Integral lattice 7.64.8.1.3

• Label: 7.64.8.1.3
• Class number: $1$
• Dimension: $7$
• Determinant: $64$
• Level: $8$

Lattice Invariants

Dimension:

$7$

Determinant:

$64$

Level:

$8$

Density:

$0.0522017821428245621779939869460\dots$

Group order:

$92160$

Hermite number:

$1.10408951367381233764950538762\dots$

Minimal vector length:

$2$

Kissing number:

$12$

Normalized minimal vectors:

$(1, 0, 0, 0, 0, 0, 0)$, $(1, 2, -1, 1, -1, -1, 0)$, $(0, 0, 1, 0, 0, 0, 0)$, $(0, 0, 0, 1, 0, 0, 0)$, $(0, 0, 0, 0, 1, 0, 0)$, $(0, 0, 0, 0, 0, 1, 0)$

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrr} 2 & -1 & 0 & 0 & 0 & 0 & 0 \\ -1 & 3 & 1 & -1 & 1 & 1 & 0 \\ 0 & 1 & 2 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 2 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 2 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 4 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrr} 2 & 0 & 0 & -1 & -1 & 1 & 0 \\ 0 & 2 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 2 & 1 & 1 & -1 & 0 \\ -1 & 1 & 1 & 3 & 2 & -1 & 0 \\ -1 & 1 & 1 & 2 & 3 & -2 & 0 \\ 1 & -1 & -1 & -1 & -2 & 3 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 4 \end{array}\right)$
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