Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1300))\).
|
Total |
New |
Old |
Modular forms
| 52080 |
27227 |
24853 |
Cusp forms
| 48721 |
26323 |
22398 |
Eisenstein series
| 3359 |
904 |
2455 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1300))\)
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 |
1300.2.a |
\(\chi_{1300}(1, \cdot)\) |
1300.2.a.a |
1 |
1 |
1300.2.a.b |
1 |
1300.2.a.c |
1 |
1300.2.a.d |
1 |
1300.2.a.e |
1 |
1300.2.a.f |
1 |
1300.2.a.g |
2 |
1300.2.a.h |
2 |
1300.2.a.i |
3 |
1300.2.a.j |
3 |
1300.2.a.k |
3 |
1300.2.c |
\(\chi_{1300}(1249, \cdot)\) |
1300.2.c.a |
2 |
1 |
1300.2.c.b |
2 |
1300.2.c.c |
2 |
1300.2.c.d |
2 |
1300.2.c.e |
4 |
1300.2.c.f |
6 |
1300.2.d |
\(\chi_{1300}(649, \cdot)\) |
1300.2.d.a |
4 |
1 |
1300.2.d.b |
4 |
1300.2.d.c |
6 |
1300.2.d.d |
6 |
1300.2.f |
\(\chi_{1300}(701, \cdot)\) |
1300.2.f.a |
2 |
1 |
1300.2.f.b |
2 |
1300.2.f.c |
2 |
1300.2.f.d |
2 |
1300.2.f.e |
6 |
1300.2.f.f |
8 |
1300.2.i |
\(\chi_{1300}(601, \cdot)\) |
1300.2.i.a |
2 |
2 |
1300.2.i.b |
2 |
1300.2.i.c |
2 |
1300.2.i.d |
2 |
1300.2.i.e |
2 |
1300.2.i.f |
2 |
1300.2.i.g |
10 |
1300.2.i.h |
10 |
1300.2.i.i |
12 |
1300.2.j |
\(\chi_{1300}(151, \cdot)\) |
n/a |
254 |
2 |
1300.2.m |
\(\chi_{1300}(57, \cdot)\) |
1300.2.m.a |
2 |
2 |
1300.2.m.b |
4 |
1300.2.m.c |
8 |
1300.2.m.d |
8 |
1300.2.m.e |
8 |
1300.2.m.f |
12 |
1300.2.o |
\(\chi_{1300}(443, \cdot)\) |
n/a |
216 |
2 |
1300.2.p |
\(\chi_{1300}(207, \cdot)\) |
n/a |
244 |
2 |
1300.2.r |
\(\chi_{1300}(957, \cdot)\) |
1300.2.r.a |
2 |
2 |
1300.2.r.b |
4 |
1300.2.r.c |
8 |
1300.2.r.d |
8 |
1300.2.r.e |
8 |
1300.2.r.f |
12 |
1300.2.u |
\(\chi_{1300}(99, \cdot)\) |
n/a |
244 |
2 |
1300.2.v |
\(\chi_{1300}(261, \cdot)\) |
n/a |
120 |
4 |
1300.2.y |
\(\chi_{1300}(101, \cdot)\) |
1300.2.y.a |
2 |
2 |
1300.2.y.b |
8 |
1300.2.y.c |
10 |
1300.2.y.d |
10 |
1300.2.y.e |
16 |
1300.2.ba |
\(\chi_{1300}(49, \cdot)\) |
1300.2.ba.a |
4 |
2 |
1300.2.ba.b |
8 |
1300.2.ba.c |
8 |
1300.2.ba.d |
20 |
1300.2.bb |
\(\chi_{1300}(549, \cdot)\) |
1300.2.bb.a |
4 |
2 |
1300.2.bb.b |
4 |
1300.2.bb.c |
4 |
1300.2.bb.d |
4 |
1300.2.bb.e |
4 |
1300.2.bb.f |
4 |
1300.2.bb.g |
20 |
1300.2.be |
\(\chi_{1300}(181, \cdot)\) |
n/a |
136 |
4 |
1300.2.bg |
\(\chi_{1300}(209, \cdot)\) |
n/a |
120 |
4 |
1300.2.bj |
\(\chi_{1300}(129, \cdot)\) |
n/a |
144 |
4 |
1300.2.bk |
\(\chi_{1300}(799, \cdot)\) |
n/a |
488 |
4 |
1300.2.bn |
\(\chi_{1300}(93, \cdot)\) |
1300.2.bn.a |
4 |
4 |
1300.2.bn.b |
4 |
1300.2.bn.c |
16 |
1300.2.bn.d |
20 |
1300.2.bn.e |
40 |
1300.2.bo |
\(\chi_{1300}(43, \cdot)\) |
n/a |
488 |
4 |
1300.2.br |
\(\chi_{1300}(107, \cdot)\) |
n/a |
488 |
4 |
1300.2.bs |
\(\chi_{1300}(193, \cdot)\) |
1300.2.bs.a |
4 |
4 |
1300.2.bs.b |
4 |
1300.2.bs.c |
16 |
1300.2.bs.d |
20 |
1300.2.bs.e |
40 |
1300.2.bv |
\(\chi_{1300}(851, \cdot)\) |
n/a |
508 |
4 |
1300.2.bw |
\(\chi_{1300}(61, \cdot)\) |
n/a |
288 |
8 |
1300.2.bx |
\(\chi_{1300}(239, \cdot)\) |
n/a |
1648 |
8 |
1300.2.bz |
\(\chi_{1300}(73, \cdot)\) |
n/a |
280 |
8 |
1300.2.cc |
\(\chi_{1300}(103, \cdot)\) |
n/a |
1648 |
8 |
1300.2.cd |
\(\chi_{1300}(27, \cdot)\) |
n/a |
1440 |
8 |
1300.2.cg |
\(\chi_{1300}(177, \cdot)\) |
n/a |
280 |
8 |
1300.2.ci |
\(\chi_{1300}(31, \cdot)\) |
n/a |
1648 |
8 |
1300.2.cj |
\(\chi_{1300}(69, \cdot)\) |
n/a |
288 |
8 |
1300.2.cm |
\(\chi_{1300}(9, \cdot)\) |
n/a |
272 |
8 |
1300.2.co |
\(\chi_{1300}(121, \cdot)\) |
n/a |
272 |
8 |
1300.2.cq |
\(\chi_{1300}(11, \cdot)\) |
n/a |
3296 |
16 |
1300.2.cs |
\(\chi_{1300}(37, \cdot)\) |
n/a |
560 |
16 |
1300.2.cu |
\(\chi_{1300}(3, \cdot)\) |
n/a |
3296 |
16 |
1300.2.cx |
\(\chi_{1300}(23, \cdot)\) |
n/a |
3296 |
16 |
1300.2.cz |
\(\chi_{1300}(33, \cdot)\) |
n/a |
560 |
16 |
1300.2.db |
\(\chi_{1300}(19, \cdot)\) |
n/a |
3296 |
16 |
"n/a" means that newforms for that character have not been added to the database yet