Integral lattice 6.32.16.1.1

• Label: 6.32.16.1.1
• Class number: $1$
• Dimension: $6$
• Determinant: $32$
• Level: $16$

Lattice Invariants

Dimension:

$6$

Determinant:

$32$

Level:

$16$

Density:

$0.114191398437428729764361846444\dots$

Group order:

$768$

Hermite number:

$1.12246204830937298143353304968\dots$

Minimal vector length:

$2$

Kissing number:

$16$

Normalized minimal vectors:

$(1, -1, -1, 0, 0, 0)$, $(1, -1, 0, 0, 0, 0)$, $(1, 0, -1, 0, 0, 0)$, $(1, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0)$, $(0, 0, 1, 0, 0, 0)$, $(0, 0, 0, 1, 0, 0)$, $(0, 0, 0, 0, 1, 0)$

Download this list for gp, magma, sage

Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrr} 2 & 1 & 1 & 0 & 0 & -1 \\ 1 & 2 & 0 & 0 & 0 & -1 \\ 1 & 0 & 2 & 0 & 0 & -1 \\ 0 & 0 & 0 & 2 & 0 & 1 \\ 0 & 0 & 0 & 0 & 2 & -1 \\ -1 & -1 & -1 & 1 & -1 & 4 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrr} 2 & 0 & 0 & 0 & 0 & -1 \\ 0 & 2 & -1 & 1 & 0 & -1 \\ 0 & -1 & 2 & -1 & 0 & 0 \\ 0 & 1 & -1 & 2 & 0 & -1 \\ 0 & 0 & 0 & 0 & 2 & 1 \\ -1 & -1 & 0 & -1 & 1 & 4 \end{array}\right)$
	Download this matrix for gp, magma, sage