Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(945))\).
|
Total |
New |
Old |
| Modular forms
| 32544 |
22068 |
10476 |
| Cusp forms
| 29665 |
21108 |
8557 |
| Eisenstein series
| 2879 |
960 |
1919 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(945))\)
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 |
| 945.2.a |
\(\chi_{945}(1, \cdot)\) |
945.2.a.a |
2 |
1 |
| 945.2.a.b |
2 |
| 945.2.a.c |
2 |
| 945.2.a.d |
2 |
| 945.2.a.e |
2 |
| 945.2.a.f |
2 |
| 945.2.a.g |
2 |
| 945.2.a.h |
2 |
| 945.2.a.i |
2 |
| 945.2.a.j |
2 |
| 945.2.a.k |
2 |
| 945.2.a.l |
2 |
| 945.2.a.m |
4 |
| 945.2.a.n |
4 |
| 945.2.b |
\(\chi_{945}(566, \cdot)\) |
945.2.b.a |
10 |
1 |
| 945.2.b.b |
10 |
| 945.2.b.c |
12 |
| 945.2.b.d |
12 |
| 945.2.d |
\(\chi_{945}(379, \cdot)\) |
945.2.d.a |
2 |
1 |
| 945.2.d.b |
2 |
| 945.2.d.c |
8 |
| 945.2.d.d |
10 |
| 945.2.d.e |
10 |
| 945.2.d.f |
16 |
| 945.2.g |
\(\chi_{945}(944, \cdot)\) |
945.2.g.a |
32 |
1 |
| 945.2.g.b |
32 |
| 945.2.i |
\(\chi_{945}(316, \cdot)\) |
945.2.i.a |
2 |
2 |
| 945.2.i.b |
2 |
| 945.2.i.c |
8 |
| 945.2.i.d |
8 |
| 945.2.i.e |
12 |
| 945.2.i.f |
16 |
| 945.2.j |
\(\chi_{945}(541, \cdot)\) |
945.2.j.a |
2 |
2 |
| 945.2.j.b |
2 |
| 945.2.j.c |
6 |
| 945.2.j.d |
6 |
| 945.2.j.e |
10 |
| 945.2.j.f |
10 |
| 945.2.j.g |
10 |
| 945.2.j.h |
10 |
| 945.2.j.i |
14 |
| 945.2.j.j |
14 |
| 945.2.k |
\(\chi_{945}(361, \cdot)\) |
945.2.k.a |
4 |
2 |
| 945.2.k.b |
24 |
| 945.2.k.c |
36 |
| 945.2.l |
\(\chi_{945}(46, \cdot)\) |
945.2.l.a |
4 |
2 |
| 945.2.l.b |
24 |
| 945.2.l.c |
36 |
| 945.2.m |
\(\chi_{945}(323, \cdot)\) |
945.2.m.a |
48 |
2 |
| 945.2.m.b |
48 |
| 945.2.p |
\(\chi_{945}(433, \cdot)\) |
945.2.p.a |
16 |
2 |
| 945.2.p.b |
48 |
| 945.2.p.c |
64 |
| 945.2.r |
\(\chi_{945}(424, \cdot)\) |
945.2.r.a |
4 |
2 |
| 945.2.r.b |
84 |
| 945.2.t |
\(\chi_{945}(341, \cdot)\) |
945.2.t.a |
2 |
2 |
| 945.2.t.b |
30 |
| 945.2.t.c |
32 |
| 945.2.u |
\(\chi_{945}(89, \cdot)\) |
945.2.u.a |
88 |
2 |
| 945.2.z |
\(\chi_{945}(314, \cdot)\) |
945.2.z.a |
8 |
2 |
| 945.2.z.b |
80 |
| 945.2.bb |
\(\chi_{945}(269, \cdot)\) |
945.2.bb.a |
32 |
2 |
| 945.2.bb.b |
32 |
| 945.2.bb.c |
64 |
| 945.2.be |
\(\chi_{945}(206, \cdot)\) |
945.2.be.a |
2 |
2 |
| 945.2.be.b |
30 |
| 945.2.be.c |
32 |
| 945.2.bf |
\(\chi_{945}(109, \cdot)\) |
945.2.bf.a |
4 |
2 |
| 945.2.bf.b |
4 |
| 945.2.bf.c |
56 |
| 945.2.bf.d |
64 |
| 945.2.bh |
\(\chi_{945}(64, \cdot)\) |
945.2.bh.a |
4 |
2 |
| 945.2.bh.b |
4 |
| 945.2.bh.c |
64 |
| 945.2.bj |
\(\chi_{945}(26, \cdot)\) |
945.2.bj.a |
2 |
2 |
| 945.2.bj.b |
2 |
| 945.2.bj.c |
2 |
| 945.2.bj.d |
2 |
| 945.2.bj.e |
4 |
| 945.2.bj.f |
4 |
| 945.2.bj.g |
6 |
| 945.2.bj.h |
6 |
| 945.2.bj.i |
8 |
| 945.2.bj.j |
8 |
| 945.2.bj.k |
20 |
| 945.2.bj.l |
20 |
| 945.2.bl |
\(\chi_{945}(251, \cdot)\) |
945.2.bl.a |
2 |
2 |
| 945.2.bl.b |
2 |
| 945.2.bl.c |
2 |
| 945.2.bl.d |
2 |
| 945.2.bl.e |
2 |
| 945.2.bl.f |
2 |
| 945.2.bl.g |
2 |
| 945.2.bl.h |
2 |
| 945.2.bl.i |
24 |
| 945.2.bl.j |
24 |
| 945.2.bo |
\(\chi_{945}(289, \cdot)\) |
945.2.bo.a |
4 |
2 |
| 945.2.bo.b |
84 |
| 945.2.bq |
\(\chi_{945}(719, \cdot)\) |
945.2.bq.a |
88 |
2 |
| 945.2.bs |
\(\chi_{945}(16, \cdot)\) |
945.2.bs.a |
276 |
6 |
| 945.2.bs.b |
300 |
| 945.2.bt |
\(\chi_{945}(106, \cdot)\) |
945.2.bt.a |
96 |
6 |
| 945.2.bt.b |
96 |
| 945.2.bt.c |
120 |
| 945.2.bt.d |
120 |
| 945.2.bu |
\(\chi_{945}(121, \cdot)\) |
945.2.bu.a |
276 |
6 |
| 945.2.bu.b |
300 |
| 945.2.bv |
\(\chi_{945}(73, \cdot)\) |
945.2.bv.a |
4 |
4 |
| 945.2.bv.b |
4 |
| 945.2.bv.c |
4 |
| 945.2.bv.d |
4 |
| 945.2.bv.e |
160 |
| 945.2.by |
\(\chi_{945}(233, \cdot)\) |
945.2.by.a |
176 |
4 |
| 945.2.ca |
\(\chi_{945}(368, \cdot)\) |
945.2.ca.a |
176 |
4 |
| 945.2.cc |
\(\chi_{945}(82, \cdot)\) |
945.2.cc.a |
128 |
4 |
| 945.2.cc.b |
128 |
| 945.2.ce |
\(\chi_{945}(118, \cdot)\) |
945.2.ce.a |
176 |
4 |
| 945.2.cf |
\(\chi_{945}(8, \cdot)\) |
945.2.cf.a |
144 |
4 |
| 945.2.ch |
\(\chi_{945}(53, \cdot)\) |
945.2.ch.a |
128 |
4 |
| 945.2.ch.b |
128 |
| 945.2.cj |
\(\chi_{945}(208, \cdot)\) |
945.2.cj.a |
4 |
4 |
| 945.2.cj.b |
4 |
| 945.2.cj.c |
4 |
| 945.2.cj.d |
4 |
| 945.2.cj.e |
160 |
| 945.2.cl |
\(\chi_{945}(164, \cdot)\) |
945.2.cl.a |
840 |
6 |
| 945.2.cq |
\(\chi_{945}(59, \cdot)\) |
945.2.cq.a |
840 |
6 |
| 945.2.cs |
\(\chi_{945}(104, \cdot)\) |
945.2.cs.a |
24 |
6 |
| 945.2.cs.b |
816 |
| 945.2.cu |
\(\chi_{945}(184, \cdot)\) |
945.2.cu.a |
840 |
6 |
| 945.2.cx |
\(\chi_{945}(236, \cdot)\) |
945.2.cx.a |
288 |
6 |
| 945.2.cx.b |
288 |
| 945.2.cz |
\(\chi_{945}(41, \cdot)\) |
945.2.cz.a |
288 |
6 |
| 945.2.cz.b |
288 |
| 945.2.db |
\(\chi_{945}(4, \cdot)\) |
945.2.db.a |
840 |
6 |
| 945.2.dd |
\(\chi_{945}(169, \cdot)\) |
945.2.dd.a |
648 |
6 |
| 945.2.de |
\(\chi_{945}(101, \cdot)\) |
945.2.de.a |
288 |
6 |
| 945.2.de.b |
288 |
| 945.2.dh |
\(\chi_{945}(23, \cdot)\) |
945.2.dh.a |
1680 |
12 |
| 945.2.di |
\(\chi_{945}(13, \cdot)\) |
945.2.di.a |
1680 |
12 |
| 945.2.dk |
\(\chi_{945}(157, \cdot)\) |
945.2.dk.a |
1680 |
12 |
| 945.2.dm |
\(\chi_{945}(92, \cdot)\) |
945.2.dm.a |
1296 |
12 |
| 945.2.do |
\(\chi_{945}(2, \cdot)\) |
945.2.do.a |
1680 |
12 |
| 945.2.dr |
\(\chi_{945}(52, \cdot)\) |
945.2.dr.a |
1680 |
12 |
