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Properties

Label 4.12.12.1.3
Class number $1$
Dimension $4$
Determinant $12$
Level $12$

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Lattice Invariants

Dimension:$4$
Determinant:$12$
Level:$12$
Density:$0.0890346680900633808059529836012\dots$
Group order:$32$
Hermite number:$0.537284965911770959776669078353\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 4 q^{2} \) \(\mathstrut +\mathstrut 10 q^{3} \) \(\mathstrut +\mathstrut 10 q^{4} \) \(\mathstrut +\mathstrut 16 q^{5} \) \(\mathstrut +\mathstrut 24 q^{6} \) \(\mathstrut +\mathstrut 12 q^{7} \) \(\mathstrut +\mathstrut 28 q^{8} \) \(\mathstrut +\mathstrut 26 q^{9} \) \(\mathstrut +\mathstrut 8 q^{10} \) \(\mathstrut +\mathstrut 48 q^{11} \) \(\mathstrut +\mathstrut 30 q^{12} \) \(\mathstrut +\mathstrut 28 q^{13} \) \(\mathstrut +\mathstrut 72 q^{14} \) \(\mathstrut +\mathstrut 32 q^{15} \) \(\mathstrut +\mathstrut 34 q^{16} \) \(\mathstrut +\mathstrut 64 q^{17} \) \(\mathstrut +\mathstrut 28 q^{18} \) \(\mathstrut +\mathstrut 36 q^{19} \) \(\mathstrut +\mathstrut 80 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 3 \end{array}\right)$
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