Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3648))\).
|
Total |
New |
Old |
Modular forms
| 373824 |
155404 |
218420 |
Cusp forms
| 363457 |
153908 |
209549 |
Eisenstein series
| 10367 |
1496 |
8871 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3648))\)
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 |
3648.2.a |
\(\chi_{3648}(1, \cdot)\) |
3648.2.a.a |
1 |
1 |
3648.2.a.b |
1 |
3648.2.a.c |
1 |
3648.2.a.d |
1 |
3648.2.a.e |
1 |
3648.2.a.f |
1 |
3648.2.a.g |
1 |
3648.2.a.h |
1 |
3648.2.a.i |
1 |
3648.2.a.j |
1 |
3648.2.a.k |
1 |
3648.2.a.l |
1 |
3648.2.a.m |
1 |
3648.2.a.n |
1 |
3648.2.a.o |
1 |
3648.2.a.p |
1 |
3648.2.a.q |
1 |
3648.2.a.r |
1 |
3648.2.a.s |
1 |
3648.2.a.t |
1 |
3648.2.a.u |
1 |
3648.2.a.v |
1 |
3648.2.a.w |
1 |
3648.2.a.x |
1 |
3648.2.a.y |
1 |
3648.2.a.z |
1 |
3648.2.a.ba |
1 |
3648.2.a.bb |
1 |
3648.2.a.bc |
1 |
3648.2.a.bd |
1 |
3648.2.a.be |
1 |
3648.2.a.bf |
1 |
3648.2.a.bg |
1 |
3648.2.a.bh |
1 |
3648.2.a.bi |
1 |
3648.2.a.bj |
1 |
3648.2.a.bk |
2 |
3648.2.a.bl |
2 |
3648.2.a.bm |
2 |
3648.2.a.bn |
2 |
3648.2.a.bo |
2 |
3648.2.a.bp |
2 |
3648.2.a.bq |
2 |
3648.2.a.br |
2 |
3648.2.a.bs |
2 |
3648.2.a.bt |
2 |
3648.2.a.bu |
2 |
3648.2.a.bv |
2 |
3648.2.a.bw |
3 |
3648.2.a.bx |
3 |
3648.2.a.by |
3 |
3648.2.a.bz |
3 |
3648.2.d |
\(\chi_{3648}(191, \cdot)\) |
n/a |
144 |
1 |
3648.2.e |
\(\chi_{3648}(607, \cdot)\) |
3648.2.e.a |
12 |
1 |
3648.2.e.b |
12 |
3648.2.e.c |
28 |
3648.2.e.d |
28 |
3648.2.f |
\(\chi_{3648}(1025, \cdot)\) |
n/a |
156 |
1 |
3648.2.g |
\(\chi_{3648}(1825, \cdot)\) |
3648.2.g.a |
4 |
1 |
3648.2.g.b |
4 |
3648.2.g.c |
4 |
3648.2.g.d |
4 |
3648.2.g.e |
4 |
3648.2.g.f |
8 |
3648.2.g.g |
8 |
3648.2.g.h |
8 |
3648.2.g.i |
12 |
3648.2.g.j |
16 |
3648.2.j |
\(\chi_{3648}(2015, \cdot)\) |
n/a |
144 |
1 |
3648.2.k |
\(\chi_{3648}(2431, \cdot)\) |
3648.2.k.a |
2 |
1 |
3648.2.k.b |
2 |
3648.2.k.c |
2 |
3648.2.k.d |
2 |
3648.2.k.e |
2 |
3648.2.k.f |
2 |
3648.2.k.g |
4 |
3648.2.k.h |
4 |
3648.2.k.i |
10 |
3648.2.k.j |
10 |
3648.2.k.k |
20 |
3648.2.k.l |
20 |
3648.2.p |
\(\chi_{3648}(2849, \cdot)\) |
n/a |
160 |
1 |
3648.2.q |
\(\chi_{3648}(577, \cdot)\) |
n/a |
160 |
2 |
3648.2.r |
\(\chi_{3648}(113, \cdot)\) |
n/a |
312 |
2 |
3648.2.u |
\(\chi_{3648}(913, \cdot)\) |
n/a |
144 |
2 |
3648.2.v |
\(\chi_{3648}(1103, \cdot)\) |
n/a |
288 |
2 |
3648.2.y |
\(\chi_{3648}(1519, \cdot)\) |
n/a |
160 |
2 |
3648.2.bb |
\(\chi_{3648}(1471, \cdot)\) |
n/a |
160 |
2 |
3648.2.bc |
\(\chi_{3648}(2591, \cdot)\) |
n/a |
320 |
2 |
3648.2.bd |
\(\chi_{3648}(1889, \cdot)\) |
n/a |
320 |
2 |
3648.2.bg |
\(\chi_{3648}(31, \cdot)\) |
n/a |
160 |
2 |
3648.2.bh |
\(\chi_{3648}(767, \cdot)\) |
n/a |
312 |
2 |
3648.2.bm |
\(\chi_{3648}(2401, \cdot)\) |
n/a |
160 |
2 |
3648.2.bn |
\(\chi_{3648}(65, \cdot)\) |
n/a |
312 |
2 |
3648.2.bq |
\(\chi_{3648}(457, \cdot)\) |
None |
0 |
4 |
3648.2.br |
\(\chi_{3648}(151, \cdot)\) |
None |
0 |
4 |
3648.2.bs |
\(\chi_{3648}(647, \cdot)\) |
None |
0 |
4 |
3648.2.bt |
\(\chi_{3648}(569, \cdot)\) |
None |
0 |
4 |
3648.2.bw |
\(\chi_{3648}(385, \cdot)\) |
n/a |
480 |
6 |
3648.2.by |
\(\chi_{3648}(49, \cdot)\) |
n/a |
320 |
4 |
3648.2.bz |
\(\chi_{3648}(977, \cdot)\) |
n/a |
624 |
4 |
3648.2.cc |
\(\chi_{3648}(559, \cdot)\) |
n/a |
320 |
4 |
3648.2.cd |
\(\chi_{3648}(239, \cdot)\) |
n/a |
624 |
4 |
3648.2.cg |
\(\chi_{3648}(379, \cdot)\) |
n/a |
2560 |
8 |
3648.2.ch |
\(\chi_{3648}(229, \cdot)\) |
n/a |
2304 |
8 |
3648.2.cj |
\(\chi_{3648}(419, \cdot)\) |
n/a |
4608 |
8 |
3648.2.cm |
\(\chi_{3648}(341, \cdot)\) |
n/a |
5088 |
8 |
3648.2.cp |
\(\chi_{3648}(545, \cdot)\) |
n/a |
960 |
6 |
3648.2.cq |
\(\chi_{3648}(289, \cdot)\) |
n/a |
480 |
6 |
3648.2.cs |
\(\chi_{3648}(257, \cdot)\) |
n/a |
936 |
6 |
3648.2.cv |
\(\chi_{3648}(223, \cdot)\) |
n/a |
480 |
6 |
3648.2.cx |
\(\chi_{3648}(575, \cdot)\) |
n/a |
936 |
6 |
3648.2.cy |
\(\chi_{3648}(127, \cdot)\) |
n/a |
480 |
6 |
3648.2.da |
\(\chi_{3648}(479, \cdot)\) |
n/a |
960 |
6 |
3648.2.dc |
\(\chi_{3648}(521, \cdot)\) |
None |
0 |
8 |
3648.2.dd |
\(\chi_{3648}(311, \cdot)\) |
None |
0 |
8 |
3648.2.di |
\(\chi_{3648}(103, \cdot)\) |
None |
0 |
8 |
3648.2.dj |
\(\chi_{3648}(121, \cdot)\) |
None |
0 |
8 |
3648.2.dl |
\(\chi_{3648}(79, \cdot)\) |
n/a |
960 |
12 |
3648.2.dn |
\(\chi_{3648}(47, \cdot)\) |
n/a |
1872 |
12 |
3648.2.do |
\(\chi_{3648}(529, \cdot)\) |
n/a |
960 |
12 |
3648.2.dq |
\(\chi_{3648}(401, \cdot)\) |
n/a |
1872 |
12 |
3648.2.ds |
\(\chi_{3648}(259, \cdot)\) |
n/a |
5120 |
16 |
3648.2.dv |
\(\chi_{3648}(277, \cdot)\) |
n/a |
5120 |
16 |
3648.2.dx |
\(\chi_{3648}(11, \cdot)\) |
n/a |
10176 |
16 |
3648.2.dy |
\(\chi_{3648}(221, \cdot)\) |
n/a |
10176 |
16 |
3648.2.eb |
\(\chi_{3648}(25, \cdot)\) |
None |
0 |
24 |
3648.2.ec |
\(\chi_{3648}(295, \cdot)\) |
None |
0 |
24 |
3648.2.ee |
\(\chi_{3648}(41, \cdot)\) |
None |
0 |
24 |
3648.2.eh |
\(\chi_{3648}(23, \cdot)\) |
None |
0 |
24 |
3648.2.ei |
\(\chi_{3648}(29, \cdot)\) |
n/a |
30528 |
48 |
3648.2.ek |
\(\chi_{3648}(35, \cdot)\) |
n/a |
30528 |
48 |
3648.2.en |
\(\chi_{3648}(61, \cdot)\) |
n/a |
15360 |
48 |
3648.2.ep |
\(\chi_{3648}(67, \cdot)\) |
n/a |
15360 |
48 |
"n/a" means that newforms for that character have not been added to the database yet