Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1045))\).
|
Total |
New |
Old |
Modular forms
| 44640 |
39643 |
4997 |
Cusp forms
| 41761 |
37811 |
3950 |
Eisenstein series
| 2879 |
1832 |
1047 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1045))\)
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 |
1045.2.a |
\(\chi_{1045}(1, \cdot)\) |
1045.2.a.a |
1 |
1 |
1045.2.a.b |
1 |
1045.2.a.c |
2 |
1045.2.a.d |
5 |
1045.2.a.e |
5 |
1045.2.a.f |
6 |
1045.2.a.g |
6 |
1045.2.a.h |
7 |
1045.2.a.i |
8 |
1045.2.a.j |
9 |
1045.2.a.k |
9 |
1045.2.b |
\(\chi_{1045}(419, \cdot)\) |
1045.2.b.a |
4 |
1 |
1045.2.b.b |
16 |
1045.2.b.c |
20 |
1045.2.b.d |
22 |
1045.2.b.e |
30 |
1045.2.e |
\(\chi_{1045}(1044, \cdot)\) |
n/a |
116 |
1 |
1045.2.f |
\(\chi_{1045}(626, \cdot)\) |
1045.2.f.a |
40 |
1 |
1045.2.f.b |
40 |
1045.2.i |
\(\chi_{1045}(771, \cdot)\) |
n/a |
128 |
2 |
1045.2.j |
\(\chi_{1045}(153, \cdot)\) |
n/a |
216 |
2 |
1045.2.m |
\(\chi_{1045}(683, \cdot)\) |
n/a |
200 |
2 |
1045.2.n |
\(\chi_{1045}(191, \cdot)\) |
n/a |
288 |
4 |
1045.2.p |
\(\chi_{1045}(791, \cdot)\) |
n/a |
160 |
2 |
1045.2.s |
\(\chi_{1045}(164, \cdot)\) |
n/a |
232 |
2 |
1045.2.t |
\(\chi_{1045}(144, \cdot)\) |
n/a |
200 |
2 |
1045.2.v |
\(\chi_{1045}(111, \cdot)\) |
n/a |
408 |
6 |
1045.2.y |
\(\chi_{1045}(151, \cdot)\) |
n/a |
320 |
4 |
1045.2.z |
\(\chi_{1045}(94, \cdot)\) |
n/a |
464 |
4 |
1045.2.bc |
\(\chi_{1045}(229, \cdot)\) |
n/a |
432 |
4 |
1045.2.bd |
\(\chi_{1045}(12, \cdot)\) |
n/a |
400 |
4 |
1045.2.bg |
\(\chi_{1045}(87, \cdot)\) |
n/a |
464 |
4 |
1045.2.bh |
\(\chi_{1045}(26, \cdot)\) |
n/a |
640 |
8 |
1045.2.bj |
\(\chi_{1045}(109, \cdot)\) |
n/a |
696 |
6 |
1045.2.bm |
\(\chi_{1045}(21, \cdot)\) |
n/a |
480 |
6 |
1045.2.bo |
\(\chi_{1045}(199, \cdot)\) |
n/a |
600 |
6 |
1045.2.bp |
\(\chi_{1045}(37, \cdot)\) |
n/a |
928 |
8 |
1045.2.bs |
\(\chi_{1045}(172, \cdot)\) |
n/a |
864 |
8 |
1045.2.bu |
\(\chi_{1045}(49, \cdot)\) |
n/a |
928 |
8 |
1045.2.bv |
\(\chi_{1045}(84, \cdot)\) |
n/a |
928 |
8 |
1045.2.by |
\(\chi_{1045}(46, \cdot)\) |
n/a |
640 |
8 |
1045.2.cb |
\(\chi_{1045}(43, \cdot)\) |
n/a |
1392 |
12 |
1045.2.cc |
\(\chi_{1045}(67, \cdot)\) |
n/a |
1200 |
12 |
1045.2.ce |
\(\chi_{1045}(16, \cdot)\) |
n/a |
1920 |
24 |
1045.2.cf |
\(\chi_{1045}(7, \cdot)\) |
n/a |
1856 |
16 |
1045.2.ci |
\(\chi_{1045}(27, \cdot)\) |
n/a |
1856 |
16 |
1045.2.ck |
\(\chi_{1045}(4, \cdot)\) |
n/a |
2784 |
24 |
1045.2.cm |
\(\chi_{1045}(41, \cdot)\) |
n/a |
1920 |
24 |
1045.2.cn |
\(\chi_{1045}(29, \cdot)\) |
n/a |
2784 |
24 |
1045.2.cr |
\(\chi_{1045}(3, \cdot)\) |
n/a |
5568 |
48 |
1045.2.cs |
\(\chi_{1045}(17, \cdot)\) |
n/a |
5568 |
48 |
"n/a" means that newforms for that character have not been added to the database yet