# 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)