Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7744))\).
|
Total |
New |
Old |
Modular forms
| 1870080 |
1031323 |
838757 |
Cusp forms
| 1847041 |
1025141 |
821900 |
Eisenstein series
| 23039 |
6182 |
16857 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7744))\)
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 |
7744.2.a |
\(\chi_{7744}(1, \cdot)\) |
7744.2.a.a |
1 |
1 |
7744.2.a.b |
1 |
7744.2.a.c |
1 |
7744.2.a.d |
1 |
7744.2.a.e |
1 |
7744.2.a.f |
1 |
7744.2.a.g |
1 |
7744.2.a.h |
1 |
7744.2.a.i |
1 |
7744.2.a.j |
1 |
7744.2.a.k |
1 |
7744.2.a.l |
1 |
7744.2.a.m |
1 |
7744.2.a.n |
1 |
7744.2.a.o |
1 |
7744.2.a.p |
1 |
7744.2.a.q |
1 |
7744.2.a.r |
1 |
7744.2.a.s |
1 |
7744.2.a.t |
1 |
7744.2.a.u |
1 |
7744.2.a.v |
1 |
7744.2.a.w |
1 |
7744.2.a.x |
1 |
7744.2.a.y |
1 |
7744.2.a.z |
1 |
7744.2.a.ba |
1 |
7744.2.a.bb |
1 |
7744.2.a.bc |
1 |
7744.2.a.bd |
1 |
7744.2.a.be |
1 |
7744.2.a.bf |
1 |
7744.2.a.bg |
1 |
7744.2.a.bh |
1 |
7744.2.a.bi |
1 |
7744.2.a.bj |
1 |
7744.2.a.bk |
1 |
7744.2.a.bl |
2 |
7744.2.a.bm |
2 |
7744.2.a.bn |
2 |
7744.2.a.bo |
2 |
7744.2.a.bp |
2 |
7744.2.a.bq |
2 |
7744.2.a.br |
2 |
7744.2.a.bs |
2 |
7744.2.a.bt |
2 |
7744.2.a.bu |
2 |
7744.2.a.bv |
2 |
7744.2.a.bw |
2 |
7744.2.a.bx |
2 |
7744.2.a.by |
2 |
7744.2.a.bz |
2 |
7744.2.a.ca |
2 |
7744.2.a.cb |
2 |
7744.2.a.cc |
2 |
7744.2.a.cd |
2 |
7744.2.a.ce |
2 |
7744.2.a.cf |
2 |
7744.2.a.cg |
2 |
7744.2.a.ch |
2 |
7744.2.a.ci |
2 |
7744.2.a.cj |
2 |
7744.2.a.ck |
2 |
7744.2.a.cl |
2 |
7744.2.a.cm |
2 |
7744.2.a.cn |
2 |
7744.2.a.co |
2 |
7744.2.a.cp |
2 |
7744.2.a.cq |
2 |
7744.2.a.cr |
2 |
7744.2.a.cs |
2 |
7744.2.a.ct |
2 |
7744.2.a.cu |
2 |
7744.2.a.cv |
2 |
7744.2.a.cw |
2 |
7744.2.a.cx |
2 |
7744.2.a.cy |
2 |
7744.2.a.cz |
2 |
7744.2.a.da |
2 |
7744.2.a.db |
2 |
7744.2.a.dc |
2 |
7744.2.a.dd |
3 |
7744.2.a.de |
3 |
7744.2.a.df |
3 |
7744.2.a.dg |
3 |
7744.2.a.dh |
4 |
7744.2.a.di |
4 |
7744.2.a.dj |
4 |
7744.2.a.dk |
4 |
7744.2.a.dl |
4 |
7744.2.a.dm |
4 |
7744.2.a.dn |
4 |
7744.2.a.do |
4 |
7744.2.a.dp |
4 |
7744.2.a.dq |
4 |
7744.2.a.dr |
4 |
7744.2.a.ds |
4 |
7744.2.a.dt |
6 |
7744.2.a.du |
6 |
7744.2.a.dv |
6 |
7744.2.a.dw |
6 |
7744.2.c |
\(\chi_{7744}(3873, \cdot)\) |
n/a |
218 |
1 |
7744.2.e |
\(\chi_{7744}(7743, \cdot)\) |
n/a |
208 |
1 |
7744.2.g |
\(\chi_{7744}(3871, \cdot)\) |
n/a |
216 |
1 |
7744.2.i |
\(\chi_{7744}(1935, \cdot)\) |
n/a |
416 |
2 |
7744.2.j |
\(\chi_{7744}(1937, \cdot)\) |
n/a |
418 |
2 |
7744.2.m |
\(\chi_{7744}(2689, \cdot)\) |
n/a |
832 |
4 |
7744.2.n |
\(\chi_{7744}(969, \cdot)\) |
None |
0 |
4 |
7744.2.q |
\(\chi_{7744}(967, \cdot)\) |
None |
0 |
4 |
7744.2.s |
\(\chi_{7744}(1183, \cdot)\) |
n/a |
864 |
4 |
7744.2.u |
\(\chi_{7744}(959, \cdot)\) |
n/a |
832 |
4 |
7744.2.w |
\(\chi_{7744}(1697, \cdot)\) |
n/a |
864 |
4 |
7744.2.y |
\(\chi_{7744}(705, \cdot)\) |
n/a |
2620 |
10 |
7744.2.ba |
\(\chi_{7744}(485, \cdot)\) |
n/a |
6904 |
8 |
7744.2.bc |
\(\chi_{7744}(483, \cdot)\) |
n/a |
6848 |
8 |
7744.2.bf |
\(\chi_{7744}(81, \cdot)\) |
n/a |
1664 |
8 |
7744.2.bg |
\(\chi_{7744}(239, \cdot)\) |
n/a |
1664 |
8 |
7744.2.bh |
\(\chi_{7744}(703, \cdot)\) |
n/a |
2620 |
10 |
7744.2.bj |
\(\chi_{7744}(353, \cdot)\) |
n/a |
2640 |
10 |
7744.2.bm |
\(\chi_{7744}(351, \cdot)\) |
n/a |
2640 |
10 |
7744.2.bo |
\(\chi_{7744}(215, \cdot)\) |
None |
0 |
16 |
7744.2.br |
\(\chi_{7744}(9, \cdot)\) |
None |
0 |
16 |
7744.2.bu |
\(\chi_{7744}(177, \cdot)\) |
n/a |
5240 |
20 |
7744.2.bv |
\(\chi_{7744}(175, \cdot)\) |
n/a |
5240 |
20 |
7744.2.bw |
\(\chi_{7744}(257, \cdot)\) |
n/a |
10480 |
40 |
7744.2.bx |
\(\chi_{7744}(403, \cdot)\) |
n/a |
27392 |
32 |
7744.2.bz |
\(\chi_{7744}(245, \cdot)\) |
n/a |
27392 |
32 |
7744.2.cb |
\(\chi_{7744}(87, \cdot)\) |
None |
0 |
40 |
7744.2.ce |
\(\chi_{7744}(89, \cdot)\) |
None |
0 |
40 |
7744.2.cg |
\(\chi_{7744}(95, \cdot)\) |
n/a |
10560 |
40 |
7744.2.cj |
\(\chi_{7744}(97, \cdot)\) |
n/a |
10560 |
40 |
7744.2.cl |
\(\chi_{7744}(63, \cdot)\) |
n/a |
10480 |
40 |
7744.2.cm |
\(\chi_{7744}(43, \cdot)\) |
n/a |
84320 |
80 |
7744.2.co |
\(\chi_{7744}(45, \cdot)\) |
n/a |
84320 |
80 |
7744.2.cq |
\(\chi_{7744}(79, \cdot)\) |
n/a |
20960 |
80 |
7744.2.cr |
\(\chi_{7744}(49, \cdot)\) |
n/a |
20960 |
80 |
7744.2.cu |
\(\chi_{7744}(25, \cdot)\) |
None |
0 |
160 |
7744.2.cx |
\(\chi_{7744}(7, \cdot)\) |
None |
0 |
160 |
7744.2.cz |
\(\chi_{7744}(5, \cdot)\) |
n/a |
337280 |
320 |
7744.2.db |
\(\chi_{7744}(19, \cdot)\) |
n/a |
337280 |
320 |
"n/a" means that newforms for that character have not been added to the database yet