Integral lattice 7.16.8.1.2

• Label: 7.16.8.1.2
• Class number: $1$
• Dimension: $7$
• Determinant: $16$
• Level: $8$

Lattice Invariants

Dimension:

$7$

Determinant:

$16$

Level:

$8$

Density:

$0.104403564285649124355987973892\dots$

Group order:

$55296$

Hermite number:

$1.34590019263235613194283260375\dots$

Minimal vector length:

$2$

Kissing number:

$36$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

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

Genus Structure

Genus representatives:

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