Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7569))\).
|
Total |
New |
Old |
| Modular forms
| 2128952 |
1678976 |
449976 |
| Cusp forms
| 2109689 |
1668639 |
441050 |
| Eisenstein series
| 19263 |
10337 |
8926 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7569))\)
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 |
| 7569.2.a |
\(\chi_{7569}(1, \cdot)\) |
7569.2.a.a |
1 |
1 |
| 7569.2.a.b |
1 |
| 7569.2.a.c |
2 |
| 7569.2.a.d |
2 |
| 7569.2.a.e |
2 |
| 7569.2.a.f |
2 |
| 7569.2.a.g |
2 |
| 7569.2.a.h |
2 |
| 7569.2.a.i |
2 |
| 7569.2.a.j |
2 |
| 7569.2.a.k |
2 |
| 7569.2.a.l |
2 |
| 7569.2.a.m |
2 |
| 7569.2.a.n |
2 |
| 7569.2.a.o |
2 |
| 7569.2.a.p |
3 |
| 7569.2.a.q |
3 |
| 7569.2.a.r |
3 |
| 7569.2.a.s |
3 |
| 7569.2.a.t |
3 |
| 7569.2.a.u |
4 |
| 7569.2.a.v |
4 |
| 7569.2.a.w |
4 |
| 7569.2.a.x |
4 |
| 7569.2.a.y |
6 |
| 7569.2.a.z |
6 |
| 7569.2.a.ba |
6 |
| 7569.2.a.bb |
6 |
| 7569.2.a.bc |
6 |
| 7569.2.a.bd |
8 |
| 7569.2.a.be |
8 |
| 7569.2.a.bf |
8 |
| 7569.2.a.bg |
8 |
| 7569.2.a.bh |
8 |
| 7569.2.a.bi |
8 |
| 7569.2.a.bj |
9 |
| 7569.2.a.bk |
9 |
| 7569.2.a.bl |
9 |
| 7569.2.a.bm |
9 |
| 7569.2.a.bn |
12 |
| 7569.2.a.bo |
12 |
| 7569.2.a.bp |
12 |
| 7569.2.a.bq |
12 |
| 7569.2.a.br |
12 |
| 7569.2.a.bs |
12 |
| 7569.2.a.bt |
12 |
| 7569.2.a.bu |
16 |
| 7569.2.a.bv |
16 |
| 7569.2.a.bw |
36 |
| 7569.2.c |
\(\chi_{7569}(4204, \cdot)\) |
n/a |
324 |
1 |
| 7569.2.e |
\(\chi_{7569}(2524, \cdot)\) |
n/a |
1568 |
2 |
| 7569.2.g |
\(\chi_{7569}(800, \cdot)\) |
n/a |
540 |
2 |
| 7569.2.i |
\(\chi_{7569}(1681, \cdot)\) |
n/a |
1568 |
2 |
| 7569.2.k |
\(\chi_{7569}(190, \cdot)\) |
n/a |
1950 |
6 |
| 7569.2.l |
\(\chi_{7569}(41, \cdot)\) |
n/a |
3136 |
4 |
| 7569.2.o |
\(\chi_{7569}(1108, \cdot)\) |
n/a |
1944 |
6 |
| 7569.2.q |
\(\chi_{7569}(571, \cdot)\) |
n/a |
9408 |
12 |
| 7569.2.r |
\(\chi_{7569}(467, \cdot)\) |
n/a |
3240 |
12 |
| 7569.2.t |
\(\chi_{7569}(262, \cdot)\) |
n/a |
10108 |
28 |
| 7569.2.v |
\(\chi_{7569}(196, \cdot)\) |
n/a |
9408 |
12 |
| 7569.2.y |
\(\chi_{7569}(28, \cdot)\) |
n/a |
10136 |
28 |
| 7569.2.bb |
\(\chi_{7569}(14, \cdot)\) |
n/a |
18816 |
24 |
| 7569.2.bc |
\(\chi_{7569}(88, \cdot)\) |
n/a |
48608 |
56 |
| 7569.2.bd |
\(\chi_{7569}(17, \cdot)\) |
n/a |
16240 |
56 |
| 7569.2.bg |
\(\chi_{7569}(115, \cdot)\) |
n/a |
48608 |
56 |
| 7569.2.bi |
\(\chi_{7569}(82, \cdot)\) |
n/a |
60648 |
168 |
| 7569.2.bk |
\(\chi_{7569}(104, \cdot)\) |
n/a |
97216 |
112 |
| 7569.2.bm |
\(\chi_{7569}(64, \cdot)\) |
n/a |
60816 |
168 |
| 7569.2.bo |
\(\chi_{7569}(7, \cdot)\) |
n/a |
291648 |
336 |
| 7569.2.bq |
\(\chi_{7569}(8, \cdot)\) |
n/a |
97440 |
336 |
| 7569.2.bs |
\(\chi_{7569}(4, \cdot)\) |
n/a |
291648 |
336 |
| 7569.2.bu |
\(\chi_{7569}(2, \cdot)\) |
n/a |
583296 |
672 |
"n/a" means that newforms for that character have not been added to the database yet
