Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1040))\).
|
Total |
New |
Old |
| Modular forms
| 162624 |
82468 |
80156 |
| Cusp forms
| 159936 |
81872 |
78064 |
| Eisenstein series
| 2688 |
596 |
2092 |
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1040))\)
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 |
| 1040.6.a |
\(\chi_{1040}(1, \cdot)\) |
1040.6.a.a |
1 |
1 |
| 1040.6.a.b |
1 |
| 1040.6.a.c |
2 |
| 1040.6.a.d |
2 |
| 1040.6.a.e |
2 |
| 1040.6.a.f |
2 |
| 1040.6.a.g |
2 |
| 1040.6.a.h |
2 |
| 1040.6.a.i |
2 |
| 1040.6.a.j |
3 |
| 1040.6.a.k |
3 |
| 1040.6.a.l |
3 |
| 1040.6.a.m |
4 |
| 1040.6.a.n |
4 |
| 1040.6.a.o |
4 |
| 1040.6.a.p |
4 |
| 1040.6.a.q |
6 |
| 1040.6.a.r |
6 |
| 1040.6.a.s |
6 |
| 1040.6.a.t |
7 |
| 1040.6.a.u |
7 |
| 1040.6.a.v |
7 |
| 1040.6.a.w |
8 |
| 1040.6.a.x |
8 |
| 1040.6.a.y |
8 |
| 1040.6.a.z |
8 |
| 1040.6.a.ba |
8 |
| 1040.6.d |
\(\chi_{1040}(209, \cdot)\) |
n/a |
180 |
1 |
| 1040.6.e |
\(\chi_{1040}(441, \cdot)\) |
None |
0 |
1 |
| 1040.6.f |
\(\chi_{1040}(129, \cdot)\) |
n/a |
208 |
1 |
| 1040.6.g |
\(\chi_{1040}(521, \cdot)\) |
None |
0 |
1 |
| 1040.6.j |
\(\chi_{1040}(729, \cdot)\) |
None |
0 |
1 |
| 1040.6.k |
\(\chi_{1040}(961, \cdot)\) |
n/a |
140 |
1 |
| 1040.6.p |
\(\chi_{1040}(649, \cdot)\) |
None |
0 |
1 |
| 1040.6.q |
\(\chi_{1040}(81, \cdot)\) |
n/a |
280 |
2 |
| 1040.6.s |
\(\chi_{1040}(437, \cdot)\) |
n/a |
1672 |
2 |
| 1040.6.u |
\(\chi_{1040}(31, \cdot)\) |
n/a |
280 |
2 |
| 1040.6.v |
\(\chi_{1040}(443, \cdot)\) |
n/a |
1440 |
2 |
| 1040.6.y |
\(\chi_{1040}(363, \cdot)\) |
n/a |
1672 |
2 |
| 1040.6.z |
\(\chi_{1040}(359, \cdot)\) |
None |
0 |
2 |
| 1040.6.bb |
\(\chi_{1040}(333, \cdot)\) |
n/a |
1672 |
2 |
| 1040.6.be |
\(\chi_{1040}(389, \cdot)\) |
n/a |
1672 |
2 |
| 1040.6.bg |
\(\chi_{1040}(577, \cdot)\) |
n/a |
416 |
2 |
| 1040.6.bi |
\(\chi_{1040}(57, \cdot)\) |
None |
0 |
2 |
| 1040.6.bj |
\(\chi_{1040}(261, \cdot)\) |
n/a |
960 |
2 |
| 1040.6.bm |
\(\chi_{1040}(291, \cdot)\) |
n/a |
1120 |
2 |
| 1040.6.bp |
\(\chi_{1040}(287, \cdot)\) |
n/a |
360 |
2 |
| 1040.6.bq |
\(\chi_{1040}(103, \cdot)\) |
None |
0 |
2 |
| 1040.6.bs |
\(\chi_{1040}(499, \cdot)\) |
n/a |
1672 |
2 |
| 1040.6.bt |
\(\chi_{1040}(811, \cdot)\) |
n/a |
1120 |
2 |
| 1040.6.bv |
\(\chi_{1040}(207, \cdot)\) |
n/a |
420 |
2 |
| 1040.6.bw |
\(\chi_{1040}(183, \cdot)\) |
None |
0 |
2 |
| 1040.6.bz |
\(\chi_{1040}(99, \cdot)\) |
n/a |
1672 |
2 |
| 1040.6.cc |
\(\chi_{1040}(469, \cdot)\) |
n/a |
1440 |
2 |
| 1040.6.cd |
\(\chi_{1040}(177, \cdot)\) |
n/a |
416 |
2 |
| 1040.6.cf |
\(\chi_{1040}(473, \cdot)\) |
None |
0 |
2 |
| 1040.6.ch |
\(\chi_{1040}(181, \cdot)\) |
n/a |
1120 |
2 |
| 1040.6.cj |
\(\chi_{1040}(213, \cdot)\) |
n/a |
1672 |
2 |
| 1040.6.cm |
\(\chi_{1040}(151, \cdot)\) |
None |
0 |
2 |
| 1040.6.cn |
\(\chi_{1040}(27, \cdot)\) |
n/a |
1440 |
2 |
| 1040.6.cq |
\(\chi_{1040}(883, \cdot)\) |
n/a |
1672 |
2 |
| 1040.6.cr |
\(\chi_{1040}(239, \cdot)\) |
n/a |
420 |
2 |
| 1040.6.cu |
\(\chi_{1040}(317, \cdot)\) |
n/a |
1672 |
2 |
| 1040.6.cv |
\(\chi_{1040}(329, \cdot)\) |
None |
0 |
2 |
| 1040.6.da |
\(\chi_{1040}(641, \cdot)\) |
n/a |
280 |
2 |
| 1040.6.db |
\(\chi_{1040}(9, \cdot)\) |
None |
0 |
2 |
| 1040.6.de |
\(\chi_{1040}(601, \cdot)\) |
None |
0 |
2 |
| 1040.6.df |
\(\chi_{1040}(49, \cdot)\) |
n/a |
416 |
2 |
| 1040.6.dg |
\(\chi_{1040}(121, \cdot)\) |
None |
0 |
2 |
| 1040.6.dh |
\(\chi_{1040}(289, \cdot)\) |
n/a |
416 |
2 |
| 1040.6.dk |
\(\chi_{1040}(293, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.dn |
\(\chi_{1040}(319, \cdot)\) |
n/a |
840 |
4 |
| 1040.6.dp |
\(\chi_{1040}(3, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.dq |
\(\chi_{1040}(563, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.ds |
\(\chi_{1040}(71, \cdot)\) |
None |
0 |
4 |
| 1040.6.dv |
\(\chi_{1040}(397, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.dx |
\(\chi_{1040}(101, \cdot)\) |
n/a |
2240 |
4 |
| 1040.6.dz |
\(\chi_{1040}(137, \cdot)\) |
None |
0 |
4 |
| 1040.6.eb |
\(\chi_{1040}(353, \cdot)\) |
n/a |
832 |
4 |
| 1040.6.ec |
\(\chi_{1040}(29, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.ee |
\(\chi_{1040}(379, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.eg |
\(\chi_{1040}(87, \cdot)\) |
None |
0 |
4 |
| 1040.6.eh |
\(\chi_{1040}(127, \cdot)\) |
n/a |
840 |
4 |
| 1040.6.ek |
\(\chi_{1040}(171, \cdot)\) |
n/a |
2240 |
4 |
| 1040.6.en |
\(\chi_{1040}(19, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.eq |
\(\chi_{1040}(23, \cdot)\) |
None |
0 |
4 |
| 1040.6.er |
\(\chi_{1040}(367, \cdot)\) |
n/a |
840 |
4 |
| 1040.6.et |
\(\chi_{1040}(11, \cdot)\) |
n/a |
2240 |
4 |
| 1040.6.ev |
\(\chi_{1040}(61, \cdot)\) |
n/a |
2240 |
4 |
| 1040.6.ew |
\(\chi_{1040}(457, \cdot)\) |
None |
0 |
4 |
| 1040.6.ey |
\(\chi_{1040}(33, \cdot)\) |
n/a |
832 |
4 |
| 1040.6.fa |
\(\chi_{1040}(69, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.fd |
\(\chi_{1040}(197, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.ff |
\(\chi_{1040}(119, \cdot)\) |
None |
0 |
4 |
| 1040.6.fh |
\(\chi_{1040}(523, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.fi |
\(\chi_{1040}(43, \cdot)\) |
n/a |
3344 |
4 |
| 1040.6.fk |
\(\chi_{1040}(111, \cdot)\) |
n/a |
560 |
4 |
| 1040.6.fm |
\(\chi_{1040}(37, \cdot)\) |
n/a |
3344 |
4 |
"n/a" means that newforms for that character have not been added to the database yet
