0,3

Also theta series of 16-dimensional lattice (SL(2,9) Y SL(2,9)).(C2 x C2). - John Cannon, Jan 10 2007

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag.

Walter Feit, Some lattices over Q(sqrt(-3)), J. Algebra 52 (1978), no. 1, 248-263.

Theta series is x^8-48*x^2*y, x = phi_0(z), y = Delta_12(z) in the notation of SPLAG, Chap. 4.

1 + 720*q^4 + 13440*q^6 + 97200*q^8 + 455040*q^10 + 1714320*q^12 + 4821120*q^14 + ...

(MAGMA definition for lattice (SL(2, 9) Y SL(2, 9)).(C2 x C2), from John Cannon:)

LatticeWithBasis(16, \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ], MatrixRing(IntegerRing(), 16) ! \[

4, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 2, 1, 1, 1, 2,

1, -1, 1, 1, 0, 1, 0, 1, 1, 2, 2, 4, 0, 1, 2, 2, 1, 1, 1, 2, 1, 0, 1,

1, 2, 1, 1, 0, 4, 1, 1, 1, 2, 0, 2, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 4,

1, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 2, 1, 2, 1, 1, 4, 1, 1, 2, 1, 2, 2,

0, 2, 1, 2, 1, 2, 2, 1, 1, 1, 4, 1, 0, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1,

2, 1, 1, 1, 4, 1, 2, 2, 2, 1, 1, 1, 0, 1, -1, 1, 0, 1, 2, 0, 1, 4, 1,

1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 0, 1, 2, 2, 1, 4, 2, 2, 1, 0, 0, -1, 2,

1, 2, 1, 0, 2, 2, 2, 1, 2, 4, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 2, 1, 2,

2, 2, 2, 4, 1, 0, -1, 1, 1, 1, 0, 2, 1, 0, 1, 1, 1, 1, 0, 1, 4, 1, 1,

1, 2, 0, 1, 1, 2, 2, 0, 1, 2, 0, 0, 0, 1, 4, 2, 1, 2, 1, 1, 1, 2, 1,

1, 1, 1, 0, 1, -1, 1, 2, 4, 1, 1, 1, 2, 0, 2, 2, 1, 0, 1, -1, 1, 1, 1,

1, 1, 4 ])

(MAGMA definition for lattice A_2 tensor E_8, from John Cannon:)

A := Lattice("A", 2);

B := Lattice("E", 8);

L := TensorProduct(A, B);

T<q> := ThetaSeries(L, 16);

Sequence in context: A052785 A052783 A112002 this_sequence A137891 A056271 A000920

Adjacent sequences: A004030 A004031 A004032 this_sequence A004034 A004035 A004036

nonn,easy

njas