Integral lattice 7.64.8.1.2

• Label: 7.64.8.1.2
• Class number: $1$
• Dimension: $7$
• Determinant: $64$
• Level: $8$

Lattice Invariants

Dimension:

$7$

Determinant:

$64$

Level:

$8$

Density:

$0.00461402926790175895468397545642\dots$

Group order:

$46080$

Hermite number:

$0.552044756836906168824752693812\dots$

Minimal vector length:

$1$

Kissing number:

$2$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrr} 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 3 & -1 & 1 & 1 & 1 & 1 \\ 0 & -1 & 3 & 1 & 1 & -1 & -1 \\ 0 & 1 & 1 & 3 & 1 & 1 & -1 \\ 0 & 1 & 1 & 1 & 3 & -1 & 1 \\ 0 & 1 & -1 & 1 & -1 & 3 & -1 \\ 0 & 1 & -1 & -1 & 1 & -1 & 3 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrr} 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 3 & 1 & 1 & -1 & 1 & -1 \\ 0 & 1 & 3 & -1 & -1 & 1 & -1 \\ 0 & 1 & -1 & 3 & 1 & 1 & -1 \\ 0 & -1 & -1 & 1 & 3 & 1 & 1 \\ 0 & 1 & 1 & 1 & 1 & 3 & -1 \\ 0 & -1 & -1 & -1 & 1 & -1 & 3 \end{array}\right)$
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