Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(693))\).
|
Total |
New |
Old |
Modular forms
| 18240 |
13298 |
4942 |
Cusp forms
| 16321 |
12486 |
3835 |
Eisenstein series
| 1919 |
812 |
1107 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(693))\)
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 |
693.2.a |
\(\chi_{693}(1, \cdot)\) |
693.2.a.a |
1 |
1 |
693.2.a.b |
1 |
693.2.a.c |
1 |
693.2.a.d |
1 |
693.2.a.e |
2 |
693.2.a.f |
2 |
693.2.a.g |
2 |
693.2.a.h |
2 |
693.2.a.i |
2 |
693.2.a.j |
2 |
693.2.a.k |
2 |
693.2.a.l |
3 |
693.2.a.m |
3 |
693.2.c |
\(\chi_{693}(307, \cdot)\) |
693.2.c.a |
2 |
1 |
693.2.c.b |
4 |
693.2.c.c |
4 |
693.2.c.d |
12 |
693.2.c.e |
16 |
693.2.e |
\(\chi_{693}(188, \cdot)\) |
693.2.e.a |
24 |
1 |
693.2.g |
\(\chi_{693}(197, \cdot)\) |
693.2.g.a |
24 |
1 |
693.2.i |
\(\chi_{693}(100, \cdot)\) |
693.2.i.a |
2 |
2 |
693.2.i.b |
2 |
693.2.i.c |
2 |
693.2.i.d |
2 |
693.2.i.e |
2 |
693.2.i.f |
4 |
693.2.i.g |
6 |
693.2.i.h |
6 |
693.2.i.i |
8 |
693.2.i.j |
10 |
693.2.i.k |
12 |
693.2.i.l |
12 |
693.2.j |
\(\chi_{693}(232, \cdot)\) |
693.2.j.a |
2 |
2 |
693.2.j.b |
2 |
693.2.j.c |
2 |
693.2.j.d |
6 |
693.2.j.e |
12 |
693.2.j.f |
18 |
693.2.j.g |
20 |
693.2.j.h |
28 |
693.2.j.i |
30 |
693.2.k |
\(\chi_{693}(67, \cdot)\) |
693.2.k.a |
6 |
2 |
693.2.k.b |
74 |
693.2.k.c |
80 |
693.2.l |
\(\chi_{693}(529, \cdot)\) |
693.2.l.a |
6 |
2 |
693.2.l.b |
74 |
693.2.l.c |
80 |
693.2.m |
\(\chi_{693}(64, \cdot)\) |
693.2.m.a |
4 |
4 |
693.2.m.b |
4 |
693.2.m.c |
4 |
693.2.m.d |
4 |
693.2.m.e |
4 |
693.2.m.f |
8 |
693.2.m.g |
8 |
693.2.m.h |
16 |
693.2.m.i |
16 |
693.2.m.j |
20 |
693.2.m.k |
32 |
693.2.n |
\(\chi_{693}(320, \cdot)\) |
693.2.n.a |
160 |
2 |
693.2.p |
\(\chi_{693}(241, \cdot)\) |
693.2.p.a |
184 |
2 |
693.2.r |
\(\chi_{693}(32, \cdot)\) |
693.2.r.a |
184 |
2 |
693.2.w |
\(\chi_{693}(428, \cdot)\) |
693.2.w.a |
144 |
2 |
693.2.x |
\(\chi_{693}(296, \cdot)\) |
693.2.x.a |
64 |
2 |
693.2.ba |
\(\chi_{693}(439, \cdot)\) |
693.2.ba.a |
184 |
2 |
693.2.bd |
\(\chi_{693}(419, \cdot)\) |
693.2.bd.a |
160 |
2 |
693.2.be |
\(\chi_{693}(89, \cdot)\) |
693.2.be.a |
56 |
2 |
693.2.bg |
\(\chi_{693}(10, \cdot)\) |
693.2.bg.a |
12 |
2 |
693.2.bg.b |
32 |
693.2.bg.c |
32 |
693.2.bj |
\(\chi_{693}(76, \cdot)\) |
693.2.bj.a |
184 |
2 |
693.2.bk |
\(\chi_{693}(122, \cdot)\) |
693.2.bk.a |
160 |
2 |
693.2.bn |
\(\chi_{693}(263, \cdot)\) |
693.2.bn.a |
184 |
2 |
693.2.bq |
\(\chi_{693}(8, \cdot)\) |
693.2.bq.a |
96 |
4 |
693.2.bs |
\(\chi_{693}(125, \cdot)\) |
693.2.bs.a |
32 |
4 |
693.2.bs.b |
96 |
693.2.bu |
\(\chi_{693}(118, \cdot)\) |
693.2.bu.a |
8 |
4 |
693.2.bu.b |
16 |
693.2.bu.c |
16 |
693.2.bu.d |
16 |
693.2.bu.e |
32 |
693.2.bu.f |
64 |
693.2.bw |
\(\chi_{693}(25, \cdot)\) |
693.2.bw.a |
736 |
8 |
693.2.bx |
\(\chi_{693}(4, \cdot)\) |
693.2.bx.a |
736 |
8 |
693.2.by |
\(\chi_{693}(37, \cdot)\) |
693.2.by.a |
8 |
8 |
693.2.by.b |
40 |
693.2.by.c |
64 |
693.2.by.d |
64 |
693.2.by.e |
128 |
693.2.bz |
\(\chi_{693}(148, \cdot)\) |
693.2.bz.a |
288 |
8 |
693.2.bz.b |
288 |
693.2.cb |
\(\chi_{693}(74, \cdot)\) |
693.2.cb.a |
736 |
8 |
693.2.ce |
\(\chi_{693}(47, \cdot)\) |
693.2.ce.a |
736 |
8 |
693.2.cg |
\(\chi_{693}(19, \cdot)\) |
693.2.cg.a |
48 |
8 |
693.2.cg.b |
128 |
693.2.cg.c |
128 |
693.2.ch |
\(\chi_{693}(13, \cdot)\) |
693.2.ch.a |
736 |
8 |
693.2.cj |
\(\chi_{693}(20, \cdot)\) |
693.2.cj.a |
736 |
8 |
693.2.cm |
\(\chi_{693}(26, \cdot)\) |
693.2.cm.a |
256 |
8 |
693.2.co |
\(\chi_{693}(61, \cdot)\) |
693.2.co.a |
736 |
8 |
693.2.cq |
\(\chi_{693}(29, \cdot)\) |
693.2.cq.a |
576 |
8 |
693.2.ct |
\(\chi_{693}(107, \cdot)\) |
693.2.ct.a |
256 |
8 |
693.2.cx |
\(\chi_{693}(2, \cdot)\) |
693.2.cx.a |
736 |
8 |
693.2.cz |
\(\chi_{693}(40, \cdot)\) |
693.2.cz.a |
736 |
8 |
693.2.db |
\(\chi_{693}(5, \cdot)\) |
693.2.db.a |
736 |
8 |