \cdot)\) |
315.2.bx.a |
176 |
4 |
315.2.bz |
\(\chi_{315}(73, \cdot)\) |
315.2.bz.a |
4 |
4 |
315.2.bz.b |
4 |
315.2.bz.c |
32 |
315.2.bz.d |
32 |
315.2.cb |
\(\chi_{315}(13, \cdot)\) |
315.2.cb.a |
176 |
4 |
315.2.cc |
\(\chi_{315}(92, \cdot)\) |
315.2.cc.a |
144 |
4 |
315.2.ce |
\(\chi_{315}(53, \cdot)\) |
315.2.ce.a |
64 |
4 |
315.2.cg |
\(\chi_{315}(157, \cdot)\) |
315.2.cg.a |
4 |
4 |
315.2.cg.b |
4 |
315.2.cg.c |
4 |
315.2.cg.d |
4 |
315.2.cg.e |
160 |