Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2880))\).
|
Total |
New |
Old |
Modular forms
| 225792 |
90882 |
134910 |
Cusp forms
| 216577 |
89694 |
126883 |
Eisenstein series
| 9215 |
1188 |
8027 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2880))\)
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 |
2880.2.a |
\(\chi_{2880}(1, \cdot)\) |
2880.2.a.a |
1 |
1 |
2880.2.a.b |
1 |
2880.2.a.c |
1 |
2880.2.a.d |
1 |
2880.2.a.e |
1 |
2880.2.a.f |
1 |
2880.2.a.g |
1 |
2880.2.a.h |
1 |
2880.2.a.i |
1 |
2880.2.a.j |
1 |
2880.2.a.k |
1 |
2880.2.a.l |
1 |
2880.2.a.m |
1 |
2880.2.a.n |
1 |
2880.2.a.o |
1 |
2880.2.a.p |
1 |
2880.2.a.q |
1 |
2880.2.a.r |
1 |
2880.2.a.s |
1 |
2880.2.a.t |
1 |
2880.2.a.u |
1 |
2880.2.a.v |
1 |
2880.2.a.w |
1 |
2880.2.a.x |
1 |
2880.2.a.y |
1 |
2880.2.a.z |
1 |
2880.2.a.ba |
1 |
2880.2.a.bb |
1 |
2880.2.a.bc |
1 |
2880.2.a.bd |
1 |
2880.2.a.be |
1 |
2880.2.a.bf |
1 |
2880.2.a.bg |
1 |
2880.2.a.bh |
1 |
2880.2.a.bi |
2 |
2880.2.a.bj |
2 |
2880.2.a.bk |
2 |
2880.2.b |
\(\chi_{2880}(2591, \cdot)\) |
2880.2.b.a |
8 |
1 |
2880.2.b.b |
8 |
2880.2.b.c |
8 |
2880.2.b.d |
8 |
2880.2.d |
\(\chi_{2880}(289, \cdot)\) |
2880.2.d.a |
2 |
1 |
2880.2.d.b |
2 |
2880.2.d.c |
2 |
2880.2.d.d |
2 |
2880.2.d.e |
4 |
2880.2.d.f |
8 |
2880.2.d.g |
8 |
2880.2.d.h |
8 |
2880.2.d.i |
8 |
2880.2.d.j |
8 |
2880.2.d.k |
8 |
2880.2.f |
\(\chi_{2880}(1729, \cdot)\) |
2880.2.f.a |
2 |
1 |
2880.2.f.b |
2 |
2880.2.f.c |
2 |
2880.2.f.d |
2 |
2880.2.f.e |
2 |
2880.2.f.f |
2 |
2880.2.f.g |
2 |
2880.2.f.h |
2 |
2880.2.f.i |
2 |
2880.2.f.j |
2 |
2880.2.f.k |
2 |
2880.2.f.l |
2 |
2880.2.f.m |
2 |
2880.2.f.n |
2 |
2880.2.f.o |
2 |
2880.2.f.p |
2 |
2880.2.f.q |
2 |
2880.2.f.r |
2 |
2880.2.f.s |
2 |
2880.2.f.t |
2 |
2880.2.f.u |
2 |
2880.2.f.v |
4 |
2880.2.f.w |
4 |
2880.2.f.x |
8 |
2880.2.h |
\(\chi_{2880}(1151, \cdot)\) |
2880.2.h.a |
4 |
1 |
2880.2.h.b |
4 |
2880.2.h.c |
4 |
2880.2.h.d |
4 |
2880.2.h.e |
8 |
2880.2.h.f |
8 |
2880.2.k |
\(\chi_{2880}(1441, \cdot)\) |
2880.2.k.a |
2 |
1 |
2880.2.k.b |
2 |
2880.2.k.c |
2 |
2880.2.k.d |
2 |
2880.2.k.e |
4 |
2880.2.k.f |
4 |
2880.2.k.g |
4 |
2880.2.k.h |
4 |
2880.2.k.i |
4 |
2880.2.k.j |
4 |
2880.2.k.k |
4 |
2880.2.k.l |
4 |
2880.2.m |
\(\chi_{2880}(1439, \cdot)\) |
2880.2.m.a |
8 |
1 |
2880.2.m.b |
8 |
2880.2.m.c |
32 |
2880.2.o |
\(\chi_{2880}(2879, \cdot)\) |
2880.2.o.a |
4 |
1 |
2880.2.o.b |
4 |
2880.2.o.c |
8 |
2880.2.o.d |
8 |
2880.2.o.e |
12 |
2880.2.o.f |
12 |
2880.2.q |
\(\chi_{2880}(961, \cdot)\) |
n/a |
192 |
2 |
2880.2.t |
\(\chi_{2880}(721, \cdot)\) |
2880.2.t.a |
4 |
2 |
2880.2.t.b |
8 |
2880.2.t.c |
16 |
2880.2.t.d |
20 |
2880.2.t.e |
32 |
2880.2.u |
\(\chi_{2880}(719, \cdot)\) |
2880.2.u.a |
96 |
2 |
2880.2.w |
\(\chi_{2880}(2177, \cdot)\) |
2880.2.w.a |
4 |
2 |
2880.2.w.b |
4 |
2880.2.w.c |
4 |
2880.2.w.d |
4 |
2880.2.w.e |
4 |
2880.2.w.f |
4 |
2880.2.w.g |
4 |
2880.2.w.h |
4 |
2880.2.w.i |
4 |
2880.2.w.j |
4 |
2880.2.w.k |
4 |
2880.2.w.l |
4 |
2880.2.w.m |
8 |
2880.2.w.n |
8 |
2880.2.w.o |
8 |
2880.2.w.p |
12 |
2880.2.w.q |
12 |
2880.2.x |
\(\chi_{2880}(127, \cdot)\) |
n/a |
116 |
2 |
2880.2.z |
\(\chi_{2880}(847, \cdot)\) |
n/a |
116 |
2 |
2880.2.bc |
\(\chi_{2880}(593, \cdot)\) |
2880.2.bc.a |
96 |
2 |
2880.2.bd |
\(\chi_{2880}(1423, \cdot)\) |
n/a |
116 |
2 |
2880.2.bg |
\(\chi_{2880}(17, \cdot)\) |
2880.2.bg.a |
96 |
2 |
2880.2.bi |
\(\chi_{2880}(1567, \cdot)\) |
n/a |
120 |
2 |
2880.2.bj |
\(\chi_{2880}(737, \cdot)\) |
2880.2.bj.a |
8 |
2 |
2880.2.bj.b |
8 |
2880.2.bj.c |
8 |
2880.2.bj.d |
8 |
2880.2.bj.e |
32 |
2880.2.bj.f |
32 |
2880.2.bl |
\(\chi_{2880}(431, \cdot)\) |
2880.2.bl.a |
8 |
2 |
2880.2.bl.b |
24 |
2880.2.bl.c |
32 |
2880.2.bm |
\(\chi_{2880}(1009, \cdot)\) |
n/a |
116 |
2 |
2880.2.br |
\(\chi_{2880}(959, \cdot)\) |
n/a |
280 |
2 |
2880.2.bt |
\(\chi_{2880}(479, \cdot)\) |
n/a |
288 |
2 |
2880.2.bv |
\(\chi_{2880}(481, \cdot)\) |
n/a |
192 |
2 |
2880.2.bw |
\(\chi_{2880}(191, \cdot)\) |
n/a |
192 |
2 |
2880.2.by |
\(\chi_{2880}(769, \cdot)\) |
n/a |
280 |
2 |
2880.2.ca |
\(\chi_{2880}(1249, \cdot)\) |
n/a |
288 |
2 |
2880.2.cc |
\(\chi_{2880}(671, \cdot)\) |
n/a |
192 |
2 |
2880.2.ce |
\(\chi_{2880}(1063, \cdot)\) |
None |
0 |
4 |
2880.2.ch |
\(\chi_{2880}(233, \cdot)\) |
None |
0 |
4 |
2880.2.ci |
\(\chi_{2880}(359, \cdot)\) |
None |
0 |
4 |
2880.2.cl |
\(\chi_{2880}(361, \cdot)\) |
None |
0 |
4 |
2880.2.cn |
\(\chi_{2880}(71, \cdot)\) |
None |
0 |
4 |
2880.2.co |
\(\chi_{2880}(649, \cdot)\) |
None |
0 |
4 |
2880.2.cr |
\(\chi_{2880}(953, \cdot)\) |
None |
0 |
4 |
2880.2.cs |
\(\chi_{2880}(343, \cdot)\) |
None |
0 |
4 |
2880.2.cu |
\(\chi_{2880}(49, \cdot)\) |
n/a |
560 |
4 |
2880.2.cv |
\(\chi_{2880}(911, \cdot)\) |
n/a |
384 |
4 |
2880.2.cy |
\(\chi_{2880}(223, \cdot)\) |
n/a |
576 |
4 |
2880.2.db |
\(\chi_{2880}(353, \cdot)\) |
n/a |
576 |
4 |
2880.2.dc |
\(\chi_{2880}(113, \cdot)\) |
n/a |
560 |
4 |
2880.2.df |
\(\chi_{2880}(367, \cdot)\) |
n/a |
560 |
4 |
2880.2.dg |
\(\chi_{2880}(497, \cdot)\) |
n/a |
560 |
4 |
2880.2.dj |
\(\chi_{2880}(943, \cdot)\) |
n/a |
560 |
4 |
2880.2.dk |
\(\chi_{2880}(257, \cdot)\) |
n/a |
560 |
4 |
2880.2.dn |
\(\chi_{2880}(1087, \cdot)\) |
n/a |
560 |
4 |
2880.2.dq |
\(\chi_{2880}(239, \cdot)\) |
n/a |
560 |
4 |
2880.2.dr |
\(\chi_{2880}(241, \cdot)\) |
n/a |
384 |
4 |
2880.2.dt |
\(\chi_{2880}(197, \cdot)\) |
n/a |
1536 |
8 |
2880.2.du |
\(\chi_{2880}(307, \cdot)\) |
n/a |
1904 |
8 |
2880.2.dw |
\(\chi_{2880}(181, \cdot)\) |
n/a |
1280 |
8 |
2880.2.dy |
\(\chi_{2880}(109, \cdot)\) |
n/a |
1904 |
8 |
2880.2.eb |
\(\chi_{2880}(251, \cdot)\) |
n/a |
1024 |
8 |
2880.2.ed |
\(\chi_{2880}(179, \cdot)\) |
n/a |
1536 |
8 |
2880.2.ef |
\(\chi_{2880}(53, \cdot)\) |
n/a |
1536 |
8 |
2880.2.eg |
\(\chi_{2880}(163, \cdot)\) |
n/a |
1904 |
8 |
2880.2.ej |
\(\chi_{2880}(7, \cdot)\) |
None |
0 |
8 |
2880.2.ek |
\(\chi_{2880}(137, \cdot)\) |
None |
0 |
8 |
2880.2.em |
\(\chi_{2880}(121, \cdot)\) |
None |
0 |
8 |
2880.2.ep |
\(\chi_{2880}(119, \cdot)\) |
None |
0 |
8 |
2880.2.er |
\(\chi_{2880}(169, \cdot)\) |
None |
0 |
8 |
2880.2.es |
\(\chi_{2880}(311, \cdot)\) |
None |
0 |
8 |
2880.2.eu |
\(\chi_{2880}(713, \cdot)\) |
None |
0 |
8 |
2880.2.ex |
\(\chi_{2880}(103, \cdot)\) |
None |
0 |
8 |
2880.2.ey |
\(\chi_{2880}(43, \cdot)\) |
n/a |
9152 |
16 |
2880.2.fb |
\(\chi_{2880}(173, \cdot)\) |
n/a |
9152 |
16 |
2880.2.fd |
\(\chi_{2880}(59, \cdot)\) |
n/a |
9152 |
16 |
2880.2.ff |
\(\chi_{2880}(11, \cdot)\) |
n/a |
6144 |
16 |
2880.2.fg |
\(\chi_{2880}(229, \cdot)\) |
n/a |
9152 |
16 |
2880.2.fi |
\(\chi_{2880}(61, \cdot)\) |
n/a |
6144 |
16 |
2880.2.fk |
\(\chi_{2880}(187, \cdot)\) |
n/a |
9152 |
16 |
2880.2.fn |
\(\chi_{2880}(77, \cdot)\) |
n/a |
9152 |
16 |
"n/a" means that newforms for that character have not been added to the database yet