Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6171))\).
|
Total |
New |
Old |
Modular forms
| 1404160 |
1025306 |
378854 |
Cusp forms
| 1383681 |
1016874 |
366807 |
Eisenstein series
| 20479 |
8432 |
12047 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6171))\)
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 |
6171.2.a |
\(\chi_{6171}(1, \cdot)\) |
6171.2.a.a |
1 |
1 |
6171.2.a.b |
1 |
6171.2.a.c |
1 |
6171.2.a.d |
1 |
6171.2.a.e |
1 |
6171.2.a.f |
1 |
6171.2.a.g |
1 |
6171.2.a.h |
1 |
6171.2.a.i |
1 |
6171.2.a.j |
2 |
6171.2.a.k |
2 |
6171.2.a.l |
2 |
6171.2.a.m |
2 |
6171.2.a.n |
2 |
6171.2.a.o |
2 |
6171.2.a.p |
2 |
6171.2.a.q |
3 |
6171.2.a.r |
3 |
6171.2.a.s |
3 |
6171.2.a.t |
4 |
6171.2.a.u |
5 |
6171.2.a.v |
5 |
6171.2.a.w |
6 |
6171.2.a.x |
6 |
6171.2.a.y |
6 |
6171.2.a.z |
6 |
6171.2.a.ba |
6 |
6171.2.a.bb |
6 |
6171.2.a.bc |
6 |
6171.2.a.bd |
7 |
6171.2.a.be |
7 |
6171.2.a.bf |
8 |
6171.2.a.bg |
8 |
6171.2.a.bh |
8 |
6171.2.a.bi |
8 |
6171.2.a.bj |
12 |
6171.2.a.bk |
12 |
6171.2.a.bl |
12 |
6171.2.a.bm |
12 |
6171.2.a.bn |
14 |
6171.2.a.bo |
14 |
6171.2.a.bp |
20 |
6171.2.a.bq |
20 |
6171.2.a.br |
20 |
6171.2.a.bs |
20 |
6171.2.f |
\(\chi_{6171}(2177, \cdot)\) |
n/a |
576 |
1 |
6171.2.g |
\(\chi_{6171}(3994, \cdot)\) |
n/a |
328 |
1 |
6171.2.h |
\(\chi_{6171}(6170, \cdot)\) |
n/a |
632 |
1 |
6171.2.i |
\(\chi_{6171}(2903, \cdot)\) |
n/a |
1264 |
2 |
6171.2.j |
\(\chi_{6171}(727, \cdot)\) |
n/a |
656 |
2 |
6171.2.m |
\(\chi_{6171}(511, \cdot)\) |
n/a |
1152 |
4 |
6171.2.o |
\(\chi_{6171}(1090, \cdot)\) |
n/a |
1304 |
4 |
6171.2.q |
\(\chi_{6171}(3266, \cdot)\) |
n/a |
2528 |
4 |
6171.2.r |
\(\chi_{6171}(2702, \cdot)\) |
n/a |
2528 |
4 |
6171.2.s |
\(\chi_{6171}(1291, \cdot)\) |
n/a |
1296 |
4 |
6171.2.t |
\(\chi_{6171}(239, \cdot)\) |
n/a |
2304 |
4 |
6171.2.y |
\(\chi_{6171}(562, \cdot)\) |
n/a |
3520 |
10 |
6171.2.z |
\(\chi_{6171}(241, \cdot)\) |
n/a |
2592 |
8 |
6171.2.ba |
\(\chi_{6171}(122, \cdot)\) |
n/a |
5088 |
8 |
6171.2.bf |
\(\chi_{6171}(565, \cdot)\) |
n/a |
2592 |
8 |
6171.2.bg |
\(\chi_{6171}(965, \cdot)\) |
n/a |
5056 |
8 |
6171.2.bh |
\(\chi_{6171}(560, \cdot)\) |
n/a |
7880 |
10 |
6171.2.bi |
\(\chi_{6171}(67, \cdot)\) |
n/a |
3960 |
10 |
6171.2.bj |
\(\chi_{6171}(494, \cdot)\) |
n/a |
7040 |
10 |
6171.2.bo |
\(\chi_{6171}(161, \cdot)\) |
n/a |
10112 |
16 |
6171.2.bq |
\(\chi_{6171}(202, \cdot)\) |
n/a |
5184 |
16 |
6171.2.bu |
\(\chi_{6171}(166, \cdot)\) |
n/a |
7920 |
20 |
6171.2.bv |
\(\chi_{6171}(98, \cdot)\) |
n/a |
15760 |
20 |
6171.2.bw |
\(\chi_{6171}(103, \cdot)\) |
n/a |
14080 |
40 |
6171.2.bz |
\(\chi_{6171}(245, \cdot)\) |
n/a |
20224 |
32 |
6171.2.ca |
\(\chi_{6171}(40, \cdot)\) |
n/a |
10368 |
32 |
6171.2.cb |
\(\chi_{6171}(32, \cdot)\) |
n/a |
31520 |
40 |
6171.2.cd |
\(\chi_{6171}(100, \cdot)\) |
n/a |
15840 |
40 |
6171.2.cj |
\(\chi_{6171}(35, \cdot)\) |
n/a |
28160 |
40 |
6171.2.ck |
\(\chi_{6171}(16, \cdot)\) |
n/a |
15840 |
40 |
6171.2.cl |
\(\chi_{6171}(50, \cdot)\) |
n/a |
31520 |
40 |
6171.2.co |
\(\chi_{6171}(23, \cdot)\) |
n/a |
63040 |
80 |
6171.2.cp |
\(\chi_{6171}(10, \cdot)\) |
n/a |
31680 |
80 |
6171.2.cq |
\(\chi_{6171}(140, \cdot)\) |
n/a |
63040 |
80 |
6171.2.cr |
\(\chi_{6171}(4, \cdot)\) |
n/a |
31680 |
80 |
6171.2.cv |
\(\chi_{6171}(25, \cdot)\) |
n/a |
63360 |
160 |
6171.2.cx |
\(\chi_{6171}(2, \cdot)\) |
n/a |
126080 |
160 |
6171.2.cy |
\(\chi_{6171}(7, \cdot)\) |
n/a |
126720 |
320 |
6171.2.cz |
\(\chi_{6171}(5, \cdot)\) |
n/a |
252160 |
320 |
"n/a" means that newforms for that character have not been added to the database yet