S_4^16 The following table gives coefficients for the two suspected lifts, unknown type. 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) 2848 0 [2 2 2 2 0 0 0 1 1 1] ( 5, 1,1) -2835 45 [2 2 2 2 1 0 0 1 0 1] ( 8, 1,1) 29640 72 [2 2 2 2 0 0 0 1 1 0] ( 9, 1,1) -112266 1782 [2 2 2 2 1 0 0 0 0 1] ( 12, 2,1) -734832 11664 [2 2 2 2 0 0 0 1 0 0] ( 16, 1,1) 10151680 -34560 [2 2 2 2 0 0 0 0 0 0] ( 4, 1,2) -1337780043776 -5480939520 [4 4 4 4 0 0 0 2 2 2] (64)