Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1421))\).
|
Total |
New |
Old |
Modular forms
| 248640 |
237729 |
10911 |
Cusp forms
| 245280 |
235111 |
10169 |
Eisenstein series
| 3360 |
2618 |
742 |
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1421))\)
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 |
1421.4.a |
\(\chi_{1421}(1, \cdot)\) |
1421.4.a.a |
1 |
1 |
1421.4.a.b |
1 |
1421.4.a.c |
2 |
1421.4.a.d |
2 |
1421.4.a.e |
5 |
1421.4.a.f |
7 |
1421.4.a.g |
10 |
1421.4.a.h |
11 |
1421.4.a.i |
12 |
1421.4.a.j |
18 |
1421.4.a.k |
24 |
1421.4.a.l |
28 |
1421.4.a.m |
28 |
1421.4.a.n |
28 |
1421.4.a.o |
28 |
1421.4.a.p |
34 |
1421.4.a.q |
48 |
1421.4.b |
\(\chi_{1421}(1275, \cdot)\) |
n/a |
302 |
1 |
1421.4.e |
\(\chi_{1421}(30, \cdot)\) |
n/a |
560 |
2 |
1421.4.g |
\(\chi_{1421}(244, \cdot)\) |
n/a |
592 |
2 |
1421.4.j |
\(\chi_{1421}(753, \cdot)\) |
n/a |
592 |
2 |
1421.4.k |
\(\chi_{1421}(239, \cdot)\) |
n/a |
2508 |
6 |
1421.4.l |
\(\chi_{1421}(36, \cdot)\) |
n/a |
2508 |
6 |
1421.4.m |
\(\chi_{1421}(190, \cdot)\) |
n/a |
2508 |
6 |
1421.4.n |
\(\chi_{1421}(204, \cdot)\) |
n/a |
2352 |
6 |
1421.4.o |
\(\chi_{1421}(197, \cdot)\) |
n/a |
1818 |
6 |
1421.4.p |
\(\chi_{1421}(484, \cdot)\) |
n/a |
2508 |
6 |
1421.4.q |
\(\chi_{1421}(141, \cdot)\) |
n/a |
2508 |
6 |
1421.4.r |
\(\chi_{1421}(78, \cdot)\) |
n/a |
2508 |
6 |
1421.4.s |
\(\chi_{1421}(215, \cdot)\) |
n/a |
1184 |
4 |
1421.4.v |
\(\chi_{1421}(71, \cdot)\) |
n/a |
2508 |
6 |
1421.4.bd |
\(\chi_{1421}(470, \cdot)\) |
n/a |
2508 |
6 |
1421.4.bk |
\(\chi_{1421}(295, \cdot)\) |
n/a |
1812 |
6 |
1421.4.bl |
\(\chi_{1421}(57, \cdot)\) |
n/a |
2508 |
6 |
1421.4.bm |
\(\chi_{1421}(183, \cdot)\) |
n/a |
2508 |
6 |
1421.4.bn |
\(\chi_{1421}(274, \cdot)\) |
n/a |
2508 |
6 |
1421.4.bo |
\(\chi_{1421}(64, \cdot)\) |
n/a |
2508 |
6 |
1421.4.bp |
\(\chi_{1421}(22, \cdot)\) |
n/a |
2508 |
6 |
1421.4.bs |
\(\chi_{1421}(123, \cdot)\) |
n/a |
5016 |
12 |
1421.4.bt |
\(\chi_{1421}(53, \cdot)\) |
n/a |
5016 |
12 |
1421.4.bu |
\(\chi_{1421}(228, \cdot)\) |
n/a |
5016 |
12 |
1421.4.bv |
\(\chi_{1421}(165, \cdot)\) |
n/a |
3552 |
12 |
1421.4.bw |
\(\chi_{1421}(88, \cdot)\) |
n/a |
4704 |
12 |
1421.4.bx |
\(\chi_{1421}(23, \cdot)\) |
n/a |
5016 |
12 |
1421.4.by |
\(\chi_{1421}(25, \cdot)\) |
n/a |
5016 |
12 |
1421.4.bz |
\(\chi_{1421}(16, \cdot)\) |
n/a |
5016 |
12 |
1421.4.ca |
\(\chi_{1421}(76, \cdot)\) |
n/a |
5016 |
12 |
1421.4.cd |
\(\chi_{1421}(27, \cdot)\) |
n/a |
5016 |
12 |
1421.4.ce |
\(\chi_{1421}(461, \cdot)\) |
n/a |
5016 |
12 |
1421.4.cf |
\(\chi_{1421}(69, \cdot)\) |
n/a |
5016 |
12 |
1421.4.cg |
\(\chi_{1421}(48, \cdot)\) |
n/a |
3552 |
12 |
1421.4.ch |
\(\chi_{1421}(41, \cdot)\) |
n/a |
5016 |
12 |
1421.4.ci |
\(\chi_{1421}(55, \cdot)\) |
n/a |
5016 |
12 |
1421.4.cp |
\(\chi_{1421}(153, \cdot)\) |
n/a |
5016 |
12 |
1421.4.cs |
\(\chi_{1421}(212, \cdot)\) |
n/a |
5016 |
12 |
1421.4.ct |
\(\chi_{1421}(151, \cdot)\) |
n/a |
5016 |
12 |
1421.4.cu |
\(\chi_{1421}(51, \cdot)\) |
n/a |
5016 |
12 |
1421.4.cv |
\(\chi_{1421}(4, \cdot)\) |
n/a |
5016 |
12 |
1421.4.cw |
\(\chi_{1421}(86, \cdot)\) |
n/a |
5016 |
12 |
1421.4.cx |
\(\chi_{1421}(67, \cdot)\) |
n/a |
3552 |
12 |
1421.4.de |
\(\chi_{1421}(9, \cdot)\) |
n/a |
5016 |
12 |
1421.4.dm |
\(\chi_{1421}(93, \cdot)\) |
n/a |
5016 |
12 |
1421.4.do |
\(\chi_{1421}(26, \cdot)\) |
n/a |
10032 |
24 |
1421.4.dv |
\(\chi_{1421}(61, \cdot)\) |
n/a |
10032 |
24 |
1421.4.dw |
\(\chi_{1421}(124, \cdot)\) |
n/a |
10032 |
24 |
1421.4.dx |
\(\chi_{1421}(40, \cdot)\) |
n/a |
10032 |
24 |
1421.4.dy |
\(\chi_{1421}(19, \cdot)\) |
n/a |
7104 |
24 |
1421.4.dz |
\(\chi_{1421}(12, \cdot)\) |
n/a |
10032 |
24 |
1421.4.ea |
\(\chi_{1421}(3, \cdot)\) |
n/a |
10032 |
24 |
1421.4.ed |
\(\chi_{1421}(66, \cdot)\) |
n/a |
10032 |
24 |
"n/a" means that newforms for that character have not been added to the database yet