Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4010))\).
|
Total |
New |
Old |
Modular forms
| 485600 |
147401 |
338199 |
Cusp forms
| 479201 |
147401 |
331800 |
Eisenstein series
| 6399 |
0 |
6399 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4010))\)
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 |
4010.2.a |
\(\chi_{4010}(1, \cdot)\) |
4010.2.a.a |
1 |
1 |
4010.2.a.b |
1 |
4010.2.a.c |
1 |
4010.2.a.d |
1 |
4010.2.a.e |
1 |
4010.2.a.f |
1 |
4010.2.a.g |
2 |
4010.2.a.h |
9 |
4010.2.a.i |
10 |
4010.2.a.j |
12 |
4010.2.a.k |
15 |
4010.2.a.l |
17 |
4010.2.a.m |
20 |
4010.2.a.n |
22 |
4010.2.a.o |
22 |
4010.2.b |
\(\chi_{4010}(3209, \cdot)\) |
n/a |
200 |
1 |
4010.2.c |
\(\chi_{4010}(801, \cdot)\) |
n/a |
134 |
1 |
4010.2.d |
\(\chi_{4010}(4009, \cdot)\) |
n/a |
200 |
1 |
4010.2.f |
\(\chi_{4010}(381, \cdot)\) |
n/a |
268 |
2 |
4010.2.i |
\(\chi_{4010}(3589, \cdot)\) |
n/a |
400 |
2 |
4010.2.k |
\(\chi_{4010}(841, \cdot)\) |
n/a |
536 |
4 |
4010.2.m |
\(\chi_{4010}(1301, \cdot)\) |
n/a |
536 |
4 |
4010.2.n |
\(\chi_{4010}(499, \cdot)\) |
n/a |
808 |
4 |
4010.2.p |
\(\chi_{4010}(29, \cdot)\) |
n/a |
800 |
4 |
4010.2.q |
\(\chi_{4010}(831, \cdot)\) |
n/a |
536 |
4 |
4010.2.r |
\(\chi_{4010}(39, \cdot)\) |
n/a |
800 |
4 |
4010.2.u |
\(\chi_{4010}(147, \cdot)\) |
n/a |
1608 |
8 |
4010.2.v |
\(\chi_{4010}(133, \cdot)\) |
n/a |
1608 |
8 |
4010.2.x |
\(\chi_{4010}(179, \cdot)\) |
n/a |
1600 |
8 |
4010.2.ba |
\(\chi_{4010}(981, \cdot)\) |
n/a |
1072 |
8 |
4010.2.bc |
\(\chi_{4010}(51, \cdot)\) |
n/a |
2680 |
20 |
4010.2.be |
\(\chi_{4010}(239, \cdot)\) |
n/a |
3232 |
16 |
4010.2.bf |
\(\chi_{4010}(151, \cdot)\) |
n/a |
2144 |
16 |
4010.2.bh |
\(\chi_{4010}(629, \cdot)\) |
n/a |
4000 |
20 |
4010.2.bi |
\(\chi_{4010}(41, \cdot)\) |
n/a |
2680 |
20 |
4010.2.bj |
\(\chi_{4010}(489, \cdot)\) |
n/a |
4000 |
20 |
4010.2.bm |
\(\chi_{4010}(153, \cdot)\) |
n/a |
6432 |
32 |
4010.2.bn |
\(\chi_{4010}(33, \cdot)\) |
n/a |
6432 |
32 |
4010.2.bo |
\(\chi_{4010}(81, \cdot)\) |
n/a |
5360 |
40 |
4010.2.bp |
\(\chi_{4010}(49, \cdot)\) |
n/a |
8000 |
40 |
4010.2.bu |
\(\chi_{4010}(11, \cdot)\) |
n/a |
10720 |
80 |
4010.2.bv |
\(\chi_{4010}(9, \cdot)\) |
n/a |
16160 |
80 |
4010.2.by |
\(\chi_{4010}(3, \cdot)\) |
n/a |
32160 |
160 |
4010.2.bz |
\(\chi_{4010}(13, \cdot)\) |
n/a |
32160 |
160 |
"n/a" means that newforms for that character have not been added to the database yet