Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8009))\).
|
Total |
New |
Old |
| Modular forms
| 2676674 |
2676674 |
0 |
| Cusp forms
| 2668667 |
2668667 |
0 |
| Eisenstein series
| 8007 |
8007 |
0 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8009))\)
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 |
| 8009.2.a |
\(\chi_{8009}(1, \cdot)\) |
8009.2.a.a |
306 |
1 |
| 8009.2.a.b |
361 |
| 8009.2.b |
\(\chi_{8009}(8008, \cdot)\) |
n/a |
666 |
1 |
| 8009.2.c |
\(\chi_{8009}(283, \cdot)\) |
n/a |
1334 |
2 |
| 8009.2.d |
\(\chi_{8009}(983, \cdot)\) |
n/a |
3996 |
6 |
| 8009.2.f |
\(\chi_{8009}(112, \cdot)\) |
n/a |
6660 |
10 |
| 8009.2.g |
\(\chi_{8009}(753, \cdot)\) |
n/a |
7992 |
12 |
| 8009.2.h |
\(\chi_{8009}(811, \cdot)\) |
n/a |
3996 |
6 |
| 8009.2.i |
\(\chi_{8009}(887, \cdot)\) |
n/a |
6660 |
10 |
| 8009.2.j |
\(\chi_{8009}(385, \cdot)\) |
n/a |
7992 |
12 |
| 8009.2.k |
\(\chi_{8009}(491, \cdot)\) |
n/a |
8004 |
12 |
| 8009.2.l |
\(\chi_{8009}(212, \cdot)\) |
n/a |
13340 |
20 |
| 8009.2.m |
\(\chi_{8009}(50, \cdot)\) |
n/a |
16008 |
24 |
| 8009.2.o |
\(\chi_{8009}(393, \cdot)\) |
n/a |
39960 |
60 |
| 8009.2.q |
\(\chi_{8009}(18, \cdot)\) |
n/a |
47952 |
72 |
| 8009.2.s |
\(\chi_{8009}(137, \cdot)\) |
n/a |
79920 |
120 |
| 8009.2.t |
\(\chi_{8009}(25, \cdot)\) |
n/a |
39960 |
60 |
| 8009.2.u |
\(\chi_{8009}(116, \cdot)\) |
n/a |
47952 |
72 |
| 8009.2.v |
\(\chi_{8009}(13, \cdot)\) |
n/a |
79920 |
120 |
| 8009.2.w |
\(\chi_{8009}(5, \cdot)\) |
n/a |
80040 |
120 |
| 8009.2.x |
\(\chi_{8009}(44, \cdot)\) |
n/a |
96048 |
144 |
| 8009.2.y |
\(\chi_{8009}(80, \cdot)\) |
n/a |
160080 |
240 |
| 8009.2.bb |
\(\chi_{8009}(7, \cdot)\) |
n/a |
479520 |
720 |
| 8009.2.bd |
\(\chi_{8009}(4, \cdot)\) |
n/a |
479520 |
720 |
| 8009.2.be |
\(\chi_{8009}(2, \cdot)\) |
n/a |
960480 |
1440 |
"n/a" means that newforms for that character have not been added to the database yet
