Properties

Space $M_{12}\left(\textrm{Sp}(8,\mathbb{Z})\right)$
Name 12_Miyawaki
Type Miyawaki lift
cusp form
Weight 12
Hecke eigenform True
Field degree 1

Basic properties

Space: $M_{12}\left(\textrm{Sp}(8,\mathbb{Z})\right)$
Type: Miyawaki lift, cusp form
Weight: 12
Hecke eigenform: True
Integral Fourier coefficients: unknown

Coefficient field

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

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

$l$$\lambda(l)$
$2$ $42762240$

Selected Fourier coefficients $c(F)$

\(\det(F)\)\(F\)$c(F)$
5 (2, 2, 2, 2, 1, 0, 0, 1, 0, 1) $-5$
8 (2, 2, 2, 2, 0, 0, 0, 1, 1, 0) $-44$
9 (2, 2, 2, 2, 1, 0, 0, 0, 0, 1) $-78$
12 (2, 2, 2, 2, 0, 0, 0, 1, 0, 0) $-816$
(2, 2, 2, 4, 1, 1, 0, 1, 0, 0) $744$
13 (2, 2, 2, 4, 1, 1, 0, 0, 1, 0) $-377$

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
$c(F)$ available for $\det(F)$ in: 4 5 8 9 12 13 16 17 20 25

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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