Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8470))\).
|
Total |
New |
Old |
Modular forms
| 2106240 |
602186 |
1504054 |
Cusp forms
| 2075521 |
602186 |
1473335 |
Eisenstein series
| 30719 |
0 |
30719 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8470))\)
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 |
8470.2.a |
\(\chi_{8470}(1, \cdot)\) |
8470.2.a.a |
1 |
1 |
8470.2.a.b |
1 |
8470.2.a.c |
1 |
8470.2.a.d |
1 |
8470.2.a.e |
1 |
8470.2.a.f |
1 |
8470.2.a.g |
1 |
8470.2.a.h |
1 |
8470.2.a.i |
1 |
8470.2.a.j |
1 |
8470.2.a.k |
1 |
8470.2.a.l |
1 |
8470.2.a.m |
1 |
8470.2.a.n |
1 |
8470.2.a.o |
1 |
8470.2.a.p |
1 |
8470.2.a.q |
1 |
8470.2.a.r |
1 |
8470.2.a.s |
1 |
8470.2.a.t |
1 |
8470.2.a.u |
1 |
8470.2.a.v |
1 |
8470.2.a.w |
1 |
8470.2.a.x |
1 |
8470.2.a.y |
1 |
8470.2.a.z |
1 |
8470.2.a.ba |
1 |
8470.2.a.bb |
1 |
8470.2.a.bc |
1 |
8470.2.a.bd |
1 |
8470.2.a.be |
1 |
8470.2.a.bf |
1 |
8470.2.a.bg |
1 |
8470.2.a.bh |
1 |
8470.2.a.bi |
2 |
8470.2.a.bj |
2 |
8470.2.a.bk |
2 |
8470.2.a.bl |
2 |
8470.2.a.bm |
2 |
8470.2.a.bn |
2 |
8470.2.a.bo |
2 |
8470.2.a.bp |
2 |
8470.2.a.bq |
2 |
8470.2.a.br |
2 |
8470.2.a.bs |
2 |
8470.2.a.bt |
2 |
8470.2.a.bu |
2 |
8470.2.a.bv |
2 |
8470.2.a.bw |
2 |
8470.2.a.bx |
2 |
8470.2.a.by |
2 |
8470.2.a.bz |
2 |
8470.2.a.ca |
2 |
8470.2.a.cb |
2 |
8470.2.a.cc |
2 |
8470.2.a.cd |
2 |
8470.2.a.ce |
2 |
8470.2.a.cf |
2 |
8470.2.a.cg |
3 |
8470.2.a.ch |
3 |
8470.2.a.ci |
3 |
8470.2.a.cj |
3 |
8470.2.a.ck |
3 |
8470.2.a.cl |
3 |
8470.2.a.cm |
3 |
8470.2.a.cn |
3 |
8470.2.a.co |
4 |
8470.2.a.cp |
4 |
8470.2.a.cq |
4 |
8470.2.a.cr |
4 |
8470.2.a.cs |
4 |
8470.2.a.ct |
4 |
8470.2.a.cu |
6 |
8470.2.a.cv |
6 |
8470.2.a.cw |
6 |
8470.2.a.cx |
6 |
8470.2.a.cy |
6 |
8470.2.a.cz |
6 |
8470.2.a.da |
6 |
8470.2.a.db |
6 |
8470.2.a.dc |
6 |
8470.2.a.dd |
6 |
8470.2.a.de |
6 |
8470.2.a.df |
6 |
8470.2.a.dg |
8 |
8470.2.a.dh |
8 |
8470.2.c |
\(\chi_{8470}(3389, \cdot)\) |
n/a |
328 |
1 |
8470.2.e |
\(\chi_{8470}(5081, \cdot)\) |
n/a |
288 |
1 |
8470.2.g |
\(\chi_{8470}(8469, \cdot)\) |
n/a |
432 |
1 |
8470.2.i |
\(\chi_{8470}(4841, \cdot)\) |
n/a |
584 |
2 |
8470.2.l |
\(\chi_{8470}(727, \cdot)\) |
n/a |
872 |
2 |
8470.2.m |
\(\chi_{8470}(967, \cdot)\) |
n/a |
648 |
2 |
8470.2.n |
\(\chi_{8470}(3711, \cdot)\) |
n/a |
864 |
4 |
8470.2.o |
\(\chi_{8470}(1209, \cdot)\) |
n/a |
864 |
2 |
8470.2.r |
\(\chi_{8470}(2179, \cdot)\) |
n/a |
872 |
2 |
8470.2.t |
\(\chi_{8470}(241, \cdot)\) |
n/a |
576 |
2 |
8470.2.w |
\(\chi_{8470}(699, \cdot)\) |
n/a |
1728 |
4 |
8470.2.y |
\(\chi_{8470}(1371, \cdot)\) |
n/a |
1152 |
4 |
8470.2.ba |
\(\chi_{8470}(729, \cdot)\) |
n/a |
1296 |
4 |
8470.2.bc |
\(\chi_{8470}(771, \cdot)\) |
n/a |
2640 |
10 |
8470.2.bd |
\(\chi_{8470}(243, \cdot)\) |
n/a |
1744 |
4 |
8470.2.be |
\(\chi_{8470}(4113, \cdot)\) |
n/a |
1728 |
4 |
8470.2.bh |
\(\chi_{8470}(81, \cdot)\) |
n/a |
2304 |
8 |
8470.2.bi |
\(\chi_{8470}(1443, \cdot)\) |
n/a |
2592 |
8 |
8470.2.bj |
\(\chi_{8470}(27, \cdot)\) |
n/a |
3456 |
8 |
8470.2.bm |
\(\chi_{8470}(461, \cdot)\) |
n/a |
3520 |
10 |
8470.2.bo |
\(\chi_{8470}(309, \cdot)\) |
n/a |
3960 |
10 |
8470.2.br |
\(\chi_{8470}(769, \cdot)\) |
n/a |
5280 |
10 |
8470.2.bu |
\(\chi_{8470}(481, \cdot)\) |
n/a |
2304 |
8 |
8470.2.bw |
\(\chi_{8470}(9, \cdot)\) |
n/a |
3456 |
8 |
8470.2.bz |
\(\chi_{8470}(1909, \cdot)\) |
n/a |
3456 |
8 |
8470.2.ca |
\(\chi_{8470}(221, \cdot)\) |
n/a |
7040 |
20 |
8470.2.cb |
\(\chi_{8470}(43, \cdot)\) |
n/a |
7920 |
20 |
8470.2.cc |
\(\chi_{8470}(573, \cdot)\) |
n/a |
10560 |
20 |
8470.2.cf |
\(\chi_{8470}(71, \cdot)\) |
n/a |
10560 |
40 |
8470.2.ci |
\(\chi_{8470}(233, \cdot)\) |
n/a |
6912 |
16 |
8470.2.cj |
\(\chi_{8470}(3, \cdot)\) |
n/a |
6912 |
16 |
8470.2.cm |
\(\chi_{8470}(439, \cdot)\) |
n/a |
10560 |
20 |
8470.2.co |
\(\chi_{8470}(131, \cdot)\) |
n/a |
7040 |
20 |
8470.2.cq |
\(\chi_{8470}(529, \cdot)\) |
n/a |
10560 |
20 |
8470.2.cs |
\(\chi_{8470}(139, \cdot)\) |
n/a |
21120 |
40 |
8470.2.cv |
\(\chi_{8470}(169, \cdot)\) |
n/a |
15840 |
40 |
8470.2.cx |
\(\chi_{8470}(41, \cdot)\) |
n/a |
14080 |
40 |
8470.2.da |
\(\chi_{8470}(263, \cdot)\) |
n/a |
21120 |
40 |
8470.2.db |
\(\chi_{8470}(353, \cdot)\) |
n/a |
21120 |
40 |
8470.2.dc |
\(\chi_{8470}(191, \cdot)\) |
n/a |
28160 |
80 |
8470.2.df |
\(\chi_{8470}(97, \cdot)\) |
n/a |
42240 |
80 |
8470.2.dg |
\(\chi_{8470}(57, \cdot)\) |
n/a |
31680 |
80 |
8470.2.dh |
\(\chi_{8470}(179, \cdot)\) |
n/a |
42240 |
80 |
8470.2.dj |
\(\chi_{8470}(61, \cdot)\) |
n/a |
28160 |
80 |
8470.2.dl |
\(\chi_{8470}(19, \cdot)\) |
n/a |
42240 |
80 |
8470.2.do |
\(\chi_{8470}(47, \cdot)\) |
n/a |
84480 |
160 |
8470.2.dp |
\(\chi_{8470}(107, \cdot)\) |
n/a |
84480 |
160 |
"n/a" means that newforms for that character have not been added to the database yet