Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1312))\).
|
Total |
New |
Old |
Modular forms
| 55040 |
30594 |
24446 |
Cusp forms
| 52481 |
29814 |
22667 |
Eisenstein series
| 2559 |
780 |
1779 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1312))\)
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 the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
1312.2.a |
\(\chi_{1312}(1, \cdot)\) |
1312.2.a.a |
1 |
1 |
1312.2.a.b |
1 |
1312.2.a.c |
2 |
1312.2.a.d |
3 |
1312.2.a.e |
3 |
1312.2.a.f |
4 |
1312.2.a.g |
4 |
1312.2.a.h |
7 |
1312.2.a.i |
7 |
1312.2.a.j |
8 |
1312.2.b |
\(\chi_{1312}(657, \cdot)\) |
1312.2.b.a |
20 |
1 |
1312.2.b.b |
20 |
1312.2.d |
\(\chi_{1312}(737, \cdot)\) |
1312.2.d.a |
2 |
1 |
1312.2.d.b |
2 |
1312.2.d.c |
2 |
1312.2.d.d |
8 |
1312.2.d.e |
8 |
1312.2.d.f |
10 |
1312.2.d.g |
10 |
1312.2.g |
\(\chi_{1312}(81, \cdot)\) |
1312.2.g.a |
40 |
1 |
1312.2.i |
\(\chi_{1312}(9, \cdot)\) |
None |
0 |
2 |
1312.2.l |
\(\chi_{1312}(993, \cdot)\) |
1312.2.l.a |
2 |
2 |
1312.2.l.b |
2 |
1312.2.l.c |
2 |
1312.2.l.d |
2 |
1312.2.l.e |
2 |
1312.2.l.f |
2 |
1312.2.l.g |
4 |
1312.2.l.h |
4 |
1312.2.l.i |
12 |
1312.2.l.j |
16 |
1312.2.l.k |
18 |
1312.2.l.l |
18 |
1312.2.n |
\(\chi_{1312}(329, \cdot)\) |
None |
0 |
2 |
1312.2.o |
\(\chi_{1312}(409, \cdot)\) |
None |
0 |
2 |
1312.2.r |
\(\chi_{1312}(337, \cdot)\) |
1312.2.r.a |
80 |
2 |
1312.2.t |
\(\chi_{1312}(73, \cdot)\) |
None |
0 |
2 |
1312.2.u |
\(\chi_{1312}(385, \cdot)\) |
n/a |
168 |
4 |
1312.2.v |
\(\chi_{1312}(355, \cdot)\) |
n/a |
664 |
4 |
1312.2.x |
\(\chi_{1312}(55, \cdot)\) |
None |
0 |
4 |
1312.2.ba |
\(\chi_{1312}(237, \cdot)\) |
n/a |
664 |
4 |
1312.2.bc |
\(\chi_{1312}(3, \cdot)\) |
n/a |
664 |
4 |
1312.2.be |
\(\chi_{1312}(219, \cdot)\) |
n/a |
664 |
4 |
1312.2.bf |
\(\chi_{1312}(165, \cdot)\) |
n/a |
640 |
4 |
1312.2.bj |
\(\chi_{1312}(79, \cdot)\) |
n/a |
160 |
4 |
1312.2.bk |
\(\chi_{1312}(191, \cdot)\) |
n/a |
168 |
4 |
1312.2.bm |
\(\chi_{1312}(245, \cdot)\) |
n/a |
664 |
4 |
1312.2.bo |
\(\chi_{1312}(173, \cdot)\) |
n/a |
664 |
4 |
1312.2.bp |
\(\chi_{1312}(407, \cdot)\) |
None |
0 |
4 |
1312.2.bs |
\(\chi_{1312}(331, \cdot)\) |
n/a |
664 |
4 |
1312.2.bu |
\(\chi_{1312}(353, \cdot)\) |
n/a |
168 |
4 |
1312.2.bw |
\(\chi_{1312}(305, \cdot)\) |
n/a |
160 |
4 |
1312.2.by |
\(\chi_{1312}(113, \cdot)\) |
n/a |
160 |
4 |
1312.2.cb |
\(\chi_{1312}(169, \cdot)\) |
None |
0 |
8 |
1312.2.cc |
\(\chi_{1312}(49, \cdot)\) |
n/a |
320 |
8 |
1312.2.cf |
\(\chi_{1312}(25, \cdot)\) |
None |
0 |
8 |
1312.2.cg |
\(\chi_{1312}(57, \cdot)\) |
None |
0 |
8 |
1312.2.ci |
\(\chi_{1312}(33, \cdot)\) |
n/a |
336 |
8 |
1312.2.ck |
\(\chi_{1312}(121, \cdot)\) |
None |
0 |
8 |
1312.2.cn |
\(\chi_{1312}(11, \cdot)\) |
n/a |
2656 |
16 |
1312.2.cp |
\(\chi_{1312}(151, \cdot)\) |
None |
0 |
16 |
1312.2.cq |
\(\chi_{1312}(197, \cdot)\) |
n/a |
2656 |
16 |
1312.2.cs |
\(\chi_{1312}(275, \cdot)\) |
n/a |
2656 |
16 |
1312.2.cu |
\(\chi_{1312}(259, \cdot)\) |
n/a |
2656 |
16 |
1312.2.cw |
\(\chi_{1312}(45, \cdot)\) |
n/a |
2656 |
16 |
1312.2.cy |
\(\chi_{1312}(63, \cdot)\) |
n/a |
672 |
16 |
1312.2.cz |
\(\chi_{1312}(15, \cdot)\) |
n/a |
640 |
16 |
1312.2.dd |
\(\chi_{1312}(37, \cdot)\) |
n/a |
2656 |
16 |
1312.2.de |
\(\chi_{1312}(5, \cdot)\) |
n/a |
2656 |
16 |
1312.2.dh |
\(\chi_{1312}(7, \cdot)\) |
None |
0 |
16 |
1312.2.di |
\(\chi_{1312}(67, \cdot)\) |
n/a |
2656 |
16 |
"n/a" means that newforms for that character have not been added to the database yet