Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4011))\).
|
Total |
New |
Old |
Modular forms
| 588240 |
421387 |
166853 |
Cusp forms
| 579121 |
417611 |
161510 |
Eisenstein series
| 9119 |
3776 |
5343 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4011))\)
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 |
4011.2.a |
\(\chi_{4011}(1, \cdot)\) |
4011.2.a.a |
1 |
1 |
4011.2.a.b |
1 |
4011.2.a.c |
1 |
4011.2.a.d |
1 |
4011.2.a.e |
3 |
4011.2.a.f |
18 |
4011.2.a.g |
18 |
4011.2.a.h |
19 |
4011.2.a.i |
19 |
4011.2.a.j |
26 |
4011.2.a.k |
27 |
4011.2.a.l |
28 |
4011.2.a.m |
29 |
4011.2.c |
\(\chi_{4011}(2864, \cdot)\) |
n/a |
384 |
1 |
4011.2.d |
\(\chi_{4011}(3821, \cdot)\) |
n/a |
508 |
1 |
4011.2.f |
\(\chi_{4011}(1336, \cdot)\) |
n/a |
256 |
1 |
4011.2.i |
\(\chi_{4011}(2293, \cdot)\) |
n/a |
508 |
2 |
4011.2.j |
\(\chi_{4011}(421, \cdot)\) |
n/a |
768 |
4 |
4011.2.m |
\(\chi_{4011}(1909, \cdot)\) |
n/a |
512 |
2 |
4011.2.o |
\(\chi_{4011}(383, \cdot)\) |
n/a |
1012 |
2 |
4011.2.p |
\(\chi_{4011}(1145, \cdot)\) |
n/a |
1016 |
2 |
4011.2.r |
\(\chi_{4011}(580, \cdot)\) |
n/a |
1024 |
4 |
4011.2.v |
\(\chi_{4011}(1037, \cdot)\) |
n/a |
1536 |
4 |
4011.2.w |
\(\chi_{4011}(230, \cdot)\) |
n/a |
2032 |
4 |
4011.2.y |
\(\chi_{4011}(109, \cdot)\) |
n/a |
2048 |
8 |
4011.2.z |
\(\chi_{4011}(316, \cdot)\) |
n/a |
3456 |
18 |
4011.2.bb |
\(\chi_{4011}(803, \cdot)\) |
n/a |
4064 |
8 |
4011.2.bc |
\(\chi_{4011}(389, \cdot)\) |
n/a |
4064 |
8 |
4011.2.bg |
\(\chi_{4011}(82, \cdot)\) |
n/a |
2048 |
8 |
4011.2.bj |
\(\chi_{4011}(55, \cdot)\) |
n/a |
4608 |
18 |
4011.2.bl |
\(\chi_{4011}(125, \cdot)\) |
n/a |
9144 |
18 |
4011.2.bm |
\(\chi_{4011}(155, \cdot)\) |
n/a |
6912 |
18 |
4011.2.bo |
\(\chi_{4011}(25, \cdot)\) |
n/a |
9216 |
36 |
4011.2.bp |
\(\chi_{4011}(43, \cdot)\) |
n/a |
13824 |
72 |
4011.2.br |
\(\chi_{4011}(11, \cdot)\) |
n/a |
18288 |
36 |
4011.2.bs |
\(\chi_{4011}(5, \cdot)\) |
n/a |
18288 |
36 |
4011.2.bu |
\(\chi_{4011}(31, \cdot)\) |
n/a |
9216 |
36 |
4011.2.by |
\(\chi_{4011}(20, \cdot)\) |
n/a |
36576 |
72 |
4011.2.bz |
\(\chi_{4011}(29, \cdot)\) |
n/a |
27648 |
72 |
4011.2.cd |
\(\chi_{4011}(76, \cdot)\) |
n/a |
18432 |
72 |
4011.2.ce |
\(\chi_{4011}(4, \cdot)\) |
n/a |
36864 |
144 |
4011.2.cf |
\(\chi_{4011}(19, \cdot)\) |
n/a |
36864 |
144 |
4011.2.cj |
\(\chi_{4011}(44, \cdot)\) |
n/a |
73152 |
144 |
4011.2.ck |
\(\chi_{4011}(17, \cdot)\) |
n/a |
73152 |
144 |
"n/a" means that newforms for that character have not been added to the database yet