Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6069))\).
|
Total |
New |
Old |
| Modular forms
| 1341312 |
954240 |
387072 |
| Cusp forms
| 1322113 |
946868 |
375245 |
| Eisenstein series
| 19199 |
7372 |
11827 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6069))\)
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 |
| 6069.2.a |
\(\chi_{6069}(1, \cdot)\) |
6069.2.a.a |
1 |
1 |
| 6069.2.a.b |
1 |
| 6069.2.a.c |
1 |
| 6069.2.a.d |
1 |
| 6069.2.a.e |
1 |
| 6069.2.a.f |
2 |
| 6069.2.a.g |
2 |
| 6069.2.a.h |
2 |
| 6069.2.a.i |
2 |
| 6069.2.a.j |
3 |
| 6069.2.a.k |
3 |
| 6069.2.a.l |
3 |
| 6069.2.a.m |
3 |
| 6069.2.a.n |
3 |
| 6069.2.a.o |
3 |
| 6069.2.a.p |
3 |
| 6069.2.a.q |
3 |
| 6069.2.a.r |
3 |
| 6069.2.a.s |
4 |
| 6069.2.a.t |
5 |
| 6069.2.a.u |
5 |
| 6069.2.a.v |
5 |
| 6069.2.a.w |
5 |
| 6069.2.a.x |
6 |
| 6069.2.a.y |
6 |
| 6069.2.a.z |
9 |
| 6069.2.a.ba |
9 |
| 6069.2.a.bb |
9 |
| 6069.2.a.bc |
9 |
| 6069.2.a.bd |
10 |
| 6069.2.a.be |
10 |
| 6069.2.a.bf |
15 |
| 6069.2.a.bg |
15 |
| 6069.2.a.bh |
15 |
| 6069.2.a.bi |
15 |
| 6069.2.a.bj |
16 |
| 6069.2.a.bk |
16 |
| 6069.2.a.bl |
24 |
| 6069.2.a.bm |
24 |
| 6069.2.c |
\(\chi_{6069}(6068, \cdot)\) |
n/a |
692 |
1 |
| 6069.2.d |
\(\chi_{6069}(3758, \cdot)\) |
n/a |
692 |
1 |
| 6069.2.f |
\(\chi_{6069}(2311, \cdot)\) |
n/a |
272 |
1 |
| 6069.2.i |
\(\chi_{6069}(3469, \cdot)\) |
n/a |
722 |
2 |
| 6069.2.k |
\(\chi_{6069}(2563, \cdot)\) |
n/a |
544 |
2 |
| 6069.2.l |
\(\chi_{6069}(251, \cdot)\) |
n/a |
1384 |
2 |
| 6069.2.p |
\(\chi_{6069}(1444, \cdot)\) |
n/a |
720 |
2 |
| 6069.2.r |
\(\chi_{6069}(290, \cdot)\) |
n/a |
1386 |
2 |
| 6069.2.s |
\(\chi_{6069}(866, \cdot)\) |
n/a |
1384 |
2 |
| 6069.2.u |
\(\chi_{6069}(757, \cdot)\) |
n/a |
1072 |
4 |
| 6069.2.w |
\(\chi_{6069}(1868, \cdot)\) |
n/a |
2768 |
4 |
| 6069.2.y |
\(\chi_{6069}(38, \cdot)\) |
n/a |
2768 |
4 |
| 6069.2.bb |
\(\chi_{6069}(1696, \cdot)\) |
n/a |
1440 |
4 |
| 6069.2.bc |
\(\chi_{6069}(538, \cdot)\) |
n/a |
2880 |
8 |
| 6069.2.bf |
\(\chi_{6069}(827, \cdot)\) |
n/a |
4320 |
8 |
| 6069.2.bg |
\(\chi_{6069}(358, \cdot)\) |
n/a |
4864 |
16 |
| 6069.2.bi |
\(\chi_{6069}(688, \cdot)\) |
n/a |
2880 |
8 |
| 6069.2.bk |
\(\chi_{6069}(110, \cdot)\) |
n/a |
5536 |
8 |
| 6069.2.bn |
\(\chi_{6069}(169, \cdot)\) |
n/a |
4864 |
16 |
| 6069.2.bp |
\(\chi_{6069}(188, \cdot)\) |
n/a |
12992 |
16 |
| 6069.2.bq |
\(\chi_{6069}(356, \cdot)\) |
n/a |
12992 |
16 |
| 6069.2.bt |
\(\chi_{6069}(40, \cdot)\) |
n/a |
5760 |
16 |
| 6069.2.bu |
\(\chi_{6069}(65, \cdot)\) |
n/a |
11072 |
16 |
| 6069.2.bw |
\(\chi_{6069}(205, \cdot)\) |
n/a |
13056 |
32 |
| 6069.2.by |
\(\chi_{6069}(293, \cdot)\) |
n/a |
25984 |
32 |
| 6069.2.bz |
\(\chi_{6069}(64, \cdot)\) |
n/a |
9728 |
32 |
| 6069.2.cc |
\(\chi_{6069}(101, \cdot)\) |
n/a |
25984 |
32 |
| 6069.2.cd |
\(\chi_{6069}(341, \cdot)\) |
n/a |
25984 |
32 |
| 6069.2.cf |
\(\chi_{6069}(16, \cdot)\) |
n/a |
13056 |
32 |
| 6069.2.ci |
\(\chi_{6069}(83, \cdot)\) |
n/a |
51968 |
64 |
| 6069.2.ck |
\(\chi_{6069}(43, \cdot)\) |
n/a |
19712 |
64 |
| 6069.2.cm |
\(\chi_{6069}(4, \cdot)\) |
n/a |
26112 |
64 |
| 6069.2.cp |
\(\chi_{6069}(47, \cdot)\) |
n/a |
51968 |
64 |
| 6069.2.cq |
\(\chi_{6069}(29, \cdot)\) |
n/a |
78336 |
128 |
| 6069.2.ct |
\(\chi_{6069}(97, \cdot)\) |
n/a |
52224 |
128 |
| 6069.2.cv |
\(\chi_{6069}(26, \cdot)\) |
n/a |
103936 |
128 |
| 6069.2.cx |
\(\chi_{6069}(25, \cdot)\) |
n/a |
52224 |
128 |
| 6069.2.cz |
\(\chi_{6069}(11, \cdot)\) |
n/a |
207872 |
256 |
| 6069.2.da |
\(\chi_{6069}(10, \cdot)\) |
n/a |
104448 |
256 |
"n/a" means that newforms for that character have not been added to the database yet
