Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6137))\).
|
Total |
New |
Old |
| Modular forms
| 1567584 |
1547150 |
20434 |
| Cusp forms
| 1551457 |
1533096 |
18361 |
| Eisenstein series
| 16127 |
14054 |
2073 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6137))\)
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 |
| 6137.2.a |
\(\chi_{6137}(1, \cdot)\) |
6137.2.a.a |
1 |
1 |
| 6137.2.a.b |
1 |
| 6137.2.a.c |
2 |
| 6137.2.a.d |
4 |
| 6137.2.a.e |
5 |
| 6137.2.a.f |
6 |
| 6137.2.a.g |
7 |
| 6137.2.a.h |
10 |
| 6137.2.a.i |
14 |
| 6137.2.a.j |
14 |
| 6137.2.a.k |
14 |
| 6137.2.a.l |
14 |
| 6137.2.a.m |
14 |
| 6137.2.a.n |
20 |
| 6137.2.a.o |
20 |
| 6137.2.a.p |
28 |
| 6137.2.a.q |
28 |
| 6137.2.a.r |
39 |
| 6137.2.a.s |
39 |
| 6137.2.a.t |
39 |
| 6137.2.a.u |
39 |
| 6137.2.a.v |
40 |
| 6137.2.a.w |
56 |
| 6137.2.d |
\(\chi_{6137}(2889, \cdot)\) |
n/a |
494 |
1 |
| 6137.2.e |
\(\chi_{6137}(3180, \cdot)\) |
n/a |
904 |
2 |
| 6137.2.f |
\(\chi_{6137}(1084, \cdot)\) |
n/a |
988 |
2 |
| 6137.2.h |
\(\chi_{6137}(1512, \cdot)\) |
n/a |
988 |
2 |
| 6137.2.k |
\(\chi_{6137}(723, \cdot)\) |
n/a |
1980 |
4 |
| 6137.2.m |
\(\chi_{6137}(460, \cdot)\) |
n/a |
2724 |
6 |
| 6137.2.o |
\(\chi_{6137}(429, \cdot)\) |
n/a |
1976 |
4 |
| 6137.2.p |
\(\chi_{6137}(360, \cdot)\) |
n/a |
3952 |
8 |
| 6137.2.s |
\(\chi_{6137}(2039, \cdot)\) |
n/a |
2964 |
6 |
| 6137.2.u |
\(\chi_{6137}(324, \cdot)\) |
n/a |
9144 |
18 |
| 6137.2.w |
\(\chi_{6137}(790, \cdot)\) |
n/a |
3952 |
8 |
| 6137.2.y |
\(\chi_{6137}(234, \cdot)\) |
n/a |
5928 |
12 |
| 6137.2.z |
\(\chi_{6137}(305, \cdot)\) |
n/a |
10224 |
18 |
| 6137.2.bc |
\(\chi_{6137}(430, \cdot)\) |
n/a |
7904 |
16 |
| 6137.2.be |
\(\chi_{6137}(239, \cdot)\) |
n/a |
18288 |
36 |
| 6137.2.bg |
\(\chi_{6137}(389, \cdot)\) |
n/a |
11856 |
24 |
| 6137.2.bi |
\(\chi_{6137}(115, \cdot)\) |
n/a |
20448 |
36 |
| 6137.2.bl |
\(\chi_{6137}(220, \cdot)\) |
n/a |
20448 |
36 |
| 6137.2.bm |
\(\chi_{6137}(116, \cdot)\) |
n/a |
23712 |
48 |
| 6137.2.bp |
\(\chi_{6137}(77, \cdot)\) |
n/a |
40896 |
72 |
| 6137.2.bq |
\(\chi_{6137}(35, \cdot)\) |
n/a |
54648 |
108 |
| 6137.2.br |
\(\chi_{6137}(30, \cdot)\) |
n/a |
40896 |
72 |
| 6137.2.bu |
\(\chi_{6137}(37, \cdot)\) |
n/a |
81792 |
144 |
| 6137.2.bw |
\(\chi_{6137}(16, \cdot)\) |
n/a |
61344 |
108 |
| 6137.2.by |
\(\chi_{6137}(26, \cdot)\) |
n/a |
81792 |
144 |
| 6137.2.ca |
\(\chi_{6137}(4, \cdot)\) |
n/a |
122688 |
216 |
| 6137.2.cd |
\(\chi_{6137}(12, \cdot)\) |
n/a |
163584 |
288 |
| 6137.2.ce |
\(\chi_{6137}(9, \cdot)\) |
n/a |
245376 |
432 |
| 6137.2.ch |
\(\chi_{6137}(3, \cdot)\) |
n/a |
490752 |
864 |
"n/a" means that newforms for that character have not been added to the database yet
