Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1968))\).
|
Total |
New |
Old |
Modular forms
| 109760 |
45658 |
64102 |
Cusp forms
| 105281 |
44954 |
60327 |
Eisenstein series
| 4479 |
704 |
3775 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1968))\)
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 |
1968.2.a |
\(\chi_{1968}(1, \cdot)\) |
1968.2.a.a |
1 |
1 |
1968.2.a.b |
1 |
1968.2.a.c |
1 |
1968.2.a.d |
1 |
1968.2.a.e |
1 |
1968.2.a.f |
1 |
1968.2.a.g |
1 |
1968.2.a.h |
1 |
1968.2.a.i |
1 |
1968.2.a.j |
1 |
1968.2.a.k |
1 |
1968.2.a.l |
1 |
1968.2.a.m |
1 |
1968.2.a.n |
1 |
1968.2.a.o |
1 |
1968.2.a.p |
2 |
1968.2.a.q |
2 |
1968.2.a.r |
2 |
1968.2.a.s |
2 |
1968.2.a.t |
3 |
1968.2.a.u |
3 |
1968.2.a.v |
3 |
1968.2.a.w |
3 |
1968.2.a.x |
5 |
1968.2.d |
\(\chi_{1968}(575, \cdot)\) |
1968.2.d.a |
4 |
1 |
1968.2.d.b |
28 |
1968.2.d.c |
48 |
1968.2.e |
\(\chi_{1968}(409, \cdot)\) |
None |
0 |
1 |
1968.2.f |
\(\chi_{1968}(985, \cdot)\) |
None |
0 |
1 |
1968.2.g |
\(\chi_{1968}(1967, \cdot)\) |
1968.2.g.a |
4 |
1 |
1968.2.g.b |
4 |
1968.2.g.c |
4 |
1968.2.g.d |
8 |
1968.2.g.e |
16 |
1968.2.g.f |
16 |
1968.2.g.g |
32 |
1968.2.j |
\(\chi_{1968}(1393, \cdot)\) |
1968.2.j.a |
2 |
1 |
1968.2.j.b |
2 |
1968.2.j.c |
4 |
1968.2.j.d |
6 |
1968.2.j.e |
8 |
1968.2.j.f |
8 |
1968.2.j.g |
12 |
1968.2.k |
\(\chi_{1968}(1559, \cdot)\) |
None |
0 |
1 |
1968.2.p |
\(\chi_{1968}(983, \cdot)\) |
None |
0 |
1 |
1968.2.s |
\(\chi_{1968}(647, \cdot)\) |
None |
0 |
2 |
1968.2.t |
\(\chi_{1968}(337, \cdot)\) |
1968.2.t.a |
4 |
2 |
1968.2.t.b |
8 |
1968.2.t.c |
8 |
1968.2.t.d |
12 |
1968.2.t.e |
16 |
1968.2.t.f |
16 |
1968.2.t.g |
20 |
1968.2.w |
\(\chi_{1968}(491, \cdot)\) |
n/a |
664 |
2 |
1968.2.x |
\(\chi_{1968}(493, \cdot)\) |
n/a |
320 |
2 |
1968.2.ba |
\(\chi_{1968}(1549, \cdot)\) |
n/a |
336 |
2 |
1968.2.bb |
\(\chi_{1968}(1139, \cdot)\) |
n/a |
664 |
2 |
1968.2.bc |
\(\chi_{1968}(155, \cdot)\) |
n/a |
664 |
2 |
1968.2.bd |
\(\chi_{1968}(565, \cdot)\) |
n/a |
336 |
2 |
1968.2.bg |
\(\chi_{1968}(83, \cdot)\) |
n/a |
640 |
2 |
1968.2.bh |
\(\chi_{1968}(901, \cdot)\) |
n/a |
336 |
2 |
1968.2.bm |
\(\chi_{1968}(911, \cdot)\) |
n/a |
168 |
2 |
1968.2.bn |
\(\chi_{1968}(73, \cdot)\) |
None |
0 |
2 |
1968.2.bo |
\(\chi_{1968}(385, \cdot)\) |
n/a |
168 |
4 |
1968.2.bp |
\(\chi_{1968}(413, \cdot)\) |
n/a |
1328 |
4 |
1968.2.bq |
\(\chi_{1968}(331, \cdot)\) |
n/a |
672 |
4 |
1968.2.bx |
\(\chi_{1968}(137, \cdot)\) |
None |
0 |
4 |
1968.2.by |
\(\chi_{1968}(161, \cdot)\) |
n/a |
328 |
4 |
1968.2.bz |
\(\chi_{1968}(55, \cdot)\) |
None |
0 |
4 |
1968.2.ca |
\(\chi_{1968}(79, \cdot)\) |
n/a |
168 |
4 |
1968.2.cb |
\(\chi_{1968}(1397, \cdot)\) |
n/a |
1328 |
4 |
1968.2.cc |
\(\chi_{1968}(1315, \cdot)\) |
n/a |
672 |
4 |
1968.2.cf |
\(\chi_{1968}(23, \cdot)\) |
None |
0 |
4 |
1968.2.ck |
\(\chi_{1968}(119, \cdot)\) |
None |
0 |
4 |
1968.2.cl |
\(\chi_{1968}(433, \cdot)\) |
n/a |
168 |
4 |
1968.2.co |
\(\chi_{1968}(1007, \cdot)\) |
n/a |
336 |
4 |
1968.2.cp |
\(\chi_{1968}(1369, \cdot)\) |
None |
0 |
4 |
1968.2.cq |
\(\chi_{1968}(25, \cdot)\) |
None |
0 |
4 |
1968.2.cr |
\(\chi_{1968}(959, \cdot)\) |
n/a |
336 |
4 |
1968.2.cu |
\(\chi_{1968}(121, \cdot)\) |
None |
0 |
8 |
1968.2.cv |
\(\chi_{1968}(143, \cdot)\) |
n/a |
672 |
8 |
1968.2.da |
\(\chi_{1968}(277, \cdot)\) |
n/a |
1344 |
8 |
1968.2.db |
\(\chi_{1968}(59, \cdot)\) |
n/a |
2656 |
8 |
1968.2.de |
\(\chi_{1968}(349, \cdot)\) |
n/a |
1344 |
8 |
1968.2.df |
\(\chi_{1968}(131, \cdot)\) |
n/a |
2656 |
8 |
1968.2.dg |
\(\chi_{1968}(203, \cdot)\) |
n/a |
2656 |
8 |
1968.2.dh |
\(\chi_{1968}(61, \cdot)\) |
n/a |
1344 |
8 |
1968.2.dk |
\(\chi_{1968}(37, \cdot)\) |
n/a |
1344 |
8 |
1968.2.dl |
\(\chi_{1968}(107, \cdot)\) |
n/a |
2656 |
8 |
1968.2.do |
\(\chi_{1968}(49, \cdot)\) |
n/a |
336 |
8 |
1968.2.dp |
\(\chi_{1968}(695, \cdot)\) |
None |
0 |
8 |
1968.2.du |
\(\chi_{1968}(259, \cdot)\) |
n/a |
2688 |
16 |
1968.2.dv |
\(\chi_{1968}(53, \cdot)\) |
n/a |
5312 |
16 |
1968.2.dw |
\(\chi_{1968}(175, \cdot)\) |
n/a |
672 |
16 |
1968.2.dx |
\(\chi_{1968}(7, \cdot)\) |
None |
0 |
16 |
1968.2.dy |
\(\chi_{1968}(17, \cdot)\) |
n/a |
1312 |
16 |
1968.2.dz |
\(\chi_{1968}(89, \cdot)\) |
None |
0 |
16 |
1968.2.eg |
\(\chi_{1968}(19, \cdot)\) |
n/a |
2688 |
16 |
1968.2.eh |
\(\chi_{1968}(29, \cdot)\) |
n/a |
5312 |
16 |
"n/a" means that newforms for that character have not been added to the database yet