Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2464))\).
|
Total |
New |
Old |
Modular forms
| 188160 |
98604 |
89556 |
Cusp forms
| 180481 |
96804 |
83677 |
Eisenstein series
| 7679 |
1800 |
5879 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2464))\)
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 |
2464.2.a |
\(\chi_{2464}(1, \cdot)\) |
2464.2.a.a |
1 |
1 |
2464.2.a.b |
1 |
2464.2.a.c |
1 |
2464.2.a.d |
1 |
2464.2.a.e |
1 |
2464.2.a.f |
1 |
2464.2.a.g |
1 |
2464.2.a.h |
1 |
2464.2.a.i |
1 |
2464.2.a.j |
1 |
2464.2.a.k |
1 |
2464.2.a.l |
1 |
2464.2.a.m |
2 |
2464.2.a.n |
2 |
2464.2.a.o |
2 |
2464.2.a.p |
2 |
2464.2.a.q |
3 |
2464.2.a.r |
3 |
2464.2.a.s |
4 |
2464.2.a.t |
4 |
2464.2.a.u |
4 |
2464.2.a.v |
4 |
2464.2.a.w |
4 |
2464.2.a.x |
4 |
2464.2.a.y |
5 |
2464.2.a.z |
5 |
2464.2.c |
\(\chi_{2464}(1233, \cdot)\) |
2464.2.c.a |
2 |
1 |
2464.2.c.b |
4 |
2464.2.c.c |
24 |
2464.2.c.d |
30 |
2464.2.e |
\(\chi_{2464}(769, \cdot)\) |
2464.2.e.a |
8 |
1 |
2464.2.e.b |
8 |
2464.2.e.c |
16 |
2464.2.e.d |
16 |
2464.2.e.e |
48 |
2464.2.f |
\(\chi_{2464}(351, \cdot)\) |
2464.2.f.a |
36 |
1 |
2464.2.f.b |
36 |
2464.2.h |
\(\chi_{2464}(111, \cdot)\) |
2464.2.h.a |
40 |
1 |
2464.2.h.b |
40 |
2464.2.j |
\(\chi_{2464}(1343, \cdot)\) |
2464.2.j.a |
8 |
1 |
2464.2.j.b |
32 |
2464.2.j.c |
40 |
2464.2.l |
\(\chi_{2464}(1583, \cdot)\) |
2464.2.l.a |
2 |
1 |
2464.2.l.b |
2 |
2464.2.l.c |
34 |
2464.2.l.d |
34 |
2464.2.o |
\(\chi_{2464}(2001, \cdot)\) |
2464.2.o.a |
2 |
1 |
2464.2.o.b |
2 |
2464.2.o.c |
88 |
2464.2.q |
\(\chi_{2464}(1409, \cdot)\) |
n/a |
160 |
2 |
2464.2.r |
\(\chi_{2464}(967, \cdot)\) |
None |
0 |
2 |
2464.2.s |
\(\chi_{2464}(727, \cdot)\) |
None |
0 |
2 |
2464.2.x |
\(\chi_{2464}(153, \cdot)\) |
None |
0 |
2 |
2464.2.y |
\(\chi_{2464}(617, \cdot)\) |
None |
0 |
2 |
2464.2.z |
\(\chi_{2464}(225, \cdot)\) |
n/a |
288 |
4 |
2464.2.ba |
\(\chi_{2464}(241, \cdot)\) |
n/a |
184 |
2 |
2464.2.be |
\(\chi_{2464}(2047, \cdot)\) |
n/a |
160 |
2 |
2464.2.bg |
\(\chi_{2464}(527, \cdot)\) |
n/a |
184 |
2 |
2464.2.bi |
\(\chi_{2464}(1759, \cdot)\) |
n/a |
192 |
2 |
2464.2.bk |
\(\chi_{2464}(815, \cdot)\) |
n/a |
160 |
2 |
2464.2.bl |
\(\chi_{2464}(177, \cdot)\) |
n/a |
160 |
2 |
2464.2.bn |
\(\chi_{2464}(1473, \cdot)\) |
n/a |
192 |
2 |
2464.2.bp |
\(\chi_{2464}(461, \cdot)\) |
n/a |
1520 |
4 |
2464.2.bq |
\(\chi_{2464}(309, \cdot)\) |
n/a |
960 |
4 |
2464.2.bv |
\(\chi_{2464}(43, \cdot)\) |
n/a |
1152 |
4 |
2464.2.bw |
\(\chi_{2464}(419, \cdot)\) |
n/a |
1280 |
4 |
2464.2.by |
\(\chi_{2464}(657, \cdot)\) |
n/a |
368 |
4 |
2464.2.cb |
\(\chi_{2464}(239, \cdot)\) |
n/a |
288 |
4 |
2464.2.cd |
\(\chi_{2464}(223, \cdot)\) |
n/a |
384 |
4 |
2464.2.cf |
\(\chi_{2464}(335, \cdot)\) |
n/a |
368 |
4 |
2464.2.ch |
\(\chi_{2464}(127, \cdot)\) |
n/a |
288 |
4 |
2464.2.ci |
\(\chi_{2464}(321, \cdot)\) |
n/a |
384 |
4 |
2464.2.ck |
\(\chi_{2464}(113, \cdot)\) |
n/a |
288 |
4 |
2464.2.co |
\(\chi_{2464}(199, \cdot)\) |
None |
0 |
4 |
2464.2.cp |
\(\chi_{2464}(263, \cdot)\) |
None |
0 |
4 |
2464.2.cq |
\(\chi_{2464}(793, \cdot)\) |
None |
0 |
4 |
2464.2.cr |
\(\chi_{2464}(857, \cdot)\) |
None |
0 |
4 |
2464.2.cu |
\(\chi_{2464}(289, \cdot)\) |
n/a |
768 |
8 |
2464.2.cv |
\(\chi_{2464}(169, \cdot)\) |
None |
0 |
8 |
2464.2.cw |
\(\chi_{2464}(41, \cdot)\) |
None |
0 |
8 |
2464.2.db |
\(\chi_{2464}(279, \cdot)\) |
None |
0 |
8 |
2464.2.dc |
\(\chi_{2464}(183, \cdot)\) |
None |
0 |
8 |
2464.2.df |
\(\chi_{2464}(221, \cdot)\) |
n/a |
2560 |
8 |
2464.2.dg |
\(\chi_{2464}(285, \cdot)\) |
n/a |
3040 |
8 |
2464.2.dh |
\(\chi_{2464}(243, \cdot)\) |
n/a |
2560 |
8 |
2464.2.di |
\(\chi_{2464}(219, \cdot)\) |
n/a |
3040 |
8 |
2464.2.dm |
\(\chi_{2464}(129, \cdot)\) |
n/a |
768 |
8 |
2464.2.do |
\(\chi_{2464}(81, \cdot)\) |
n/a |
736 |
8 |
2464.2.dp |
\(\chi_{2464}(47, \cdot)\) |
n/a |
736 |
8 |
2464.2.dr |
\(\chi_{2464}(95, \cdot)\) |
n/a |
768 |
8 |
2464.2.dt |
\(\chi_{2464}(79, \cdot)\) |
n/a |
736 |
8 |
2464.2.dv |
\(\chi_{2464}(31, \cdot)\) |
n/a |
768 |
8 |
2464.2.dz |
\(\chi_{2464}(17, \cdot)\) |
n/a |
736 |
8 |
2464.2.ea |
\(\chi_{2464}(27, \cdot)\) |
n/a |
6080 |
16 |
2464.2.eb |
\(\chi_{2464}(211, \cdot)\) |
n/a |
4608 |
16 |
2464.2.eg |
\(\chi_{2464}(141, \cdot)\) |
n/a |
4608 |
16 |
2464.2.eh |
\(\chi_{2464}(13, \cdot)\) |
n/a |
6080 |
16 |
2464.2.ek |
\(\chi_{2464}(73, \cdot)\) |
None |
0 |
16 |
2464.2.el |
\(\chi_{2464}(9, \cdot)\) |
None |
0 |
16 |
2464.2.em |
\(\chi_{2464}(39, \cdot)\) |
None |
0 |
16 |
2464.2.en |
\(\chi_{2464}(103, \cdot)\) |
None |
0 |
16 |
2464.2.es |
\(\chi_{2464}(51, \cdot)\) |
n/a |
12160 |
32 |
2464.2.et |
\(\chi_{2464}(3, \cdot)\) |
n/a |
12160 |
32 |
2464.2.eu |
\(\chi_{2464}(61, \cdot)\) |
n/a |
12160 |
32 |
2464.2.ev |
\(\chi_{2464}(37, \cdot)\) |
n/a |
12160 |
32 |
"n/a" means that newforms for that character have not been added to the database yet