Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2280))\).
|
Total |
New |
Old |
Modular forms
| 141696 |
53572 |
88124 |
Cusp forms
| 134785 |
52756 |
82029 |
Eisenstein series
| 6911 |
816 |
6095 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2280))\)
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 |
2280.2.a |
\(\chi_{2280}(1, \cdot)\) |
2280.2.a.a |
1 |
1 |
2280.2.a.b |
1 |
2280.2.a.c |
1 |
2280.2.a.d |
1 |
2280.2.a.e |
1 |
2280.2.a.f |
1 |
2280.2.a.g |
1 |
2280.2.a.h |
1 |
2280.2.a.i |
1 |
2280.2.a.j |
1 |
2280.2.a.k |
2 |
2280.2.a.l |
2 |
2280.2.a.m |
2 |
2280.2.a.n |
2 |
2280.2.a.o |
2 |
2280.2.a.p |
2 |
2280.2.a.q |
2 |
2280.2.a.r |
3 |
2280.2.a.s |
3 |
2280.2.a.t |
3 |
2280.2.a.u |
3 |
2280.2.c |
\(\chi_{2280}(1331, \cdot)\) |
n/a |
288 |
1 |
2280.2.d |
\(\chi_{2280}(151, \cdot)\) |
None |
0 |
1 |
2280.2.f |
\(\chi_{2280}(229, \cdot)\) |
n/a |
216 |
1 |
2280.2.i |
\(\chi_{2280}(569, \cdot)\) |
n/a |
120 |
1 |
2280.2.j |
\(\chi_{2280}(1369, \cdot)\) |
2280.2.j.a |
2 |
1 |
2280.2.j.b |
2 |
2280.2.j.c |
2 |
2280.2.j.d |
2 |
2280.2.j.e |
2 |
2280.2.j.f |
6 |
2280.2.j.g |
10 |
2280.2.j.h |
12 |
2280.2.j.i |
18 |
2280.2.m |
\(\chi_{2280}(1709, \cdot)\) |
n/a |
472 |
1 |
2280.2.o |
\(\chi_{2280}(191, \cdot)\) |
None |
0 |
1 |
2280.2.p |
\(\chi_{2280}(1291, \cdot)\) |
n/a |
160 |
1 |
2280.2.r |
\(\chi_{2280}(1481, \cdot)\) |
2280.2.r.a |
40 |
1 |
2280.2.r.b |
40 |
2280.2.u |
\(\chi_{2280}(1141, \cdot)\) |
n/a |
144 |
1 |
2280.2.w |
\(\chi_{2280}(1519, \cdot)\) |
None |
0 |
1 |
2280.2.x |
\(\chi_{2280}(419, \cdot)\) |
n/a |
432 |
1 |
2280.2.ba |
\(\chi_{2280}(379, \cdot)\) |
n/a |
240 |
1 |
2280.2.bb |
\(\chi_{2280}(1559, \cdot)\) |
None |
0 |
1 |
2280.2.bd |
\(\chi_{2280}(341, \cdot)\) |
n/a |
320 |
1 |
2280.2.bg |
\(\chi_{2280}(121, \cdot)\) |
2280.2.bg.a |
2 |
2 |
2280.2.bg.b |
2 |
2280.2.bg.c |
2 |
2280.2.bg.d |
2 |
2280.2.bg.e |
2 |
2280.2.bg.f |
2 |
2280.2.bg.g |
2 |
2280.2.bg.h |
2 |
2280.2.bg.i |
2 |
2280.2.bg.j |
2 |
2280.2.bg.k |
2 |
2280.2.bg.l |
4 |
2280.2.bg.m |
4 |
2280.2.bg.n |
4 |
2280.2.bg.o |
4 |
2280.2.bg.p |
4 |
2280.2.bg.q |
4 |
2280.2.bg.r |
4 |
2280.2.bg.s |
6 |
2280.2.bg.t |
8 |
2280.2.bg.u |
8 |
2280.2.bg.v |
8 |
2280.2.bh |
\(\chi_{2280}(37, \cdot)\) |
n/a |
480 |
2 |
2280.2.bk |
\(\chi_{2280}(343, \cdot)\) |
None |
0 |
2 |
2280.2.bm |
\(\chi_{2280}(1217, \cdot)\) |
n/a |
216 |
2 |
2280.2.bn |
\(\chi_{2280}(227, \cdot)\) |
n/a |
944 |
2 |
2280.2.bp |
\(\chi_{2280}(77, \cdot)\) |
n/a |
864 |
2 |
2280.2.bs |
\(\chi_{2280}(1367, \cdot)\) |
None |
0 |
2 |
2280.2.bu |
\(\chi_{2280}(1177, \cdot)\) |
n/a |
120 |
2 |
2280.2.bv |
\(\chi_{2280}(1027, \cdot)\) |
n/a |
432 |
2 |
2280.2.bx |
\(\chi_{2280}(449, \cdot)\) |
n/a |
240 |
2 |
2280.2.ca |
\(\chi_{2280}(349, \cdot)\) |
n/a |
480 |
2 |
2280.2.cc |
\(\chi_{2280}(31, \cdot)\) |
None |
0 |
2 |
2280.2.cd |
\(\chi_{2280}(11, \cdot)\) |
n/a |
640 |
2 |
2280.2.cg |
\(\chi_{2280}(331, \cdot)\) |
n/a |
320 |
2 |
2280.2.ch |
\(\chi_{2280}(311, \cdot)\) |
None |
0 |
2 |
2280.2.cj |
\(\chi_{2280}(749, \cdot)\) |
n/a |
944 |
2 |
2280.2.cm |
\(\chi_{2280}(49, \cdot)\) |
n/a |
120 |
2 |
2280.2.co |
\(\chi_{2280}(539, \cdot)\) |
n/a |
944 |
2 |
2280.2.cp |
\(\chi_{2280}(559, \cdot)\) |
None |
0 |
2 |
2280.2.cr |
\(\chi_{2280}(1261, \cdot)\) |
n/a |
320 |
2 |
2280.2.cu |
\(\chi_{2280}(521, \cdot)\) |
n/a |
160 |
2 |
2280.2.cx |
\(\chi_{2280}(221, \cdot)\) |
n/a |
640 |
2 |
2280.2.cz |
\(\chi_{2280}(239, \cdot)\) |
None |
0 |
2 |
2280.2.da |
\(\chi_{2280}(259, \cdot)\) |
n/a |
480 |
2 |
2280.2.dc |
\(\chi_{2280}(481, \cdot)\) |
n/a |
240 |
6 |
2280.2.de |
\(\chi_{2280}(107, \cdot)\) |
n/a |
1888 |
4 |
2280.2.df |
\(\chi_{2280}(353, \cdot)\) |
n/a |
480 |
4 |
2280.2.dh |
\(\chi_{2280}(7, \cdot)\) |
None |
0 |
4 |
2280.2.dk |
\(\chi_{2280}(373, \cdot)\) |
n/a |
960 |
4 |
2280.2.dm |
\(\chi_{2280}(163, \cdot)\) |
n/a |
960 |
4 |
2280.2.dn |
\(\chi_{2280}(217, \cdot)\) |
n/a |
240 |
4 |
2280.2.dp |
\(\chi_{2280}(407, \cdot)\) |
None |
0 |
4 |
2280.2.ds |
\(\chi_{2280}(197, \cdot)\) |
n/a |
1888 |
4 |
2280.2.du |
\(\chi_{2280}(979, \cdot)\) |
n/a |
1440 |
6 |
2280.2.dx |
\(\chi_{2280}(119, \cdot)\) |
None |
0 |
6 |
2280.2.dy |
\(\chi_{2280}(941, \cdot)\) |
n/a |
1920 |
6 |
2280.2.eb |
\(\chi_{2280}(61, \cdot)\) |
n/a |
960 |
6 |
2280.2.ec |
\(\chi_{2280}(79, \cdot)\) |
None |
0 |
6 |
2280.2.ef |
\(\chi_{2280}(41, \cdot)\) |
n/a |
480 |
6 |
2280.2.eg |
\(\chi_{2280}(899, \cdot)\) |
n/a |
2832 |
6 |
2280.2.ej |
\(\chi_{2280}(169, \cdot)\) |
n/a |
360 |
6 |
2280.2.ek |
\(\chi_{2280}(91, \cdot)\) |
n/a |
960 |
6 |
2280.2.en |
\(\chi_{2280}(29, \cdot)\) |
n/a |
2832 |
6 |
2280.2.eo |
\(\chi_{2280}(671, \cdot)\) |
None |
0 |
6 |
2280.2.er |
\(\chi_{2280}(751, \cdot)\) |
None |
0 |
6 |
2280.2.es |
\(\chi_{2280}(709, \cdot)\) |
n/a |
1440 |
6 |
2280.2.ev |
\(\chi_{2280}(131, \cdot)\) |
n/a |
1920 |
6 |
2280.2.ew |
\(\chi_{2280}(89, \cdot)\) |
n/a |
720 |
6 |
2280.2.ez |
\(\chi_{2280}(143, \cdot)\) |
None |
0 |
12 |
2280.2.fa |
\(\chi_{2280}(557, \cdot)\) |
n/a |
5664 |
12 |
2280.2.fd |
\(\chi_{2280}(97, \cdot)\) |
n/a |
720 |
12 |
2280.2.fe |
\(\chi_{2280}(43, \cdot)\) |
n/a |
2880 |
12 |
2280.2.fg |
\(\chi_{2280}(17, \cdot)\) |
n/a |
1440 |
12 |
2280.2.fj |
\(\chi_{2280}(203, \cdot)\) |
n/a |
5664 |
12 |
2280.2.fk |
\(\chi_{2280}(367, \cdot)\) |
None |
0 |
12 |
2280.2.fn |
\(\chi_{2280}(13, \cdot)\) |
n/a |
2880 |
12 |
"n/a" means that newforms for that character have not been added to the database yet