Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1480))\).
|
Total |
New |
Old |
Modular forms
| 67392 |
34228 |
33164 |
Cusp forms
| 63937 |
33388 |
30549 |
Eisenstein series
| 3455 |
840 |
2615 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1480))\)
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 |
1480.2.a |
\(\chi_{1480}(1, \cdot)\) |
1480.2.a.a |
1 |
1 |
1480.2.a.b |
1 |
1480.2.a.c |
1 |
1480.2.a.d |
1 |
1480.2.a.e |
3 |
1480.2.a.f |
3 |
1480.2.a.g |
5 |
1480.2.a.h |
5 |
1480.2.a.i |
5 |
1480.2.a.j |
5 |
1480.2.a.k |
6 |
1480.2.d |
\(\chi_{1480}(889, \cdot)\) |
1480.2.d.a |
2 |
1 |
1480.2.d.b |
20 |
1480.2.d.c |
32 |
1480.2.e |
\(\chi_{1480}(369, \cdot)\) |
1480.2.e.a |
4 |
1 |
1480.2.e.b |
4 |
1480.2.e.c |
24 |
1480.2.e.d |
24 |
1480.2.f |
\(\chi_{1480}(741, \cdot)\) |
n/a |
144 |
1 |
1480.2.g |
\(\chi_{1480}(221, \cdot)\) |
n/a |
152 |
1 |
1480.2.j |
\(\chi_{1480}(1109, \cdot)\) |
n/a |
224 |
1 |
1480.2.k |
\(\chi_{1480}(149, \cdot)\) |
n/a |
216 |
1 |
1480.2.p |
\(\chi_{1480}(961, \cdot)\) |
1480.2.p.a |
2 |
1 |
1480.2.p.b |
4 |
1480.2.p.c |
12 |
1480.2.p.d |
20 |
1480.2.q |
\(\chi_{1480}(121, \cdot)\) |
1480.2.q.a |
18 |
2 |
1480.2.q.b |
18 |
1480.2.q.c |
20 |
1480.2.q.d |
20 |
1480.2.r |
\(\chi_{1480}(771, \cdot)\) |
n/a |
304 |
2 |
1480.2.u |
\(\chi_{1480}(919, \cdot)\) |
None |
0 |
2 |
1480.2.w |
\(\chi_{1480}(697, \cdot)\) |
n/a |
114 |
2 |
1480.2.y |
\(\chi_{1480}(887, \cdot)\) |
None |
0 |
2 |
1480.2.ba |
\(\chi_{1480}(223, \cdot)\) |
None |
0 |
2 |
1480.2.bb |
\(\chi_{1480}(857, \cdot)\) |
n/a |
114 |
2 |
1480.2.bd |
\(\chi_{1480}(117, \cdot)\) |
n/a |
448 |
2 |
1480.2.bf |
\(\chi_{1480}(667, \cdot)\) |
n/a |
432 |
2 |
1480.2.bh |
\(\chi_{1480}(147, \cdot)\) |
n/a |
448 |
2 |
1480.2.bk |
\(\chi_{1480}(413, \cdot)\) |
n/a |
448 |
2 |
1480.2.bm |
\(\chi_{1480}(31, \cdot)\) |
None |
0 |
2 |
1480.2.bn |
\(\chi_{1480}(179, \cdot)\) |
n/a |
448 |
2 |
1480.2.br |
\(\chi_{1480}(841, \cdot)\) |
1480.2.br.a |
36 |
2 |
1480.2.br.b |
40 |
1480.2.bs |
\(\chi_{1480}(269, \cdot)\) |
n/a |
448 |
2 |
1480.2.bt |
\(\chi_{1480}(989, \cdot)\) |
n/a |
448 |
2 |
1480.2.bw |
\(\chi_{1480}(101, \cdot)\) |
n/a |
304 |
2 |
1480.2.bx |
\(\chi_{1480}(581, \cdot)\) |
n/a |
304 |
2 |
1480.2.cc |
\(\chi_{1480}(249, \cdot)\) |
n/a |
112 |
2 |
1480.2.cd |
\(\chi_{1480}(729, \cdot)\) |
n/a |
116 |
2 |
1480.2.ce |
\(\chi_{1480}(81, \cdot)\) |
n/a |
228 |
6 |
1480.2.cf |
\(\chi_{1480}(859, \cdot)\) |
n/a |
896 |
4 |
1480.2.ci |
\(\chi_{1480}(711, \cdot)\) |
None |
0 |
4 |
1480.2.ck |
\(\chi_{1480}(97, \cdot)\) |
n/a |
228 |
4 |
1480.2.cl |
\(\chi_{1480}(47, \cdot)\) |
None |
0 |
4 |
1480.2.cn |
\(\chi_{1480}(767, \cdot)\) |
None |
0 |
4 |
1480.2.cp |
\(\chi_{1480}(177, \cdot)\) |
n/a |
228 |
4 |
1480.2.cr |
\(\chi_{1480}(717, \cdot)\) |
n/a |
896 |
4 |
1480.2.cu |
\(\chi_{1480}(27, \cdot)\) |
n/a |
896 |
4 |
1480.2.cw |
\(\chi_{1480}(507, \cdot)\) |
n/a |
896 |
4 |
1480.2.cy |
\(\chi_{1480}(637, \cdot)\) |
n/a |
896 |
4 |
1480.2.da |
\(\chi_{1480}(119, \cdot)\) |
None |
0 |
4 |
1480.2.db |
\(\chi_{1480}(51, \cdot)\) |
n/a |
608 |
4 |
1480.2.df |
\(\chi_{1480}(169, \cdot)\) |
n/a |
336 |
6 |
1480.2.dg |
\(\chi_{1480}(41, \cdot)\) |
n/a |
228 |
6 |
1480.2.di |
\(\chi_{1480}(9, \cdot)\) |
n/a |
348 |
6 |
1480.2.dk |
\(\chi_{1480}(189, \cdot)\) |
n/a |
1344 |
6 |
1480.2.dm |
\(\chi_{1480}(181, \cdot)\) |
n/a |
912 |
6 |
1480.2.dp |
\(\chi_{1480}(229, \cdot)\) |
n/a |
1344 |
6 |
1480.2.dr |
\(\chi_{1480}(21, \cdot)\) |
n/a |
912 |
6 |
1480.2.ds |
\(\chi_{1480}(533, \cdot)\) |
n/a |
2688 |
12 |
1480.2.dv |
\(\chi_{1480}(311, \cdot)\) |
None |
0 |
12 |
1480.2.dw |
\(\chi_{1480}(83, \cdot)\) |
n/a |
2688 |
12 |
1480.2.dz |
\(\chi_{1480}(3, \cdot)\) |
n/a |
2688 |
12 |
1480.2.ea |
\(\chi_{1480}(39, \cdot)\) |
None |
0 |
12 |
1480.2.ed |
\(\chi_{1480}(13, \cdot)\) |
n/a |
2688 |
12 |
1480.2.ef |
\(\chi_{1480}(17, \cdot)\) |
n/a |
684 |
12 |
1480.2.eg |
\(\chi_{1480}(19, \cdot)\) |
n/a |
2688 |
12 |
1480.2.ei |
\(\chi_{1480}(247, \cdot)\) |
None |
0 |
12 |
1480.2.el |
\(\chi_{1480}(7, \cdot)\) |
None |
0 |
12 |
1480.2.en |
\(\chi_{1480}(91, \cdot)\) |
n/a |
1824 |
12 |
1480.2.eo |
\(\chi_{1480}(57, \cdot)\) |
n/a |
684 |
12 |
"n/a" means that newforms for that character have not been added to the database yet