Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8673))\).
|
Total |
New |
Old |
Modular forms
| 2742240 |
1967990 |
774250 |
Cusp forms
| 2714401 |
1956930 |
757471 |
Eisenstein series
| 27839 |
11060 |
16779 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8673))\)
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 the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
8673.2.a |
\(\chi_{8673}(1, \cdot)\) |
8673.2.a.a |
1 |
1 |
8673.2.a.b |
1 |
8673.2.a.c |
1 |
8673.2.a.d |
1 |
8673.2.a.e |
1 |
8673.2.a.f |
1 |
8673.2.a.g |
1 |
8673.2.a.h |
1 |
8673.2.a.i |
1 |
8673.2.a.j |
2 |
8673.2.a.k |
2 |
8673.2.a.l |
2 |
8673.2.a.m |
2 |
8673.2.a.n |
2 |
8673.2.a.o |
3 |
8673.2.a.p |
3 |
8673.2.a.q |
3 |
8673.2.a.r |
3 |
8673.2.a.s |
3 |
8673.2.a.t |
4 |
8673.2.a.u |
4 |
8673.2.a.v |
10 |
8673.2.a.w |
11 |
8673.2.a.x |
11 |
8673.2.a.y |
12 |
8673.2.a.z |
12 |
8673.2.a.ba |
12 |
8673.2.a.bb |
14 |
8673.2.a.bc |
14 |
8673.2.a.bd |
16 |
8673.2.a.be |
16 |
8673.2.a.bf |
17 |
8673.2.a.bg |
17 |
8673.2.a.bh |
20 |
8673.2.a.bi |
20 |
8673.2.a.bj |
20 |
8673.2.a.bk |
20 |
8673.2.a.bl |
26 |
8673.2.a.bm |
26 |
8673.2.a.bn |
30 |
8673.2.a.bo |
30 |
8673.2.b |
\(\chi_{8673}(2890, \cdot)\) |
n/a |
400 |
1 |
8673.2.d |
\(\chi_{8673}(8084, \cdot)\) |
n/a |
772 |
1 |
8673.2.g |
\(\chi_{8673}(6371, \cdot)\) |
n/a |
810 |
1 |
8673.2.i |
\(\chi_{8673}(2125, \cdot)\) |
n/a |
772 |
2 |
8673.2.k |
\(\chi_{8673}(3362, \cdot)\) |
n/a |
1584 |
2 |
8673.2.n |
\(\chi_{8673}(2420, \cdot)\) |
n/a |
1548 |
2 |
8673.2.p |
\(\chi_{8673}(766, \cdot)\) |
n/a |
800 |
2 |
8673.2.q |
\(\chi_{8673}(1240, \cdot)\) |
n/a |
3240 |
6 |
8673.2.t |
\(\chi_{8673}(176, \cdot)\) |
n/a |
6696 |
6 |
8673.2.u |
\(\chi_{8673}(650, \cdot)\) |
n/a |
6504 |
6 |
8673.2.w |
\(\chi_{8673}(412, \cdot)\) |
n/a |
3360 |
6 |
8673.2.y |
\(\chi_{8673}(709, \cdot)\) |
n/a |
6504 |
12 |
8673.2.z |
\(\chi_{8673}(442, \cdot)\) |
n/a |
11480 |
28 |
8673.2.bb |
\(\chi_{8673}(943, \cdot)\) |
n/a |
6720 |
12 |
8673.2.bd |
\(\chi_{8673}(1004, \cdot)\) |
n/a |
12984 |
12 |
8673.2.be |
\(\chi_{8673}(884, \cdot)\) |
n/a |
13392 |
12 |
8673.2.bi |
\(\chi_{8673}(50, \cdot)\) |
n/a |
22680 |
28 |
8673.2.bl |
\(\chi_{8673}(146, \cdot)\) |
n/a |
22176 |
28 |
8673.2.bn |
\(\chi_{8673}(97, \cdot)\) |
n/a |
11200 |
28 |
8673.2.bo |
\(\chi_{8673}(79, \cdot)\) |
n/a |
22400 |
56 |
8673.2.bp |
\(\chi_{8673}(31, \cdot)\) |
n/a |
22400 |
56 |
8673.2.br |
\(\chi_{8673}(68, \cdot)\) |
n/a |
44352 |
56 |
8673.2.bu |
\(\chi_{8673}(128, \cdot)\) |
n/a |
44352 |
56 |
8673.2.bw |
\(\chi_{8673}(22, \cdot)\) |
n/a |
94080 |
168 |
8673.2.by |
\(\chi_{8673}(13, \cdot)\) |
n/a |
94080 |
168 |
8673.2.ca |
\(\chi_{8673}(20, \cdot)\) |
n/a |
187488 |
168 |
8673.2.cb |
\(\chi_{8673}(8, \cdot)\) |
n/a |
187488 |
168 |
8673.2.ce |
\(\chi_{8673}(4, \cdot)\) |
n/a |
188160 |
336 |
8673.2.ch |
\(\chi_{8673}(2, \cdot)\) |
n/a |
374976 |
336 |
8673.2.ci |
\(\chi_{8673}(5, \cdot)\) |
n/a |
374976 |
336 |
8673.2.ck |
\(\chi_{8673}(10, \cdot)\) |
n/a |
188160 |
336 |
"n/a" means that newforms for that character have not been added to the database yet