Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3549))\).
|
Total |
New |
Old |
Modular forms
| 459744 |
324700 |
135044 |
Cusp forms
| 448801 |
320608 |
128193 |
Eisenstein series
| 10943 |
4092 |
6851 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3549))\)
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 |
3549.2.a |
\(\chi_{3549}(1, \cdot)\) |
3549.2.a.a |
1 |
1 |
3549.2.a.b |
1 |
3549.2.a.c |
1 |
3549.2.a.d |
1 |
3549.2.a.e |
1 |
3549.2.a.f |
2 |
3549.2.a.g |
3 |
3549.2.a.h |
3 |
3549.2.a.i |
3 |
3549.2.a.j |
3 |
3549.2.a.k |
3 |
3549.2.a.l |
3 |
3549.2.a.m |
3 |
3549.2.a.n |
3 |
3549.2.a.o |
3 |
3549.2.a.p |
3 |
3549.2.a.q |
3 |
3549.2.a.r |
3 |
3549.2.a.s |
3 |
3549.2.a.t |
3 |
3549.2.a.u |
3 |
3549.2.a.v |
4 |
3549.2.a.w |
4 |
3549.2.a.x |
4 |
3549.2.a.y |
6 |
3549.2.a.z |
6 |
3549.2.a.ba |
8 |
3549.2.a.bb |
8 |
3549.2.a.bc |
8 |
3549.2.a.bd |
8 |
3549.2.a.be |
9 |
3549.2.a.bf |
9 |
3549.2.a.bg |
15 |
3549.2.a.bh |
15 |
3549.2.c |
\(\chi_{3549}(337, \cdot)\) |
n/a |
152 |
1 |
3549.2.e |
\(\chi_{3549}(3212, \cdot)\) |
n/a |
392 |
1 |
3549.2.g |
\(\chi_{3549}(3548, \cdot)\) |
n/a |
392 |
1 |
3549.2.i |
\(\chi_{3549}(508, \cdot)\) |
n/a |
414 |
2 |
3549.2.j |
\(\chi_{3549}(991, \cdot)\) |
n/a |
410 |
2 |
3549.2.k |
\(\chi_{3549}(22, \cdot)\) |
n/a |
312 |
2 |
3549.2.l |
\(\chi_{3549}(529, \cdot)\) |
n/a |
410 |
2 |
3549.2.n |
\(\chi_{3549}(239, \cdot)\) |
n/a |
616 |
2 |
3549.2.p |
\(\chi_{3549}(1084, \cdot)\) |
n/a |
408 |
2 |
3549.2.r |
\(\chi_{3549}(1160, \cdot)\) |
n/a |
782 |
2 |
3549.2.t |
\(\chi_{3549}(823, \cdot)\) |
n/a |
410 |
2 |
3549.2.u |
\(\chi_{3549}(3065, \cdot)\) |
n/a |
780 |
2 |
3549.2.y |
\(\chi_{3549}(992, \cdot)\) |
n/a |
782 |
2 |
3549.2.ba |
\(\chi_{3549}(1013, \cdot)\) |
n/a |
780 |
2 |
3549.2.bd |
\(\chi_{3549}(316, \cdot)\) |
n/a |
304 |
2 |
3549.2.bf |
\(\chi_{3549}(698, \cdot)\) |
n/a |
782 |
2 |
3549.2.bh |
\(\chi_{3549}(677, \cdot)\) |
n/a |
782 |
2 |
3549.2.bj |
\(\chi_{3549}(844, \cdot)\) |
n/a |
412 |
2 |
3549.2.bl |
\(\chi_{3549}(361, \cdot)\) |
n/a |
410 |
2 |
3549.2.bn |
\(\chi_{3549}(146, \cdot)\) |
n/a |
780 |
2 |
3549.2.br |
\(\chi_{3549}(530, \cdot)\) |
n/a |
782 |
2 |
3549.2.bt |
\(\chi_{3549}(418, \cdot)\) |
n/a |
820 |
4 |
3549.2.bv |
\(\chi_{3549}(1094, \cdot)\) |
n/a |
1564 |
4 |
3549.2.bw |
\(\chi_{3549}(695, \cdot)\) |
n/a |
1564 |
4 |
3549.2.by |
\(\chi_{3549}(1441, \cdot)\) |
n/a |
824 |
4 |
3549.2.bz |
\(\chi_{3549}(577, \cdot)\) |
n/a |
824 |
4 |
3549.2.cc |
\(\chi_{3549}(596, \cdot)\) |
n/a |
1232 |
4 |
3549.2.cd |
\(\chi_{3549}(746, \cdot)\) |
n/a |
1560 |
4 |
3549.2.cg |
\(\chi_{3549}(19, \cdot)\) |
n/a |
820 |
4 |
3549.2.ci |
\(\chi_{3549}(274, \cdot)\) |
n/a |
2160 |
12 |
3549.2.ck |
\(\chi_{3549}(272, \cdot)\) |
n/a |
5760 |
12 |
3549.2.cm |
\(\chi_{3549}(209, \cdot)\) |
n/a |
5760 |
12 |
3549.2.co |
\(\chi_{3549}(64, \cdot)\) |
n/a |
2208 |
12 |
3549.2.cq |
\(\chi_{3549}(16, \cdot)\) |
n/a |
5832 |
24 |
3549.2.cr |
\(\chi_{3549}(211, \cdot)\) |
n/a |
4320 |
24 |
3549.2.cs |
\(\chi_{3549}(100, \cdot)\) |
n/a |
5832 |
24 |
3549.2.ct |
\(\chi_{3549}(79, \cdot)\) |
n/a |
5808 |
24 |
3549.2.cu |
\(\chi_{3549}(34, \cdot)\) |
n/a |
5856 |
24 |
3549.2.cw |
\(\chi_{3549}(8, \cdot)\) |
n/a |
8736 |
24 |
3549.2.cy |
\(\chi_{3549}(17, \cdot)\) |
n/a |
11544 |
24 |
3549.2.dc |
\(\chi_{3549}(230, \cdot)\) |
n/a |
11568 |
24 |
3549.2.de |
\(\chi_{3549}(88, \cdot)\) |
n/a |
5832 |
24 |
3549.2.dg |
\(\chi_{3549}(25, \cdot)\) |
n/a |
5808 |
24 |
3549.2.di |
\(\chi_{3549}(131, \cdot)\) |
n/a |
11568 |
24 |
3549.2.dk |
\(\chi_{3549}(152, \cdot)\) |
n/a |
11544 |
24 |
3549.2.dm |
\(\chi_{3549}(43, \cdot)\) |
n/a |
4416 |
24 |
3549.2.dp |
\(\chi_{3549}(38, \cdot)\) |
n/a |
11568 |
24 |
3549.2.dr |
\(\chi_{3549}(101, \cdot)\) |
n/a |
11544 |
24 |
3549.2.dv |
\(\chi_{3549}(62, \cdot)\) |
n/a |
11568 |
24 |
3549.2.dw |
\(\chi_{3549}(4, \cdot)\) |
n/a |
5832 |
24 |
3549.2.dy |
\(\chi_{3549}(68, \cdot)\) |
n/a |
11544 |
24 |
3549.2.eb |
\(\chi_{3549}(115, \cdot)\) |
n/a |
11664 |
48 |
3549.2.ee |
\(\chi_{3549}(50, \cdot)\) |
n/a |
17472 |
48 |
3549.2.ef |
\(\chi_{3549}(44, \cdot)\) |
n/a |
23136 |
48 |
3549.2.ei |
\(\chi_{3549}(76, \cdot)\) |
n/a |
11616 |
48 |
3549.2.ej |
\(\chi_{3549}(31, \cdot)\) |
n/a |
11616 |
48 |
3549.2.el |
\(\chi_{3549}(11, \cdot)\) |
n/a |
23088 |
48 |
3549.2.em |
\(\chi_{3549}(2, \cdot)\) |
n/a |
23088 |
48 |
3549.2.eo |
\(\chi_{3549}(136, \cdot)\) |
n/a |
11664 |
48 |
"n/a" means that newforms for that character have not been added to the database yet