Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1421))\).
|
Total |
New |
Old |
Modular forms
| 84000 |
80117 |
3883 |
Cusp forms
| 80641 |
77499 |
3142 |
Eisenstein series
| 3359 |
2618 |
741 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1421))\)
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 |
1421.2.a |
\(\chi_{1421}(1, \cdot)\) |
1421.2.a.a |
1 |
1 |
1421.2.a.b |
1 |
1421.2.a.c |
1 |
1421.2.a.d |
1 |
1421.2.a.e |
1 |
1421.2.a.f |
1 |
1421.2.a.g |
1 |
1421.2.a.h |
1 |
1421.2.a.i |
1 |
1421.2.a.j |
2 |
1421.2.a.k |
2 |
1421.2.a.l |
2 |
1421.2.a.m |
2 |
1421.2.a.n |
3 |
1421.2.a.o |
4 |
1421.2.a.p |
4 |
1421.2.a.q |
5 |
1421.2.a.r |
8 |
1421.2.a.s |
8 |
1421.2.a.t |
8 |
1421.2.a.u |
8 |
1421.2.a.v |
10 |
1421.2.a.w |
20 |
1421.2.b |
\(\chi_{1421}(1275, \cdot)\) |
1421.2.b.a |
2 |
1 |
1421.2.b.b |
2 |
1421.2.b.c |
2 |
1421.2.b.d |
4 |
1421.2.b.e |
4 |
1421.2.b.f |
4 |
1421.2.b.g |
6 |
1421.2.b.h |
6 |
1421.2.b.i |
12 |
1421.2.b.j |
18 |
1421.2.b.k |
18 |
1421.2.b.l |
20 |
1421.2.e |
\(\chi_{1421}(30, \cdot)\) |
n/a |
188 |
2 |
1421.2.g |
\(\chi_{1421}(244, \cdot)\) |
n/a |
192 |
2 |
1421.2.j |
\(\chi_{1421}(753, \cdot)\) |
n/a |
192 |
2 |
1421.2.k |
\(\chi_{1421}(239, \cdot)\) |
n/a |
828 |
6 |
1421.2.l |
\(\chi_{1421}(36, \cdot)\) |
n/a |
828 |
6 |
1421.2.m |
\(\chi_{1421}(190, \cdot)\) |
n/a |
828 |
6 |
1421.2.n |
\(\chi_{1421}(204, \cdot)\) |
n/a |
792 |
6 |
1421.2.o |
\(\chi_{1421}(197, \cdot)\) |
n/a |
582 |
6 |
1421.2.p |
\(\chi_{1421}(484, \cdot)\) |
n/a |
828 |
6 |
1421.2.q |
\(\chi_{1421}(141, \cdot)\) |
n/a |
828 |
6 |
1421.2.r |
\(\chi_{1421}(78, \cdot)\) |
n/a |
828 |
6 |
1421.2.s |
\(\chi_{1421}(215, \cdot)\) |
n/a |
384 |
4 |
1421.2.v |
\(\chi_{1421}(71, \cdot)\) |
n/a |
828 |
6 |
1421.2.bd |
\(\chi_{1421}(470, \cdot)\) |
n/a |
828 |
6 |
1421.2.bk |
\(\chi_{1421}(295, \cdot)\) |
n/a |
588 |
6 |
1421.2.bl |
\(\chi_{1421}(57, \cdot)\) |
n/a |
828 |
6 |
1421.2.bm |
\(\chi_{1421}(183, \cdot)\) |
n/a |
828 |
6 |
1421.2.bn |
\(\chi_{1421}(274, \cdot)\) |
n/a |
828 |
6 |
1421.2.bo |
\(\chi_{1421}(64, \cdot)\) |
n/a |
828 |
6 |
1421.2.bp |
\(\chi_{1421}(22, \cdot)\) |
n/a |
828 |
6 |
1421.2.bs |
\(\chi_{1421}(123, \cdot)\) |
n/a |
1656 |
12 |
1421.2.bt |
\(\chi_{1421}(53, \cdot)\) |
n/a |
1656 |
12 |
1421.2.bu |
\(\chi_{1421}(228, \cdot)\) |
n/a |
1656 |
12 |
1421.2.bv |
\(\chi_{1421}(165, \cdot)\) |
n/a |
1152 |
12 |
1421.2.bw |
\(\chi_{1421}(88, \cdot)\) |
n/a |
1560 |
12 |
1421.2.bx |
\(\chi_{1421}(23, \cdot)\) |
n/a |
1656 |
12 |
1421.2.by |
\(\chi_{1421}(25, \cdot)\) |
n/a |
1656 |
12 |
1421.2.bz |
\(\chi_{1421}(16, \cdot)\) |
n/a |
1656 |
12 |
1421.2.ca |
\(\chi_{1421}(76, \cdot)\) |
n/a |
1656 |
12 |
1421.2.cd |
\(\chi_{1421}(27, \cdot)\) |
n/a |
1656 |
12 |
1421.2.ce |
\(\chi_{1421}(461, \cdot)\) |
n/a |
1656 |
12 |
1421.2.cf |
\(\chi_{1421}(69, \cdot)\) |
n/a |
1656 |
12 |
1421.2.cg |
\(\chi_{1421}(48, \cdot)\) |
n/a |
1152 |
12 |
1421.2.ch |
\(\chi_{1421}(41, \cdot)\) |
n/a |
1656 |
12 |
1421.2.ci |
\(\chi_{1421}(55, \cdot)\) |
n/a |
1656 |
12 |
1421.2.cp |
\(\chi_{1421}(153, \cdot)\) |
n/a |
1656 |
12 |
1421.2.cs |
\(\chi_{1421}(212, \cdot)\) |
n/a |
1656 |
12 |
1421.2.ct |
\(\chi_{1421}(151, \cdot)\) |
n/a |
1656 |
12 |
1421.2.cu |
\(\chi_{1421}(51, \cdot)\) |
n/a |
1656 |
12 |
1421.2.cv |
\(\chi_{1421}(4, \cdot)\) |
n/a |
1656 |
12 |
1421.2.cw |
\(\chi_{1421}(86, \cdot)\) |
n/a |
1656 |
12 |
1421.2.cx |
\(\chi_{1421}(67, \cdot)\) |
n/a |
1152 |
12 |
1421.2.de |
\(\chi_{1421}(9, \cdot)\) |
n/a |
1656 |
12 |
1421.2.dm |
\(\chi_{1421}(93, \cdot)\) |
n/a |
1656 |
12 |
1421.2.do |
\(\chi_{1421}(26, \cdot)\) |
n/a |
3312 |
24 |
1421.2.dv |
\(\chi_{1421}(61, \cdot)\) |
n/a |
3312 |
24 |
1421.2.dw |
\(\chi_{1421}(124, \cdot)\) |
n/a |
3312 |
24 |
1421.2.dx |
\(\chi_{1421}(40, \cdot)\) |
n/a |
3312 |
24 |
1421.2.dy |
\(\chi_{1421}(19, \cdot)\) |
n/a |
2304 |
24 |
1421.2.dz |
\(\chi_{1421}(12, \cdot)\) |
n/a |
3312 |
24 |
1421.2.ea |
\(\chi_{1421}(3, \cdot)\) |
n/a |
3312 |
24 |
1421.2.ed |
\(\chi_{1421}(66, \cdot)\) |
n/a |
3312 |
24 |
"n/a" means that newforms for that character have not been added to the database yet