S_4^16
The following table gives coefficients for the 
two
Miyawaki lifts.

The format is: 
(   d, g,m)  coefficient1 coefficient2  [matrix             ]  (true det)

where 
the matrix is given in form [m11 m22 m33 m44 m12 m13 m23 m14 m24 m34] 
d is the determinant of the associated PRIMITIVE form if the matrix is not primitive. 
g is the genus of the associated primitive form (from Gordon Nipp's Table of Quaternary Forms) 
m is the content of the matrix. 
If not primitive, "true det" gives the determinant. 

--------------------------------------------------------------------------------

(   d, g,m)     coefficient   [matrix             ]  (true det)
(   4, 1,1)             15628       0     [2 2 2 2 0 0 0 1 1 1]
(   5, 1,1)             4725     25       [2 2 2 2 1 0 0 1 0 1]
(   8, 1,1)             660960    -968    [2 2 2 2 0 0 0 1 1 0]
(   9, 1,1)           -378966  -5478      [2 2 2 2 1 0 0 0 0 1]
(  12, 2,1)             5753328   58224   [2 2 2 2 0 0 0 1 0 0]
(  16, 1,1)           -70031360   1203840 [2 2 2 2 0 0 0 0 0 0]
(   4, 1,2)    10564640180224 3570739200  [4 4 4 4 0 0 0 2 2 2]  (64)