Integral lattice 7.1048576.16.1.1

• Label: 7.1048576.16.1.1
• Class number: $1$
• Dimension: $7$
• Determinant: $1048576$
• Level: $16$

Lattice Invariants

Dimension:

$7$

Determinant:

$1048576$

Level:

$16$

Density:

$0.0327124834125048815942058915852\dots$

Group order:

$2304$

Hermite number:

$0.966078324464585795443317214171\dots$

Minimal vector length:

$7$

Kissing number:

$8$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrr} 7 & -1 & -2 & -2 & 2 & 1 & -2 \\ -1 & 7 & -2 & -2 & 2 & 1 & -2 \\ -2 & -2 & 12 & 4 & 4 & 2 & 4 \\ -2 & -2 & 4 & 12 & -4 & 2 & 4 \\ 2 & 2 & 4 & -4 & 12 & -2 & -4 \\ 1 & 1 & 2 & 2 & -2 & 7 & 2 \\ -2 & -2 & 4 & 4 & -4 & 2 & 12 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrr} 7 & -1 & 1 & 1 & 2 & -2 & 2 \\ -1 & 7 & 1 & 1 & 2 & -2 & 2 \\ 1 & 1 & 7 & -1 & -2 & 2 & -2 \\ 1 & 1 & -1 & 7 & -2 & 2 & -2 \\ 2 & 2 & -2 & -2 & 12 & -4 & 4 \\ -2 & -2 & 2 & 2 & -4 & 12 & -4 \\ 2 & 2 & -2 & -2 & 4 & -4 & 12 \end{array}\right)$
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