Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6008))\).
|
Total |
New |
Old |
Modular forms
| 1132500 |
635996 |
496504 |
Cusp forms
| 1123501 |
633000 |
490501 |
Eisenstein series
| 8999 |
2996 |
6003 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6008))\)
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 |
6008.2.a |
\(\chi_{6008}(1, \cdot)\) |
6008.2.a.a |
1 |
1 |
6008.2.a.b |
44 |
6008.2.a.c |
44 |
6008.2.a.d |
49 |
6008.2.a.e |
50 |
6008.2.b |
\(\chi_{6008}(3003, \cdot)\) |
n/a |
750 |
1 |
6008.2.c |
\(\chi_{6008}(3005, \cdot)\) |
n/a |
750 |
1 |
6008.2.h |
\(\chi_{6008}(6007, \cdot)\) |
None |
0 |
1 |
6008.2.i |
\(\chi_{6008}(4433, \cdot)\) |
n/a |
376 |
2 |
6008.2.j |
\(\chi_{6008}(569, \cdot)\) |
n/a |
752 |
4 |
6008.2.k |
\(\chi_{6008}(679, \cdot)\) |
None |
0 |
2 |
6008.2.p |
\(\chi_{6008}(1429, \cdot)\) |
n/a |
1500 |
2 |
6008.2.q |
\(\chi_{6008}(3683, \cdot)\) |
n/a |
1500 |
2 |
6008.2.r |
\(\chi_{6008}(359, \cdot)\) |
None |
0 |
4 |
6008.2.w |
\(\chi_{6008}(2333, \cdot)\) |
n/a |
3000 |
4 |
6008.2.x |
\(\chi_{6008}(291, \cdot)\) |
n/a |
3000 |
4 |
6008.2.y |
\(\chi_{6008}(673, \cdot)\) |
n/a |
1504 |
8 |
6008.2.z |
\(\chi_{6008}(193, \cdot)\) |
n/a |
3760 |
20 |
6008.2.ba |
\(\chi_{6008}(675, \cdot)\) |
n/a |
6000 |
8 |
6008.2.bb |
\(\chi_{6008}(437, \cdot)\) |
n/a |
6000 |
8 |
6008.2.bg |
\(\chi_{6008}(583, \cdot)\) |
None |
0 |
8 |
6008.2.bi |
\(\chi_{6008}(799, \cdot)\) |
None |
0 |
20 |
6008.2.bl |
\(\chi_{6008}(53, \cdot)\) |
n/a |
15000 |
20 |
6008.2.bn |
\(\chi_{6008}(195, \cdot)\) |
n/a |
15000 |
20 |
6008.2.bo |
\(\chi_{6008}(121, \cdot)\) |
n/a |
7520 |
40 |
6008.2.bp |
\(\chi_{6008}(49, \cdot)\) |
n/a |
18800 |
100 |
6008.2.br |
\(\chi_{6008}(61, \cdot)\) |
n/a |
30000 |
40 |
6008.2.bt |
\(\chi_{6008}(11, \cdot)\) |
n/a |
30000 |
40 |
6008.2.bv |
\(\chi_{6008}(223, \cdot)\) |
None |
0 |
40 |
6008.2.bz |
\(\chi_{6008}(7, \cdot)\) |
None |
0 |
100 |
6008.2.ca |
\(\chi_{6008}(27, \cdot)\) |
n/a |
75000 |
100 |
6008.2.cb |
\(\chi_{6008}(45, \cdot)\) |
n/a |
75000 |
100 |
6008.2.ce |
\(\chi_{6008}(9, \cdot)\) |
n/a |
37600 |
200 |
6008.2.ch |
\(\chi_{6008}(5, \cdot)\) |
n/a |
150000 |
200 |
6008.2.ci |
\(\chi_{6008}(15, \cdot)\) |
None |
0 |
200 |
6008.2.cj |
\(\chi_{6008}(3, \cdot)\) |
n/a |
150000 |
200 |
"n/a" means that newforms for that character have not been added to the database yet