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Properties

Space $M_{20}\left({\textrm{Sp}}(4,\mathbb{Z})\right)$
Name 20_Ups
Type interesting cusp form
Weight $20$
Hecke eigenform yes
Field degree $1$

Basic properties

Space: $M_{20}\left({\textrm{Sp}}(4,\mathbb{Z})\right)$
Type: interesting cusp form
Weight: 20
Hecke eigenform: yes
Integral Fourier coefficients: yes

Coefficient field

Field: \(\Q\)
Degree: 1
Field generator:$a$

Explicit formula

$-A*B*C - A^2*D + 1785600*C^2$

Selected eigenvalues $\lambda(l)$ of $T(l)$

$l$$\lambda(l)$
$2$ $-840960$
$3$ $346935960$
$4$ $248256200704$
$5$ $-5232247240500$

Selected Fourier coefficients $c(F)$

\(\det(F)\)\(F\)$c(F)$
4 (1, 0, 1) $-8$
7 (1, 1, 2) $-112$
8 (1, 0, 2) $-5232$
11 (1, 1, 3) $110154$
12 (1, 0, 3) $-817664$
(2, 2, 2) $1681920$

Select different $\lambda(l)$ and $c(F)$ to display or specify a modulus $\mathfrak{m}$ to reduce them by

$\lambda(l)$ available for $l$ in: 2 3 4 5
$c(F)$ available for $\det(F)$ in: 3 4 7 8 11 12 15 16 19 20 ... 83 84 87 88 91 92 95 96 99 100

List or range of $l$: e.g. 2, or 2,3,5,8, or 2..10
List or range of $\det(F):$ e.g. 3 or 3 7 41
Reduction modulus $\mathfrak{m}$: e.g. 17 or 3*a+14 or 3,a+1
(for best results, specify an ideal of prime norm)

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