Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1248))\).
|
Total |
New |
Old |
Modular forms
| 44544 |
18148 |
26396 |
Cusp forms
| 41473 |
17708 |
23765 |
Eisenstein series
| 3071 |
440 |
2631 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1248))\)
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 |
1248.2.a |
\(\chi_{1248}(1, \cdot)\) |
1248.2.a.a |
1 |
1 |
1248.2.a.b |
1 |
1248.2.a.c |
1 |
1248.2.a.d |
1 |
1248.2.a.e |
1 |
1248.2.a.f |
1 |
1248.2.a.g |
1 |
1248.2.a.h |
1 |
1248.2.a.i |
1 |
1248.2.a.j |
1 |
1248.2.a.k |
2 |
1248.2.a.l |
2 |
1248.2.a.m |
2 |
1248.2.a.n |
2 |
1248.2.a.o |
3 |
1248.2.a.p |
3 |
1248.2.c |
\(\chi_{1248}(961, \cdot)\) |
1248.2.c.a |
6 |
1 |
1248.2.c.b |
6 |
1248.2.c.c |
8 |
1248.2.c.d |
8 |
1248.2.d |
\(\chi_{1248}(287, \cdot)\) |
1248.2.d.a |
4 |
1 |
1248.2.d.b |
8 |
1248.2.d.c |
16 |
1248.2.d.d |
20 |
1248.2.g |
\(\chi_{1248}(625, \cdot)\) |
1248.2.g.a |
8 |
1 |
1248.2.g.b |
16 |
1248.2.h |
\(\chi_{1248}(623, \cdot)\) |
1248.2.h.a |
8 |
1 |
1248.2.h.b |
12 |
1248.2.h.c |
32 |
1248.2.j |
\(\chi_{1248}(911, \cdot)\) |
1248.2.j.a |
48 |
1 |
1248.2.m |
\(\chi_{1248}(337, \cdot)\) |
1248.2.m.a |
2 |
1 |
1248.2.m.b |
2 |
1248.2.m.c |
24 |
1248.2.n |
\(\chi_{1248}(1247, \cdot)\) |
1248.2.n.a |
4 |
1 |
1248.2.n.b |
4 |
1248.2.n.c |
4 |
1248.2.n.d |
4 |
1248.2.n.e |
40 |
1248.2.q |
\(\chi_{1248}(289, \cdot)\) |
1248.2.q.a |
2 |
2 |
1248.2.q.b |
2 |
1248.2.q.c |
2 |
1248.2.q.d |
2 |
1248.2.q.e |
2 |
1248.2.q.f |
2 |
1248.2.q.g |
4 |
1248.2.q.h |
4 |
1248.2.q.i |
4 |
1248.2.q.j |
4 |
1248.2.q.k |
6 |
1248.2.q.l |
6 |
1248.2.q.m |
8 |
1248.2.q.n |
8 |
1248.2.r |
\(\chi_{1248}(343, \cdot)\) |
None |
0 |
2 |
1248.2.u |
\(\chi_{1248}(473, \cdot)\) |
None |
0 |
2 |
1248.2.v |
\(\chi_{1248}(311, \cdot)\) |
None |
0 |
2 |
1248.2.x |
\(\chi_{1248}(313, \cdot)\) |
None |
0 |
2 |
1248.2.bb |
\(\chi_{1248}(463, \cdot)\) |
1248.2.bb.a |
2 |
2 |
1248.2.bb.b |
2 |
1248.2.bb.c |
2 |
1248.2.bb.d |
2 |
1248.2.bb.e |
24 |
1248.2.bb.f |
24 |
1248.2.bc |
\(\chi_{1248}(31, \cdot)\) |
1248.2.bc.a |
2 |
2 |
1248.2.bc.b |
2 |
1248.2.bc.c |
2 |
1248.2.bc.d |
2 |
1248.2.bc.e |
2 |
1248.2.bc.f |
2 |
1248.2.bc.g |
2 |
1248.2.bc.h |
2 |
1248.2.bc.i |
2 |
1248.2.bc.j |
2 |
1248.2.bc.k |
2 |
1248.2.bc.l |
2 |
1248.2.bc.m |
2 |
1248.2.bc.n |
2 |
1248.2.bc.o |
4 |
1248.2.bc.p |
4 |
1248.2.bc.q |
4 |
1248.2.bc.r |
4 |
1248.2.bc.s |
6 |
1248.2.bc.t |
6 |
1248.2.bf |
\(\chi_{1248}(161, \cdot)\) |
n/a |
112 |
2 |
1248.2.bg |
\(\chi_{1248}(593, \cdot)\) |
n/a |
104 |
2 |
1248.2.bh |
\(\chi_{1248}(599, \cdot)\) |
None |
0 |
2 |
1248.2.bj |
\(\chi_{1248}(25, \cdot)\) |
None |
0 |
2 |
1248.2.bm |
\(\chi_{1248}(281, \cdot)\) |
None |
0 |
2 |
1248.2.bn |
\(\chi_{1248}(151, \cdot)\) |
None |
0 |
2 |
1248.2.bq |
\(\chi_{1248}(335, \cdot)\) |
n/a |
104 |
2 |
1248.2.br |
\(\chi_{1248}(529, \cdot)\) |
1248.2.br.a |
56 |
2 |
1248.2.bu |
\(\chi_{1248}(191, \cdot)\) |
n/a |
112 |
2 |
1248.2.bv |
\(\chi_{1248}(673, \cdot)\) |
1248.2.bv.a |
12 |
2 |
1248.2.bv.b |
12 |
1248.2.bv.c |
16 |
1248.2.bv.d |
16 |
1248.2.bz |
\(\chi_{1248}(95, \cdot)\) |
n/a |
112 |
2 |
1248.2.ca |
\(\chi_{1248}(49, \cdot)\) |
1248.2.ca.a |
8 |
2 |
1248.2.ca.b |
48 |
1248.2.cd |
\(\chi_{1248}(815, \cdot)\) |
n/a |
104 |
2 |
1248.2.cf |
\(\chi_{1248}(5, \cdot)\) |
n/a |
880 |
4 |
1248.2.ch |
\(\chi_{1248}(499, \cdot)\) |
n/a |
448 |
4 |
1248.2.ci |
\(\chi_{1248}(181, \cdot)\) |
n/a |
448 |
4 |
1248.2.ck |
\(\chi_{1248}(157, \cdot)\) |
n/a |
384 |
4 |
1248.2.cn |
\(\chi_{1248}(131, \cdot)\) |
n/a |
768 |
4 |
1248.2.cp |
\(\chi_{1248}(155, \cdot)\) |
n/a |
880 |
4 |
1248.2.cq |
\(\chi_{1248}(317, \cdot)\) |
n/a |
880 |
4 |
1248.2.cs |
\(\chi_{1248}(187, \cdot)\) |
n/a |
448 |
4 |
1248.2.cu |
\(\chi_{1248}(137, \cdot)\) |
None |
0 |
4 |
1248.2.cx |
\(\chi_{1248}(7, \cdot)\) |
None |
0 |
4 |
1248.2.cz |
\(\chi_{1248}(121, \cdot)\) |
None |
0 |
4 |
1248.2.db |
\(\chi_{1248}(263, \cdot)\) |
None |
0 |
4 |
1248.2.dc |
\(\chi_{1248}(305, \cdot)\) |
n/a |
208 |
4 |
1248.2.dd |
\(\chi_{1248}(353, \cdot)\) |
n/a |
224 |
4 |
1248.2.dg |
\(\chi_{1248}(223, \cdot)\) |
n/a |
112 |
4 |
1248.2.dh |
\(\chi_{1248}(175, \cdot)\) |
n/a |
112 |
4 |
1248.2.dl |
\(\chi_{1248}(217, \cdot)\) |
None |
0 |
4 |
1248.2.dn |
\(\chi_{1248}(23, \cdot)\) |
None |
0 |
4 |
1248.2.dp |
\(\chi_{1248}(487, \cdot)\) |
None |
0 |
4 |
1248.2.dq |
\(\chi_{1248}(41, \cdot)\) |
None |
0 |
4 |
1248.2.dt |
\(\chi_{1248}(115, \cdot)\) |
n/a |
896 |
8 |
1248.2.dv |
\(\chi_{1248}(245, \cdot)\) |
n/a |
1760 |
8 |
1248.2.dx |
\(\chi_{1248}(35, \cdot)\) |
n/a |
1760 |
8 |
1248.2.dz |
\(\chi_{1248}(179, \cdot)\) |
n/a |
1760 |
8 |
1248.2.ea |
\(\chi_{1248}(205, \cdot)\) |
n/a |
896 |
8 |
1248.2.ec |
\(\chi_{1248}(61, \cdot)\) |
n/a |
896 |
8 |
1248.2.ee |
\(\chi_{1248}(19, \cdot)\) |
n/a |
896 |
8 |
1248.2.eg |
\(\chi_{1248}(149, \cdot)\) |
n/a |
1760 |
8 |
"n/a" means that newforms for that character have not been added to the database yet