Integral lattice 7.16777216.16.1.1

• Label: 7.16777216.16.1.1
• Class number: $1$
• Dimension: $7$
• Determinant: $16777216$
• Level: $16$

Lattice Invariants

Dimension:

$7$

Determinant:

$16777216$

Level:

$16$

Density:

$0.00817812085312622039855147289631\dots$

Group order:

$10080$

Hermite number:

$0.650122501497414935849935812938\dots$

Minimal vector length:

$7$

Kissing number:

$2$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrr} 7 & 3 & -3 & 3 & 3 & -3 & -3 \\ 3 & 15 & 1 & -1 & -1 & 1 & 1 \\ -3 & 1 & 15 & 1 & 1 & -1 & -1 \\ 3 & -1 & 1 & 15 & -1 & 1 & 1 \\ 3 & -1 & 1 & -1 & 15 & 1 & 1 \\ -3 & 1 & -1 & 1 & 1 & 15 & -1 \\ -3 & 1 & -1 & 1 & 1 & -1 & 15 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrr} 7 & -3 & 3 & 3 & -3 & -3 & 3 \\ -3 & 15 & 1 & 1 & -1 & -1 & 1 \\ 3 & 1 & 15 & -1 & 1 & 1 & -1 \\ 3 & 1 & -1 & 15 & 1 & 1 & -1 \\ -3 & -1 & 1 & 1 & 15 & -1 & 1 \\ -3 & -1 & 1 & 1 & -1 & 15 & 1 \\ 3 & 1 & -1 & -1 & 1 & 1 & 15 \end{array}\right)$
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