Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2669))\).
|
Total |
New |
Old |
Modular forms
| 298272 |
296023 |
2249 |
Cusp forms
| 293281 |
291371 |
1910 |
Eisenstein series
| 4991 |
4652 |
339 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2669))\)
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 |
2669.2.a |
\(\chi_{2669}(1, \cdot)\) |
2669.2.a.a |
44 |
1 |
2669.2.a.b |
45 |
2669.2.a.c |
60 |
2669.2.a.d |
60 |
2669.2.b |
\(\chi_{2669}(2668, \cdot)\) |
n/a |
236 |
1 |
2669.2.c |
\(\chi_{2669}(1412, \cdot)\) |
n/a |
212 |
1 |
2669.2.d |
\(\chi_{2669}(1257, \cdot)\) |
n/a |
234 |
1 |
2669.2.e |
\(\chi_{2669}(1582, \cdot)\) |
n/a |
420 |
2 |
2669.2.f |
\(\chi_{2669}(472, \cdot)\) |
n/a |
468 |
2 |
2669.2.k |
\(\chi_{2669}(1883, \cdot)\) |
n/a |
472 |
2 |
2669.2.l |
\(\chi_{2669}(2211, \cdot)\) |
n/a |
420 |
2 |
2669.2.m |
\(\chi_{2669}(798, \cdot)\) |
n/a |
472 |
2 |
2669.2.n |
\(\chi_{2669}(169, \cdot)\) |
n/a |
468 |
2 |
2669.2.p |
\(\chi_{2669}(627, \cdot)\) |
n/a |
936 |
4 |
2669.2.q |
\(\chi_{2669}(315, \cdot)\) |
n/a |
936 |
4 |
2669.2.s |
\(\chi_{2669}(2053, \cdot)\) |
n/a |
936 |
4 |
2669.2.x |
\(\chi_{2669}(13, \cdot)\) |
n/a |
944 |
4 |
2669.2.y |
\(\chi_{2669}(171, \cdot)\) |
n/a |
2544 |
12 |
2669.2.ba |
\(\chi_{2669}(129, \cdot)\) |
n/a |
1880 |
8 |
2669.2.bb |
\(\chi_{2669}(28, \cdot)\) |
n/a |
1880 |
8 |
2669.2.be |
\(\chi_{2669}(144, \cdot)\) |
n/a |
1888 |
8 |
2669.2.bf |
\(\chi_{2669}(145, \cdot)\) |
n/a |
1872 |
8 |
2669.2.bh |
\(\chi_{2669}(16, \cdot)\) |
n/a |
2808 |
12 |
2669.2.bi |
\(\chi_{2669}(239, \cdot)\) |
n/a |
2544 |
12 |
2669.2.bj |
\(\chi_{2669}(118, \cdot)\) |
n/a |
2832 |
12 |
2669.2.bk |
\(\chi_{2669}(35, \cdot)\) |
n/a |
5040 |
24 |
2669.2.bm |
\(\chi_{2669}(207, \cdot)\) |
n/a |
3760 |
16 |
2669.2.bn |
\(\chi_{2669}(22, \cdot)\) |
n/a |
3760 |
16 |
2669.2.bp |
\(\chi_{2669}(4, \cdot)\) |
n/a |
5664 |
24 |
2669.2.bu |
\(\chi_{2669}(310, \cdot)\) |
n/a |
5616 |
24 |
2669.2.bv |
\(\chi_{2669}(560, \cdot)\) |
n/a |
5616 |
24 |
2669.2.bw |
\(\chi_{2669}(33, \cdot)\) |
n/a |
5664 |
24 |
2669.2.bx |
\(\chi_{2669}(86, \cdot)\) |
n/a |
5040 |
24 |
2669.2.bz |
\(\chi_{2669}(93, \cdot)\) |
n/a |
11328 |
48 |
2669.2.ca |
\(\chi_{2669}(49, \cdot)\) |
n/a |
11232 |
48 |
2669.2.cc |
\(\chi_{2669}(140, \cdot)\) |
n/a |
11328 |
48 |
2669.2.ch |
\(\chi_{2669}(30, \cdot)\) |
n/a |
11232 |
48 |
2669.2.cj |
\(\chi_{2669}(41, \cdot)\) |
n/a |
22560 |
96 |
2669.2.ck |
\(\chi_{2669}(7, \cdot)\) |
n/a |
22560 |
96 |
2669.2.cn |
\(\chi_{2669}(25, \cdot)\) |
n/a |
22464 |
96 |
2669.2.co |
\(\chi_{2669}(9, \cdot)\) |
n/a |
22656 |
96 |
2669.2.cr |
\(\chi_{2669}(5, \cdot)\) |
n/a |
45120 |
192 |
2669.2.cs |
\(\chi_{2669}(20, \cdot)\) |
n/a |
45120 |
192 |
"n/a" means that newforms for that character have not been added to the database yet