Properties

Label 8.4096.4.1.2
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:$161280$
Hermite number:$0.707106781186547524400844362105\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 32 q^{4} \) \(\mathstrut +\mathstrut 56 q^{6} \) \(\mathstrut +\mathstrut 496 q^{8} \) \(\mathstrut +\mathstrut 252 q^{10} \) \(\mathstrut +\mathstrut 896 q^{12} \) \(\mathstrut +\mathstrut 688 q^{14} \) \(\mathstrut +\mathstrut 4208 q^{16} \) \(\mathstrut +\mathstrut 1514 q^{18} \) \(\mathstrut +\mathstrut 4032 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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