Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8381))\).
|
Total |
New |
Old |
Modular forms
| 2924320 |
2896057 |
28263 |
Cusp forms
| 2901921 |
2876159 |
25762 |
Eisenstein series
| 22399 |
19898 |
2501 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8381))\)
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 |
8381.2.a |
\(\chi_{8381}(1, \cdot)\) |
8381.2.a.a |
1 |
1 |
8381.2.a.b |
1 |
8381.2.a.c |
1 |
8381.2.a.d |
1 |
8381.2.a.e |
2 |
8381.2.a.f |
2 |
8381.2.a.g |
4 |
8381.2.a.h |
5 |
8381.2.a.i |
6 |
8381.2.a.j |
8 |
8381.2.a.k |
10 |
8381.2.a.l |
14 |
8381.2.a.m |
14 |
8381.2.a.n |
21 |
8381.2.a.o |
21 |
8381.2.a.p |
21 |
8381.2.a.q |
21 |
8381.2.a.r |
42 |
8381.2.a.s |
42 |
8381.2.a.t |
48 |
8381.2.a.u |
48 |
8381.2.a.v |
66 |
8381.2.a.w |
66 |
8381.2.a.x |
84 |
8381.2.a.y |
84 |
8381.2.b |
\(\chi_{8381}(579, \cdot)\) |
n/a |
662 |
1 |
8381.2.c |
\(\chi_{8381}(8380, \cdot)\) |
n/a |
660 |
1 |
8381.2.d |
\(\chi_{8381}(7802, \cdot)\) |
n/a |
630 |
1 |
8381.2.e |
\(\chi_{8381}(2350, \cdot)\) |
n/a |
1260 |
2 |
8381.2.j |
\(\chi_{8381}(2928, \cdot)\) |
n/a |
1320 |
2 |
8381.2.k |
\(\chi_{8381}(1446, \cdot)\) |
n/a |
3978 |
6 |
8381.2.m |
\(\chi_{8381}(1913, \cdot)\) |
n/a |
2648 |
4 |
8381.2.n |
\(\chi_{8381}(1335, \cdot)\) |
n/a |
2520 |
4 |
8381.2.p |
\(\chi_{8381}(866, \cdot)\) |
n/a |
3972 |
6 |
8381.2.q |
\(\chi_{8381}(1733, \cdot)\) |
n/a |
3960 |
6 |
8381.2.r |
\(\chi_{8381}(2313, \cdot)\) |
n/a |
3972 |
6 |
8381.2.t |
\(\chi_{8381}(1380, \cdot)\) |
n/a |
5288 |
8 |
8381.2.u |
\(\chi_{8381}(75, \cdot)\) |
n/a |
5288 |
8 |
8381.2.w |
\(\chi_{8381}(494, \cdot)\) |
n/a |
11424 |
16 |
8381.2.x |
\(\chi_{8381}(38, \cdot)\) |
n/a |
7920 |
12 |
8381.2.bc |
\(\chi_{8381}(616, \cdot)\) |
n/a |
7944 |
12 |
8381.2.bd |
\(\chi_{8381}(407, \cdot)\) |
n/a |
11424 |
16 |
8381.2.be |
\(\chi_{8381}(492, \cdot)\) |
n/a |
12224 |
16 |
8381.2.bf |
\(\chi_{8381}(86, \cdot)\) |
n/a |
12224 |
16 |
8381.2.bh |
\(\chi_{8381}(110, \cdot)\) |
n/a |
15840 |
24 |
8381.2.bi |
\(\chi_{8381}(179, \cdot)\) |
n/a |
15888 |
24 |
8381.2.bk |
\(\chi_{8381}(115, \cdot)\) |
n/a |
24448 |
32 |
8381.2.bp |
\(\chi_{8381}(30, \cdot)\) |
n/a |
22848 |
32 |
8381.2.br |
\(\chi_{8381}(40, \cdot)\) |
n/a |
31728 |
48 |
8381.2.bs |
\(\chi_{8381}(224, \cdot)\) |
n/a |
31728 |
48 |
8381.2.bu |
\(\chi_{8381}(52, \cdot)\) |
n/a |
73152 |
96 |
8381.2.bw |
\(\chi_{8381}(59, \cdot)\) |
n/a |
45696 |
64 |
8381.2.bx |
\(\chi_{8381}(144, \cdot)\) |
n/a |
48768 |
64 |
8381.2.bz |
\(\chi_{8381}(35, \cdot)\) |
n/a |
73344 |
96 |
8381.2.ca |
\(\chi_{8381}(33, \cdot)\) |
n/a |
73344 |
96 |
8381.2.cb |
\(\chi_{8381}(16, \cdot)\) |
n/a |
73152 |
96 |
8381.2.cd |
\(\chi_{8381}(12, \cdot)\) |
n/a |
97664 |
128 |
8381.2.ce |
\(\chi_{8381}(41, \cdot)\) |
n/a |
97664 |
128 |
8381.2.cg |
\(\chi_{8381}(81, \cdot)\) |
n/a |
146304 |
192 |
8381.2.cl |
\(\chi_{8381}(4, \cdot)\) |
n/a |
146688 |
192 |
8381.2.cn |
\(\chi_{8381}(9, \cdot)\) |
n/a |
292608 |
384 |
8381.2.co |
\(\chi_{8381}(25, \cdot)\) |
n/a |
293376 |
384 |
8381.2.cr |
\(\chi_{8381}(3, \cdot)\) |
n/a |
585984 |
768 |
8381.2.cs |
\(\chi_{8381}(11, \cdot)\) |
n/a |
585984 |
768 |
"n/a" means that newforms for that character have not been added to the database yet