Properties

Label 8.4096.4.1.1
Class number $1$
Dimension $8$
Determinant $4096$
Level $4$

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Lattice Invariants

Dimension:$8$
Determinant:$4096$
Level:$4$
Density:$0.00396358606095387521307130259962\dots$
Group order:$622080$
Hermite number:$0.707106781186547524400844362105\dots$
Minimal vector length:$2$
Kissing number:$6$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, 0, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 168 q^{6} \) \(\mathstrut +\mathstrut 240 q^{8} \) \(\mathstrut +\mathstrut 756 q^{10} \) \(\mathstrut +\mathstrut 2064 q^{14} \) \(\mathstrut +\mathstrut 2160 q^{16} \) \(\mathstrut +\mathstrut 4542 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrrrrr} 2 & -1 & 1 & -1 & 1 & 1 & 1 & 1 \\ -1 & 2 & -1 & 1 & 0 & 0 & 0 & 0 \\ 1 & -1 & 6 & -2 & 3 & 3 & 3 & 3 \\ -1 & 1 & -2 & 6 & -3 & -3 & -3 & -3 \\ 1 & 0 & 3 & -3 & 6 & 2 & 2 & 2 \\ 1 & 0 & 3 & -3 & 2 & 6 & 2 & 2 \\ 1 & 0 & 3 & -3 & 2 & 2 & 6 & 2 \\ 1 & 0 & 3 & -3 & 2 & 2 & 2 & 6 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrrrrr} 2 & -1 & 1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 2 & -1 & 1 & 1 & 1 & 1 & 1 \\ 1 & -1 & 6 & 2 & -2 & 2 & 2 & 2 \\ -1 & 1 & 2 & 6 & -2 & 2 & 2 & 2 \\ -1 & 1 & -2 & -2 & 6 & -2 & -2 & -2 \\ -1 & 1 & 2 & 2 & -2 & 6 & 2 & 2 \\ -1 & 1 & 2 & 2 & -2 & 2 & 6 & 2 \\ -1 & 1 & 2 & 2 & -2 & 2 & 2 & 6 \end{array}\right)$
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