Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6909))\).
|
Total |
New |
Old |
| Modular forms
| 1742112 |
1249100 |
493012 |
| Cusp forms
| 1720033 |
1240368 |
479665 |
| Eisenstein series
| 22079 |
8732 |
13347 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6909))\)
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 |
| 6909.2.a |
\(\chi_{6909}(1, \cdot)\) |
6909.2.a.a |
1 |
1 |
| 6909.2.a.b |
1 |
| 6909.2.a.c |
1 |
| 6909.2.a.d |
1 |
| 6909.2.a.e |
1 |
| 6909.2.a.f |
1 |
| 6909.2.a.g |
1 |
| 6909.2.a.h |
1 |
| 6909.2.a.i |
1 |
| 6909.2.a.j |
1 |
| 6909.2.a.k |
1 |
| 6909.2.a.l |
1 |
| 6909.2.a.m |
2 |
| 6909.2.a.n |
2 |
| 6909.2.a.o |
3 |
| 6909.2.a.p |
3 |
| 6909.2.a.q |
3 |
| 6909.2.a.r |
4 |
| 6909.2.a.s |
4 |
| 6909.2.a.t |
5 |
| 6909.2.a.u |
9 |
| 6909.2.a.v |
9 |
| 6909.2.a.w |
10 |
| 6909.2.a.x |
10 |
| 6909.2.a.y |
14 |
| 6909.2.a.z |
14 |
| 6909.2.a.ba |
15 |
| 6909.2.a.bb |
15 |
| 6909.2.a.bc |
15 |
| 6909.2.a.bd |
15 |
| 6909.2.a.be |
15 |
| 6909.2.a.bf |
15 |
| 6909.2.a.bg |
16 |
| 6909.2.a.bh |
16 |
| 6909.2.a.bi |
18 |
| 6909.2.a.bj |
18 |
| 6909.2.a.bk |
26 |
| 6909.2.a.bl |
26 |
| 6909.2.d |
\(\chi_{6909}(2351, \cdot)\) |
n/a |
612 |
1 |
| 6909.2.e |
\(\chi_{6909}(2255, \cdot)\) |
n/a |
646 |
1 |
| 6909.2.h |
\(\chi_{6909}(2302, \cdot)\) |
n/a |
320 |
1 |
| 6909.2.i |
\(\chi_{6909}(5077, \cdot)\) |
n/a |
612 |
2 |
| 6909.2.j |
\(\chi_{6909}(3853, \cdot)\) |
n/a |
640 |
2 |
| 6909.2.m |
\(\chi_{6909}(422, \cdot)\) |
n/a |
1264 |
2 |
| 6909.2.n |
\(\chi_{6909}(3902, \cdot)\) |
n/a |
1228 |
2 |
| 6909.2.q |
\(\chi_{6909}(988, \cdot)\) |
n/a |
2568 |
6 |
| 6909.2.r |
\(\chi_{6909}(328, \cdot)\) |
n/a |
2688 |
6 |
| 6909.2.u |
\(\chi_{6909}(281, \cdot)\) |
n/a |
5352 |
6 |
| 6909.2.v |
\(\chi_{6909}(377, \cdot)\) |
n/a |
5160 |
6 |
| 6909.2.y |
\(\chi_{6909}(142, \cdot)\) |
n/a |
5160 |
12 |
| 6909.2.z |
\(\chi_{6909}(148, \cdot)\) |
n/a |
7216 |
22 |
| 6909.2.bc |
\(\chi_{6909}(236, \cdot)\) |
n/a |
10296 |
12 |
| 6909.2.bd |
\(\chi_{6909}(1409, \cdot)\) |
n/a |
10704 |
12 |
| 6909.2.bg |
\(\chi_{6909}(187, \cdot)\) |
n/a |
5376 |
12 |
| 6909.2.bh |
\(\chi_{6909}(391, \cdot)\) |
n/a |
7040 |
22 |
| 6909.2.bk |
\(\chi_{6909}(344, \cdot)\) |
n/a |
14212 |
22 |
| 6909.2.bl |
\(\chi_{6909}(440, \cdot)\) |
n/a |
13904 |
22 |
| 6909.2.bo |
\(\chi_{6909}(79, \cdot)\) |
n/a |
14080 |
44 |
| 6909.2.br |
\(\chi_{6909}(68, \cdot)\) |
n/a |
27808 |
44 |
| 6909.2.bs |
\(\chi_{6909}(116, \cdot)\) |
n/a |
27808 |
44 |
| 6909.2.bv |
\(\chi_{6909}(19, \cdot)\) |
n/a |
14080 |
44 |
| 6909.2.bw |
\(\chi_{6909}(64, \cdot)\) |
n/a |
59136 |
132 |
| 6909.2.bz |
\(\chi_{6909}(83, \cdot)\) |
n/a |
117744 |
132 |
| 6909.2.ca |
\(\chi_{6909}(29, \cdot)\) |
n/a |
117744 |
132 |
| 6909.2.cd |
\(\chi_{6909}(13, \cdot)\) |
n/a |
59136 |
132 |
| 6909.2.ce |
\(\chi_{6909}(4, \cdot)\) |
n/a |
118272 |
264 |
| 6909.2.cf |
\(\chi_{6909}(10, \cdot)\) |
n/a |
118272 |
264 |
| 6909.2.ci |
\(\chi_{6909}(11, \cdot)\) |
n/a |
235488 |
264 |
| 6909.2.cj |
\(\chi_{6909}(17, \cdot)\) |
n/a |
235488 |
264 |
"n/a" means that newforms for that character have not been added to the database yet
