Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1305))\).
|
Total |
New |
Old |
Modular forms
| 62272 |
44516 |
17756 |
Cusp forms
| 58689 |
43056 |
15633 |
Eisenstein series
| 3583 |
1460 |
2123 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1305))\)
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 |
1305.2.a |
\(\chi_{1305}(1, \cdot)\) |
1305.2.a.a |
1 |
1 |
1305.2.a.b |
1 |
1305.2.a.c |
1 |
1305.2.a.d |
1 |
1305.2.a.e |
1 |
1305.2.a.f |
1 |
1305.2.a.g |
1 |
1305.2.a.h |
2 |
1305.2.a.i |
2 |
1305.2.a.j |
2 |
1305.2.a.k |
2 |
1305.2.a.l |
2 |
1305.2.a.m |
2 |
1305.2.a.n |
2 |
1305.2.a.o |
3 |
1305.2.a.p |
3 |
1305.2.a.q |
3 |
1305.2.a.r |
4 |
1305.2.a.s |
7 |
1305.2.a.t |
7 |
1305.2.c |
\(\chi_{1305}(784, \cdot)\) |
1305.2.c.a |
2 |
1 |
1305.2.c.b |
2 |
1305.2.c.c |
2 |
1305.2.c.d |
2 |
1305.2.c.e |
4 |
1305.2.c.f |
4 |
1305.2.c.g |
4 |
1305.2.c.h |
6 |
1305.2.c.i |
10 |
1305.2.c.j |
10 |
1305.2.c.k |
12 |
1305.2.c.l |
12 |
1305.2.d |
\(\chi_{1305}(811, \cdot)\) |
1305.2.d.a |
4 |
1 |
1305.2.d.b |
6 |
1305.2.d.c |
10 |
1305.2.d.d |
10 |
1305.2.d.e |
10 |
1305.2.d.f |
10 |
1305.2.f |
\(\chi_{1305}(289, \cdot)\) |
1305.2.f.a |
2 |
1 |
1305.2.f.b |
2 |
1305.2.f.c |
2 |
1305.2.f.d |
2 |
1305.2.f.e |
4 |
1305.2.f.f |
4 |
1305.2.f.g |
4 |
1305.2.f.h |
4 |
1305.2.f.i |
4 |
1305.2.f.j |
4 |
1305.2.f.k |
12 |
1305.2.f.l |
12 |
1305.2.f.m |
16 |
1305.2.i |
\(\chi_{1305}(436, \cdot)\) |
n/a |
224 |
2 |
1305.2.k |
\(\chi_{1305}(568, \cdot)\) |
n/a |
146 |
2 |
1305.2.m |
\(\chi_{1305}(539, \cdot)\) |
n/a |
120 |
2 |
1305.2.n |
\(\chi_{1305}(233, \cdot)\) |
n/a |
112 |
2 |
1305.2.q |
\(\chi_{1305}(782, \cdot)\) |
n/a |
120 |
2 |
1305.2.r |
\(\chi_{1305}(476, \cdot)\) |
1305.2.r.a |
8 |
2 |
1305.2.r.b |
8 |
1305.2.r.c |
32 |
1305.2.r.d |
32 |
1305.2.t |
\(\chi_{1305}(307, \cdot)\) |
n/a |
146 |
2 |
1305.2.w |
\(\chi_{1305}(724, \cdot)\) |
n/a |
352 |
2 |
1305.2.y |
\(\chi_{1305}(376, \cdot)\) |
n/a |
240 |
2 |
1305.2.bb |
\(\chi_{1305}(349, \cdot)\) |
n/a |
336 |
2 |
1305.2.bc |
\(\chi_{1305}(136, \cdot)\) |
n/a |
300 |
6 |
1305.2.bd |
\(\chi_{1305}(418, \cdot)\) |
n/a |
704 |
4 |
1305.2.bg |
\(\chi_{1305}(41, \cdot)\) |
n/a |
480 |
4 |
1305.2.bi |
\(\chi_{1305}(173, \cdot)\) |
n/a |
704 |
4 |
1305.2.bj |
\(\chi_{1305}(407, \cdot)\) |
n/a |
672 |
4 |
1305.2.bl |
\(\chi_{1305}(104, \cdot)\) |
n/a |
704 |
4 |
1305.2.bo |
\(\chi_{1305}(133, \cdot)\) |
n/a |
704 |
4 |
1305.2.br |
\(\chi_{1305}(64, \cdot)\) |
n/a |
432 |
6 |
1305.2.bt |
\(\chi_{1305}(91, \cdot)\) |
n/a |
300 |
6 |
1305.2.bu |
\(\chi_{1305}(199, \cdot)\) |
n/a |
444 |
6 |
1305.2.bw |
\(\chi_{1305}(16, \cdot)\) |
n/a |
1440 |
12 |
1305.2.by |
\(\chi_{1305}(73, \cdot)\) |
n/a |
876 |
12 |
1305.2.ca |
\(\chi_{1305}(26, \cdot)\) |
n/a |
480 |
12 |
1305.2.cb |
\(\chi_{1305}(62, \cdot)\) |
n/a |
720 |
12 |
1305.2.ce |
\(\chi_{1305}(53, \cdot)\) |
n/a |
720 |
12 |
1305.2.cf |
\(\chi_{1305}(44, \cdot)\) |
n/a |
720 |
12 |
1305.2.ch |
\(\chi_{1305}(37, \cdot)\) |
n/a |
876 |
12 |
1305.2.cj |
\(\chi_{1305}(49, \cdot)\) |
n/a |
2112 |
12 |
1305.2.cm |
\(\chi_{1305}(121, \cdot)\) |
n/a |
1440 |
12 |
1305.2.co |
\(\chi_{1305}(4, \cdot)\) |
n/a |
2112 |
12 |
1305.2.cq |
\(\chi_{1305}(43, \cdot)\) |
n/a |
4224 |
24 |
1305.2.ct |
\(\chi_{1305}(14, \cdot)\) |
n/a |
4224 |
24 |
1305.2.cv |
\(\chi_{1305}(23, \cdot)\) |
n/a |
4224 |
24 |
1305.2.cw |
\(\chi_{1305}(38, \cdot)\) |
n/a |
4224 |
24 |
1305.2.cy |
\(\chi_{1305}(11, \cdot)\) |
n/a |
2880 |
24 |
1305.2.db |
\(\chi_{1305}(292, \cdot)\) |
n/a |
4224 |
24 |
"n/a" means that newforms for that character have not been added to the database yet