Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2240))\).
|
Total |
New |
Old |
Modular forms
| 150912 |
73524 |
77388 |
Cusp forms
| 144001 |
72204 |
71797 |
Eisenstein series
| 6911 |
1320 |
5591 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2240))\)
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 |
2240.2.a |
\(\chi_{2240}(1, \cdot)\) |
2240.2.a.a |
1 |
1 |
2240.2.a.b |
1 |
2240.2.a.c |
1 |
2240.2.a.d |
1 |
2240.2.a.e |
1 |
2240.2.a.f |
1 |
2240.2.a.g |
1 |
2240.2.a.h |
1 |
2240.2.a.i |
1 |
2240.2.a.j |
1 |
2240.2.a.k |
1 |
2240.2.a.l |
1 |
2240.2.a.m |
1 |
2240.2.a.n |
1 |
2240.2.a.o |
1 |
2240.2.a.p |
1 |
2240.2.a.q |
1 |
2240.2.a.r |
1 |
2240.2.a.s |
1 |
2240.2.a.t |
1 |
2240.2.a.u |
1 |
2240.2.a.v |
1 |
2240.2.a.w |
1 |
2240.2.a.x |
1 |
2240.2.a.y |
1 |
2240.2.a.z |
1 |
2240.2.a.ba |
1 |
2240.2.a.bb |
1 |
2240.2.a.bc |
2 |
2240.2.a.bd |
2 |
2240.2.a.be |
2 |
2240.2.a.bf |
2 |
2240.2.a.bg |
2 |
2240.2.a.bh |
2 |
2240.2.a.bi |
2 |
2240.2.a.bj |
2 |
2240.2.a.bk |
2 |
2240.2.a.bl |
2 |
2240.2.b |
\(\chi_{2240}(1121, \cdot)\) |
2240.2.b.a |
2 |
1 |
2240.2.b.b |
2 |
2240.2.b.c |
4 |
2240.2.b.d |
4 |
2240.2.b.e |
6 |
2240.2.b.f |
6 |
2240.2.b.g |
12 |
2240.2.b.h |
12 |
2240.2.e |
\(\chi_{2240}(2239, \cdot)\) |
2240.2.e.a |
4 |
1 |
2240.2.e.b |
4 |
2240.2.e.c |
4 |
2240.2.e.d |
8 |
2240.2.e.e |
8 |
2240.2.e.f |
16 |
2240.2.e.g |
48 |
2240.2.g |
\(\chi_{2240}(449, \cdot)\) |
2240.2.g.a |
2 |
1 |
2240.2.g.b |
2 |
2240.2.g.c |
2 |
2240.2.g.d |
2 |
2240.2.g.e |
2 |
2240.2.g.f |
2 |
2240.2.g.g |
2 |
2240.2.g.h |
2 |
2240.2.g.i |
4 |
2240.2.g.j |
4 |
2240.2.g.k |
4 |
2240.2.g.l |
6 |
2240.2.g.m |
6 |
2240.2.g.n |
10 |
2240.2.g.o |
10 |
2240.2.g.p |
12 |
2240.2.h |
\(\chi_{2240}(671, \cdot)\) |
2240.2.h.a |
4 |
1 |
2240.2.h.b |
4 |
2240.2.h.c |
4 |
2240.2.h.d |
4 |
2240.2.h.e |
24 |
2240.2.h.f |
24 |
2240.2.k |
\(\chi_{2240}(1791, \cdot)\) |
2240.2.k.a |
4 |
1 |
2240.2.k.b |
4 |
2240.2.k.c |
8 |
2240.2.k.d |
8 |
2240.2.k.e |
8 |
2240.2.k.f |
16 |
2240.2.k.g |
16 |
2240.2.l |
\(\chi_{2240}(1569, \cdot)\) |
2240.2.l.a |
12 |
1 |
2240.2.l.b |
12 |
2240.2.l.c |
24 |
2240.2.l.d |
24 |
2240.2.n |
\(\chi_{2240}(1119, \cdot)\) |
2240.2.n.a |
8 |
1 |
2240.2.n.b |
8 |
2240.2.n.c |
8 |
2240.2.n.d |
8 |
2240.2.n.e |
8 |
2240.2.n.f |
8 |
2240.2.n.g |
8 |
2240.2.n.h |
8 |
2240.2.n.i |
16 |
2240.2.n.j |
16 |
2240.2.q |
\(\chi_{2240}(641, \cdot)\) |
n/a |
128 |
2 |
2240.2.r |
\(\chi_{2240}(433, \cdot)\) |
n/a |
184 |
2 |
2240.2.t |
\(\chi_{2240}(463, \cdot)\) |
n/a |
144 |
2 |
2240.2.w |
\(\chi_{2240}(97, \cdot)\) |
n/a |
192 |
2 |
2240.2.x |
\(\chi_{2240}(127, \cdot)\) |
n/a |
144 |
2 |
2240.2.bb |
\(\chi_{2240}(1009, \cdot)\) |
n/a |
144 |
2 |
2240.2.bc |
\(\chi_{2240}(111, \cdot)\) |
n/a |
128 |
2 |
2240.2.bd |
\(\chi_{2240}(561, \cdot)\) |
2240.2.bd.a |
44 |
2 |
2240.2.bd.b |
52 |
2240.2.be |
\(\chi_{2240}(559, \cdot)\) |
n/a |
184 |
2 |
2240.2.bi |
\(\chi_{2240}(1247, \cdot)\) |
n/a |
144 |
2 |
2240.2.bj |
\(\chi_{2240}(1217, \cdot)\) |
n/a |
184 |
2 |
2240.2.bl |
\(\chi_{2240}(1583, \cdot)\) |
n/a |
144 |
2 |
2240.2.bn |
\(\chi_{2240}(1553, \cdot)\) |
n/a |
184 |
2 |
2240.2.bq |
\(\chi_{2240}(159, \cdot)\) |
n/a |
192 |
2 |
2240.2.bs |
\(\chi_{2240}(831, \cdot)\) |
n/a |
128 |
2 |
2240.2.bv |
\(\chi_{2240}(289, \cdot)\) |
n/a |
192 |
2 |
2240.2.bw |
\(\chi_{2240}(1089, \cdot)\) |
n/a |
184 |
2 |
2240.2.bz |
\(\chi_{2240}(31, \cdot)\) |
n/a |
128 |
2 |
2240.2.cb |
\(\chi_{2240}(1761, \cdot)\) |
n/a |
128 |
2 |
2240.2.cc |
\(\chi_{2240}(1279, \cdot)\) |
n/a |
184 |
2 |
2240.2.cg |
\(\chi_{2240}(281, \cdot)\) |
None |
0 |
4 |
2240.2.ch |
\(\chi_{2240}(279, \cdot)\) |
None |
0 |
4 |
2240.2.ci |
\(\chi_{2240}(377, \cdot)\) |
None |
0 |
4 |
2240.2.cj |
\(\chi_{2240}(407, \cdot)\) |
None |
0 |
4 |
2240.2.cm |
\(\chi_{2240}(183, \cdot)\) |
None |
0 |
4 |
2240.2.cn |
\(\chi_{2240}(153, \cdot)\) |
None |
0 |
4 |
2240.2.cs |
\(\chi_{2240}(391, \cdot)\) |
None |
0 |
4 |
2240.2.ct |
\(\chi_{2240}(169, \cdot)\) |
None |
0 |
4 |
2240.2.cv |
\(\chi_{2240}(207, \cdot)\) |
n/a |
368 |
4 |
2240.2.cx |
\(\chi_{2240}(593, \cdot)\) |
n/a |
368 |
4 |
2240.2.cy |
\(\chi_{2240}(257, \cdot)\) |
n/a |
368 |
4 |
2240.2.db |
\(\chi_{2240}(543, \cdot)\) |
n/a |
384 |
4 |
2240.2.de |
\(\chi_{2240}(719, \cdot)\) |
n/a |
368 |
4 |
2240.2.df |
\(\chi_{2240}(81, \cdot)\) |
n/a |
256 |
4 |
2240.2.dg |
\(\chi_{2240}(271, \cdot)\) |
n/a |
256 |
4 |
2240.2.dh |
\(\chi_{2240}(529, \cdot)\) |
n/a |
368 |
4 |
2240.2.dk |
\(\chi_{2240}(767, \cdot)\) |
n/a |
368 |
4 |
2240.2.dn |
\(\chi_{2240}(33, \cdot)\) |
n/a |
384 |
4 |
2240.2.dp |
\(\chi_{2240}(17, \cdot)\) |
n/a |
368 |
4 |
2240.2.dr |
\(\chi_{2240}(1103, \cdot)\) |
n/a |
368 |
4 |
2240.2.du |
\(\chi_{2240}(13, \cdot)\) |
n/a |
3040 |
8 |
2240.2.dv |
\(\chi_{2240}(43, \cdot)\) |
n/a |
2304 |
8 |
2240.2.dw |
\(\chi_{2240}(139, \cdot)\) |
n/a |
3040 |
8 |
2240.2.dx |
\(\chi_{2240}(141, \cdot)\) |
n/a |
1536 |
8 |
2240.2.dy |
\(\chi_{2240}(251, \cdot)\) |
n/a |
2048 |
8 |
2240.2.dz |
\(\chi_{2240}(29, \cdot)\) |
n/a |
2304 |
8 |
2240.2.eg |
\(\chi_{2240}(267, \cdot)\) |
n/a |
2304 |
8 |
2240.2.eh |
\(\chi_{2240}(237, \cdot)\) |
n/a |
3040 |
8 |
2240.2.ei |
\(\chi_{2240}(9, \cdot)\) |
None |
0 |
8 |
2240.2.ej |
\(\chi_{2240}(311, \cdot)\) |
None |
0 |
8 |
2240.2.eo |
\(\chi_{2240}(23, \cdot)\) |
None |
0 |
8 |
2240.2.ep |
\(\chi_{2240}(297, \cdot)\) |
None |
0 |
8 |
2240.2.es |
\(\chi_{2240}(73, \cdot)\) |
None |
0 |
8 |
2240.2.et |
\(\chi_{2240}(247, \cdot)\) |
None |
0 |
8 |
2240.2.eu |
\(\chi_{2240}(199, \cdot)\) |
None |
0 |
8 |
2240.2.ev |
\(\chi_{2240}(121, \cdot)\) |
None |
0 |
8 |
2240.2.ey |
\(\chi_{2240}(157, \cdot)\) |
n/a |
6080 |
16 |
2240.2.ez |
\(\chi_{2240}(107, \cdot)\) |
n/a |
6080 |
16 |
2240.2.fg |
\(\chi_{2240}(109, \cdot)\) |
n/a |
6080 |
16 |
2240.2.fh |
\(\chi_{2240}(131, \cdot)\) |
n/a |
4096 |
16 |
2240.2.fi |
\(\chi_{2240}(221, \cdot)\) |
n/a |
4096 |
16 |
2240.2.fj |
\(\chi_{2240}(19, \cdot)\) |
n/a |
6080 |
16 |
2240.2.fk |
\(\chi_{2240}(67, \cdot)\) |
n/a |
6080 |
16 |
2240.2.fl |
\(\chi_{2240}(117, \cdot)\) |
n/a |
6080 |
16 |
"n/a" means that newforms for that character have not been added to the database yet