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Properties

Label 4.16.32.1.1
Class number $1$
Dimension $4$
Determinant $16$
Level $32$

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Lattice Invariants

Dimension:$4$
Determinant:$16$
Level:$32$
Density:$0.308425137534042456838577843746\dots$
Group order:$24$
Hermite number:$1.00000000000000000000000000000\dots$
Minimal vector length:$2$
Kissing number:$6$
Normalized minimal vectors: $(1, -1, 0, 0)$, $(1, 0, 0, 0)$, $(0, 1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 12 q^{3} \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 12 q^{5} \) \(\mathstrut +\mathstrut 24 q^{6} \) \(\mathstrut +\mathstrut 24 q^{7} \) \(\mathstrut +\mathstrut 12 q^{8} \) \(\mathstrut +\mathstrut 36 q^{10} \) \(\mathstrut +\mathstrut 36 q^{11} \) \(\mathstrut +\mathstrut 24 q^{12} \) \(\mathstrut +\mathstrut 28 q^{13} \) \(\mathstrut +\mathstrut 48 q^{14} \) \(\mathstrut +\mathstrut 72 q^{15} \) \(\mathstrut +\mathstrut 8 q^{16} \) \(\mathstrut +\mathstrut 78 q^{18} \) \(\mathstrut +\mathstrut 60 q^{19} \) \(\mathstrut +\mathstrut 12 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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