Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1596))\).
|
Total |
New |
Old |
Modular forms
| 71280 |
29164 |
42116 |
Cusp forms
| 66961 |
28476 |
38485 |
Eisenstein series
| 4319 |
688 |
3631 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1596))\)
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 |
1596.2.a |
\(\chi_{1596}(1, \cdot)\) |
1596.2.a.a |
1 |
1 |
1596.2.a.b |
1 |
1596.2.a.c |
1 |
1596.2.a.d |
1 |
1596.2.a.e |
1 |
1596.2.a.f |
2 |
1596.2.a.g |
2 |
1596.2.a.h |
2 |
1596.2.a.i |
2 |
1596.2.a.j |
3 |
1596.2.b |
\(\chi_{1596}(113, \cdot)\) |
1596.2.b.a |
2 |
1 |
1596.2.b.b |
2 |
1596.2.b.c |
8 |
1596.2.b.d |
12 |
1596.2.b.e |
16 |
1596.2.c |
\(\chi_{1596}(1483, \cdot)\) |
n/a |
144 |
1 |
1596.2.h |
\(\chi_{1596}(1331, \cdot)\) |
n/a |
216 |
1 |
1596.2.i |
\(\chi_{1596}(265, \cdot)\) |
1596.2.i.a |
14 |
1 |
1596.2.i.b |
14 |
1596.2.j |
\(\chi_{1596}(1217, \cdot)\) |
1596.2.j.a |
48 |
1 |
1596.2.k |
\(\chi_{1596}(379, \cdot)\) |
n/a |
120 |
1 |
1596.2.p |
\(\chi_{1596}(1595, \cdot)\) |
n/a |
312 |
1 |
1596.2.q |
\(\chi_{1596}(961, \cdot)\) |
1596.2.q.a |
2 |
2 |
1596.2.q.b |
2 |
1596.2.q.c |
2 |
1596.2.q.d |
2 |
1596.2.q.e |
18 |
1596.2.q.f |
26 |
1596.2.r |
\(\chi_{1596}(457, \cdot)\) |
1596.2.r.a |
2 |
2 |
1596.2.r.b |
2 |
1596.2.r.c |
2 |
1596.2.r.d |
2 |
1596.2.r.e |
8 |
1596.2.r.f |
8 |
1596.2.r.g |
10 |
1596.2.r.h |
14 |
1596.2.s |
\(\chi_{1596}(505, \cdot)\) |
1596.2.s.a |
2 |
2 |
1596.2.s.b |
2 |
1596.2.s.c |
8 |
1596.2.s.d |
8 |
1596.2.s.e |
8 |
1596.2.s.f |
12 |
1596.2.t |
\(\chi_{1596}(121, \cdot)\) |
1596.2.t.a |
2 |
2 |
1596.2.t.b |
2 |
1596.2.t.c |
2 |
1596.2.t.d |
2 |
1596.2.t.e |
18 |
1596.2.t.f |
26 |
1596.2.u |
\(\chi_{1596}(145, \cdot)\) |
1596.2.u.a |
2 |
2 |
1596.2.u.b |
24 |
1596.2.u.c |
26 |
1596.2.v |
\(\chi_{1596}(11, \cdot)\) |
n/a |
624 |
2 |
1596.2.ba |
\(\chi_{1596}(619, \cdot)\) |
n/a |
320 |
2 |
1596.2.bb |
\(\chi_{1596}(905, \cdot)\) |
n/a |
108 |
2 |
1596.2.be |
\(\chi_{1596}(125, \cdot)\) |
n/a |
104 |
2 |
1596.2.bf |
\(\chi_{1596}(715, \cdot)\) |
n/a |
240 |
2 |
1596.2.bi |
\(\chi_{1596}(563, \cdot)\) |
n/a |
624 |
2 |
1596.2.bl |
\(\chi_{1596}(227, \cdot)\) |
n/a |
624 |
2 |
1596.2.bm |
\(\chi_{1596}(151, \cdot)\) |
n/a |
320 |
2 |
1596.2.bn |
\(\chi_{1596}(761, \cdot)\) |
1596.2.bn.a |
96 |
2 |
1596.2.bq |
\(\chi_{1596}(331, \cdot)\) |
n/a |
320 |
2 |
1596.2.br |
\(\chi_{1596}(1109, \cdot)\) |
n/a |
108 |
2 |
1596.2.bu |
\(\chi_{1596}(335, \cdot)\) |
n/a |
624 |
2 |
1596.2.bz |
\(\chi_{1596}(449, \cdot)\) |
1596.2.bz.a |
2 |
2 |
1596.2.bz.b |
2 |
1596.2.bz.c |
4 |
1596.2.bz.d |
16 |
1596.2.bz.e |
24 |
1596.2.bz.f |
32 |
1596.2.ca |
\(\chi_{1596}(391, \cdot)\) |
n/a |
320 |
2 |
1596.2.cd |
\(\chi_{1596}(829, \cdot)\) |
1596.2.cd.a |
2 |
2 |
1596.2.cd.b |
24 |
1596.2.cd.c |
26 |
1596.2.ce |
\(\chi_{1596}(695, \cdot)\) |
n/a |
624 |
2 |
1596.2.ch |
\(\chi_{1596}(493, \cdot)\) |
1596.2.ch.a |
2 |
2 |
1596.2.ch.b |
2 |
1596.2.ch.c |
24 |
1596.2.ch.d |
24 |
1596.2.ci |
\(\chi_{1596}(191, \cdot)\) |
n/a |
576 |
2 |
1596.2.cj |
\(\chi_{1596}(115, \cdot)\) |
n/a |
288 |
2 |
1596.2.ck |
\(\chi_{1596}(569, \cdot)\) |
n/a |
108 |
2 |
1596.2.cn |
\(\chi_{1596}(1375, \cdot)\) |
n/a |
320 |
2 |
1596.2.co |
\(\chi_{1596}(65, \cdot)\) |
n/a |
108 |
2 |
1596.2.cr |
\(\chi_{1596}(239, \cdot)\) |
n/a |
480 |
2 |
1596.2.cs |
\(\chi_{1596}(601, \cdot)\) |
1596.2.cs.a |
28 |
2 |
1596.2.cs.b |
28 |
1596.2.cv |
\(\chi_{1596}(1319, \cdot)\) |
n/a |
624 |
2 |
1596.2.da |
\(\chi_{1596}(1171, \cdot)\) |
n/a |
320 |
2 |
1596.2.db |
\(\chi_{1596}(353, \cdot)\) |
n/a |
108 |
2 |
1596.2.dc |
\(\chi_{1596}(85, \cdot)\) |
n/a |
120 |
6 |
1596.2.dd |
\(\chi_{1596}(289, \cdot)\) |
n/a |
162 |
6 |
1596.2.de |
\(\chi_{1596}(25, \cdot)\) |
n/a |
162 |
6 |
1596.2.df |
\(\chi_{1596}(187, \cdot)\) |
n/a |
960 |
6 |
1596.2.di |
\(\chi_{1596}(67, \cdot)\) |
n/a |
960 |
6 |
1596.2.dk |
\(\chi_{1596}(5, \cdot)\) |
n/a |
318 |
6 |
1596.2.dl |
\(\chi_{1596}(53, \cdot)\) |
n/a |
318 |
6 |
1596.2.dn |
\(\chi_{1596}(23, \cdot)\) |
n/a |
1872 |
6 |
1596.2.dq |
\(\chi_{1596}(59, \cdot)\) |
n/a |
1872 |
6 |
1596.2.ds |
\(\chi_{1596}(13, \cdot)\) |
n/a |
156 |
6 |
1596.2.du |
\(\chi_{1596}(167, \cdot)\) |
n/a |
1872 |
6 |
1596.2.dx |
\(\chi_{1596}(491, \cdot)\) |
n/a |
1440 |
6 |
1596.2.dz |
\(\chi_{1596}(325, \cdot)\) |
n/a |
162 |
6 |
1596.2.eb |
\(\chi_{1596}(17, \cdot)\) |
n/a |
318 |
6 |
1596.2.ee |
\(\chi_{1596}(317, \cdot)\) |
n/a |
318 |
6 |
1596.2.eg |
\(\chi_{1596}(127, \cdot)\) |
n/a |
720 |
6 |
1596.2.eh |
\(\chi_{1596}(55, \cdot)\) |
n/a |
960 |
6 |
1596.2.ej |
\(\chi_{1596}(29, \cdot)\) |
n/a |
240 |
6 |
1596.2.em |
\(\chi_{1596}(377, \cdot)\) |
n/a |
324 |
6 |
1596.2.eo |
\(\chi_{1596}(283, \cdot)\) |
n/a |
960 |
6 |
1596.2.ep |
\(\chi_{1596}(583, \cdot)\) |
n/a |
960 |
6 |
1596.2.et |
\(\chi_{1596}(241, \cdot)\) |
n/a |
162 |
6 |
1596.2.ev |
\(\chi_{1596}(359, \cdot)\) |
n/a |
1872 |
6 |
1596.2.ew |
\(\chi_{1596}(143, \cdot)\) |
n/a |
1872 |
6 |
"n/a" means that newforms for that character have not been added to the database yet