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Properties

Label 4.8.16.1.2
Class number $1$
Dimension $4$
Determinant $8$
Level $16$

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Lattice Invariants

Dimension:$4$
Determinant:$8$
Level:$16$
Density:$0.109044753119357492721211889628\dots$
Group order:$96$
Hermite number:$0.594603557501360533358749985280\dots$
Minimal vector length:$1$
Kissing number:$6$
Normalized minimal vectors: $(1, 0, 0, 0)$, $(0, 1, 0, 0)$, $(0, 0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q \) \(\mathstrut +\mathstrut 12 q^{2} \) \(\mathstrut +\mathstrut 8 q^{3} \) \(\mathstrut +\mathstrut 6 q^{4} \) \(\mathstrut +\mathstrut 24 q^{5} \) \(\mathstrut +\mathstrut 24 q^{6} \) \(\mathstrut +\mathstrut 14 q^{8} \) \(\mathstrut +\mathstrut 42 q^{9} \) \(\mathstrut +\mathstrut 48 q^{10} \) \(\mathstrut +\mathstrut 40 q^{11} \) \(\mathstrut +\mathstrut 20 q^{12} \) \(\mathstrut +\mathstrut 72 q^{13} \) \(\mathstrut +\mathstrut 96 q^{14} \) \(\mathstrut +\mathstrut 30 q^{16} \) \(\mathstrut +\mathstrut 108 q^{17} \) \(\mathstrut +\mathstrut 84 q^{18} \) \(\mathstrut +\mathstrut 72 q^{19} \) \(\mathstrut +\mathstrut 40 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 8 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 8 \end{array}\right)$
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