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Properties

Label 8.4.2.1.1
Class number $1$
Dimension $8$
Determinant $4$
Level $2$

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Lattice Invariants

Dimension:$8$
Determinant:$4$
Level:$2$
Density:$0.126834753950524006818281683188\dots$
Group order:$10321920$
Hermite number:$1.68179283050742908606225095247\dots$
Minimal vector length:$2$
Kissing number:$112$
Normalized minimal vectors: $(1, -1, 0, 0, 0, 0, 0, 0)$, $(1, 0, 0, -1, 0, 0, 0, 0)$, $(1, 0, 0, 0, -1, 0, 0, 0)$, $(1, 0, 0, 0, 0, -1, 0, 0)$, $(1, 0, 0, 0, 0, 0, -1, 0)$, $(1, 0, 0, 0, 0, 0, 0, -1)$, $(1, 0, 0, 0, 0, 0, 0, 0)$, $(1, 0, 1, -1, 0, 0, 0, 0)$, $(1, 0, 1, 0, -1, 0, 0, 0)$, $(1, 0, 1, 0, 0, -1, 0, 0)$, $(1, 0, 1, 0, 0, 0, -1, 0)$, $(1, 0, 1, 0, 0, 0, 0, -1)$, $(1, 0, 1, 0, 0, 0, 0, 0)$ ...
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 112 q^{2} \) \(\mathstrut +\mathstrut 1136 q^{4} \) \(\mathstrut +\mathstrut 3136 q^{6} \) \(\mathstrut +\mathstrut 9328 q^{8} \) \(\mathstrut +\mathstrut 14112 q^{10} \) \(\mathstrut +\mathstrut 31808 q^{12} \) \(\mathstrut +\mathstrut 38528 q^{14} \) \(\mathstrut +\mathstrut 74864 q^{16} \) \(\mathstrut +\mathstrut 84784 q^{18} \) \(\mathstrut +\mathstrut 143136 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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