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Properties

Label 4.4.8.1.1
Class number $1$
Dimension $4$
Determinant $4$
Level $8$

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Lattice Invariants

Dimension:$4$
Determinant:$4$
Level:$8$
Density:$0.154212568767021228419288921873\dots$
Group order:$96$
Hermite number:$0.707106781186547524400844362105\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 12 q^{2} \) \(\mathstrut +\mathstrut 24 q^{3} \) \(\mathstrut +\mathstrut 8 q^{4} \) \(\mathstrut +\mathstrut 12 q^{5} \) \(\mathstrut +\mathstrut 48 q^{6} \) \(\mathstrut +\mathstrut 48 q^{7} \) \(\mathstrut +\mathstrut 24 q^{8} \) \(\mathstrut +\mathstrut 26 q^{9} \) \(\mathstrut +\mathstrut 72 q^{10} \) \(\mathstrut +\mathstrut 72 q^{11} \) \(\mathstrut +\mathstrut 32 q^{12} \) \(\mathstrut +\mathstrut 28 q^{13} \) \(\mathstrut +\mathstrut 96 q^{14} \) \(\mathstrut +\mathstrut 144 q^{15} \) \(\mathstrut +\mathstrut 24 q^{16} \) \(\mathstrut +\mathstrut 36 q^{17} \) \(\mathstrut +\mathstrut 156 q^{18} \) \(\mathstrut +\mathstrut 120 q^{19} \) \(\mathstrut +\mathstrut 48 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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