Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(925))\).
|
Total |
New |
Old |
Modular forms
| 35208 |
32193 |
3015 |
Cusp forms
| 33193 |
30759 |
2434 |
Eisenstein series
| 2015 |
1434 |
581 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(925))\)
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 |
925.2.a |
\(\chi_{925}(1, \cdot)\) |
925.2.a.a |
1 |
1 |
925.2.a.b |
1 |
925.2.a.c |
1 |
925.2.a.d |
1 |
925.2.a.e |
1 |
925.2.a.f |
5 |
925.2.a.g |
5 |
925.2.a.h |
5 |
925.2.a.i |
5 |
925.2.a.j |
7 |
925.2.a.k |
7 |
925.2.a.l |
9 |
925.2.a.m |
9 |
925.2.b |
\(\chi_{925}(149, \cdot)\) |
925.2.b.a |
2 |
1 |
925.2.b.b |
2 |
925.2.b.c |
2 |
925.2.b.d |
2 |
925.2.b.e |
2 |
925.2.b.f |
10 |
925.2.b.g |
10 |
925.2.b.h |
10 |
925.2.b.i |
14 |
925.2.c |
\(\chi_{925}(776, \cdot)\) |
925.2.c.a |
2 |
1 |
925.2.c.b |
2 |
925.2.c.c |
12 |
925.2.c.d |
12 |
925.2.c.e |
12 |
925.2.c.f |
16 |
925.2.d |
\(\chi_{925}(924, \cdot)\) |
925.2.d.a |
2 |
1 |
925.2.d.b |
2 |
925.2.d.c |
2 |
925.2.d.d |
2 |
925.2.d.e |
12 |
925.2.d.f |
12 |
925.2.d.g |
24 |
925.2.e |
\(\chi_{925}(26, \cdot)\) |
925.2.e.a |
2 |
2 |
925.2.e.b |
14 |
925.2.e.c |
14 |
925.2.e.d |
24 |
925.2.e.e |
24 |
925.2.e.f |
36 |
925.2.f |
\(\chi_{925}(43, \cdot)\) |
925.2.f.a |
2 |
2 |
925.2.f.b |
2 |
925.2.f.c |
6 |
925.2.f.d |
24 |
925.2.f.e |
28 |
925.2.f.f |
48 |
925.2.k |
\(\chi_{925}(68, \cdot)\) |
925.2.k.a |
2 |
2 |
925.2.k.b |
2 |
925.2.k.c |
6 |
925.2.k.d |
24 |
925.2.k.e |
28 |
925.2.k.f |
48 |
925.2.l |
\(\chi_{925}(186, \cdot)\) |
925.2.l.a |
4 |
4 |
925.2.l.b |
176 |
925.2.l.c |
180 |
925.2.m |
\(\chi_{925}(249, \cdot)\) |
925.2.m.a |
4 |
2 |
925.2.m.b |
4 |
925.2.m.c |
28 |
925.2.m.d |
28 |
925.2.m.e |
48 |
925.2.n |
\(\chi_{925}(101, \cdot)\) |
925.2.n.a |
4 |
2 |
925.2.n.b |
24 |
925.2.n.c |
24 |
925.2.n.d |
28 |
925.2.n.e |
32 |
925.2.o |
\(\chi_{925}(174, \cdot)\) |
925.2.o.a |
4 |
2 |
925.2.o.b |
28 |
925.2.o.c |
28 |
925.2.o.d |
48 |
925.2.p |
\(\chi_{925}(201, \cdot)\) |
925.2.p.a |
6 |
6 |
925.2.p.b |
6 |
925.2.p.c |
36 |
925.2.p.d |
36 |
925.2.p.e |
78 |
925.2.p.f |
78 |
925.2.p.g |
108 |
925.2.q |
\(\chi_{925}(184, \cdot)\) |
925.2.q.a |
368 |
4 |
925.2.r |
\(\chi_{925}(36, \cdot)\) |
925.2.r.a |
376 |
4 |
925.2.s |
\(\chi_{925}(334, \cdot)\) |
925.2.s.a |
360 |
4 |
925.2.t |
\(\chi_{925}(82, \cdot)\) |
925.2.t.a |
56 |
4 |
925.2.t.b |
68 |
925.2.t.c |
96 |
925.2.y |
\(\chi_{925}(193, \cdot)\) |
925.2.y.a |
56 |
4 |
925.2.y.b |
68 |
925.2.y.c |
96 |
925.2.z |
\(\chi_{925}(121, \cdot)\) |
925.2.z.a |
736 |
8 |
925.2.ba |
\(\chi_{925}(99, \cdot)\) |
925.2.ba.a |
36 |
6 |
925.2.ba.b |
72 |
925.2.ba.c |
72 |
925.2.ba.d |
156 |
925.2.bb |
\(\chi_{925}(151, \cdot)\) |
925.2.bb.a |
18 |
6 |
925.2.bb.b |
72 |
925.2.bb.c |
78 |
925.2.bb.d |
78 |
925.2.bb.e |
96 |
925.2.bc |
\(\chi_{925}(49, \cdot)\) |
925.2.bc.a |
12 |
6 |
925.2.bc.b |
12 |
925.2.bc.c |
72 |
925.2.bc.d |
72 |
925.2.bc.e |
156 |
925.2.bd |
\(\chi_{925}(117, \cdot)\) |
925.2.bd.a |
744 |
8 |
925.2.bi |
\(\chi_{925}(142, \cdot)\) |
925.2.bi.a |
744 |
8 |
925.2.bj |
\(\chi_{925}(84, \cdot)\) |
925.2.bj.a |
752 |
8 |
925.2.bk |
\(\chi_{925}(11, \cdot)\) |
925.2.bk.a |
752 |
8 |
925.2.bl |
\(\chi_{925}(64, \cdot)\) |
925.2.bl.a |
736 |
8 |
925.2.bn |
\(\chi_{925}(18, \cdot)\) |
925.2.bn.a |
144 |
12 |
925.2.bn.b |
204 |
925.2.bn.c |
312 |
925.2.bq |
\(\chi_{925}(32, \cdot)\) |
925.2.bq.a |
144 |
12 |
925.2.bq.b |
204 |
925.2.bq.c |
312 |
925.2.bs |
\(\chi_{925}(16, \cdot)\) |
925.2.bs.a |
2208 |
24 |
925.2.bt |
\(\chi_{925}(8, \cdot)\) |
925.2.bt.a |
1488 |
16 |
925.2.by |
\(\chi_{925}(88, \cdot)\) |
925.2.by.a |
1488 |
16 |
925.2.bz |
\(\chi_{925}(9, \cdot)\) |
925.2.bz.a |
2256 |
24 |
925.2.ca |
\(\chi_{925}(21, \cdot)\) |
925.2.ca.a |
2256 |
24 |
925.2.cb |
\(\chi_{925}(4, \cdot)\) |
925.2.cb.a |
2208 |
24 |
925.2.cd |
\(\chi_{925}(2, \cdot)\) |
925.2.cd.a |
4464 |
48 |
925.2.cg |
\(\chi_{925}(17, \cdot)\) |
925.2.cg.a |
4464 |
48 |