Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5415))\).
|
Total |
New |
Old |
| Modular forms
| 1047744 |
713636 |
334108 |
| Cusp forms
| 1031617 |
708012 |
323605 |
| Eisenstein series
| 16127 |
5624 |
10503 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5415))\)
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 |
| 5415.2.a |
\(\chi_{5415}(1, \cdot)\) |
5415.2.a.a |
1 |
1 |
| 5415.2.a.b |
1 |
| 5415.2.a.c |
1 |
| 5415.2.a.d |
1 |
| 5415.2.a.e |
1 |
| 5415.2.a.f |
1 |
| 5415.2.a.g |
1 |
| 5415.2.a.h |
1 |
| 5415.2.a.i |
1 |
| 5415.2.a.j |
1 |
| 5415.2.a.k |
1 |
| 5415.2.a.l |
1 |
| 5415.2.a.m |
2 |
| 5415.2.a.n |
2 |
| 5415.2.a.o |
2 |
| 5415.2.a.p |
2 |
| 5415.2.a.q |
2 |
| 5415.2.a.r |
2 |
| 5415.2.a.s |
2 |
| 5415.2.a.t |
2 |
| 5415.2.a.u |
2 |
| 5415.2.a.v |
2 |
| 5415.2.a.w |
3 |
| 5415.2.a.x |
3 |
| 5415.2.a.y |
5 |
| 5415.2.a.z |
5 |
| 5415.2.a.ba |
6 |
| 5415.2.a.bb |
6 |
| 5415.2.a.bc |
6 |
| 5415.2.a.bd |
6 |
| 5415.2.a.be |
6 |
| 5415.2.a.bf |
6 |
| 5415.2.a.bg |
6 |
| 5415.2.a.bh |
6 |
| 5415.2.a.bi |
6 |
| 5415.2.a.bj |
6 |
| 5415.2.a.bk |
9 |
| 5415.2.a.bl |
9 |
| 5415.2.a.bm |
12 |
| 5415.2.a.bn |
12 |
| 5415.2.a.bo |
12 |
| 5415.2.a.bp |
12 |
| 5415.2.a.bq |
12 |
| 5415.2.a.br |
12 |
| 5415.2.a.bs |
15 |
| 5415.2.a.bt |
15 |
| 5415.2.b |
\(\chi_{5415}(5414, \cdot)\) |
n/a |
648 |
1 |
| 5415.2.c |
\(\chi_{5415}(1084, \cdot)\) |
n/a |
340 |
1 |
| 5415.2.h |
\(\chi_{5415}(4331, \cdot)\) |
n/a |
452 |
1 |
| 5415.2.i |
\(\chi_{5415}(2956, \cdot)\) |
n/a |
456 |
2 |
| 5415.2.k |
\(\chi_{5415}(362, \cdot)\) |
n/a |
1296 |
2 |
| 5415.2.m |
\(\chi_{5415}(2887, \cdot)\) |
n/a |
680 |
2 |
| 5415.2.p |
\(\chi_{5415}(791, \cdot)\) |
n/a |
904 |
2 |
| 5415.2.q |
\(\chi_{5415}(1874, \cdot)\) |
n/a |
1296 |
2 |
| 5415.2.r |
\(\chi_{5415}(4039, \cdot)\) |
n/a |
680 |
2 |
| 5415.2.u |
\(\chi_{5415}(1111, \cdot)\) |
n/a |
1356 |
6 |
| 5415.2.v |
\(\chi_{5415}(68, \cdot)\) |
n/a |
2592 |
4 |
| 5415.2.x |
\(\chi_{5415}(1513, \cdot)\) |
n/a |
1360 |
4 |
| 5415.2.z |
\(\chi_{5415}(116, \cdot)\) |
n/a |
2724 |
6 |
| 5415.2.be |
\(\chi_{5415}(784, \cdot)\) |
n/a |
2040 |
6 |
| 5415.2.bf |
\(\chi_{5415}(299, \cdot)\) |
n/a |
3888 |
6 |
| 5415.2.bg |
\(\chi_{5415}(286, \cdot)\) |
n/a |
4536 |
18 |
| 5415.2.bi |
\(\chi_{5415}(127, \cdot)\) |
n/a |
4080 |
12 |
| 5415.2.bj |
\(\chi_{5415}(62, \cdot)\) |
n/a |
7776 |
12 |
| 5415.2.bl |
\(\chi_{5415}(56, \cdot)\) |
n/a |
9144 |
18 |
| 5415.2.bq |
\(\chi_{5415}(229, \cdot)\) |
n/a |
6840 |
18 |
| 5415.2.br |
\(\chi_{5415}(284, \cdot)\) |
n/a |
13608 |
18 |
| 5415.2.bs |
\(\chi_{5415}(106, \cdot)\) |
n/a |
9072 |
36 |
| 5415.2.bt |
\(\chi_{5415}(37, \cdot)\) |
n/a |
13680 |
36 |
| 5415.2.bv |
\(\chi_{5415}(77, \cdot)\) |
n/a |
27216 |
36 |
| 5415.2.bz |
\(\chi_{5415}(49, \cdot)\) |
n/a |
13680 |
36 |
| 5415.2.ca |
\(\chi_{5415}(164, \cdot)\) |
n/a |
27216 |
36 |
| 5415.2.cb |
\(\chi_{5415}(221, \cdot)\) |
n/a |
18288 |
36 |
| 5415.2.ce |
\(\chi_{5415}(16, \cdot)\) |
n/a |
27432 |
108 |
| 5415.2.cg |
\(\chi_{5415}(88, \cdot)\) |
n/a |
27360 |
72 |
| 5415.2.ci |
\(\chi_{5415}(83, \cdot)\) |
n/a |
54432 |
72 |
| 5415.2.cj |
\(\chi_{5415}(14, \cdot)\) |
n/a |
81648 |
108 |
| 5415.2.ck |
\(\chi_{5415}(4, \cdot)\) |
n/a |
41040 |
108 |
| 5415.2.cp |
\(\chi_{5415}(41, \cdot)\) |
n/a |
54648 |
108 |
| 5415.2.cr |
\(\chi_{5415}(17, \cdot)\) |
n/a |
163296 |
216 |
| 5415.2.cs |
\(\chi_{5415}(13, \cdot)\) |
n/a |
82080 |
216 |
"n/a" means that newforms for that character have not been added to the database yet
