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Properties

Label 5.2.4.1.1
Class number $1$
Dimension $5$
Determinant $2$
Level $4$

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Lattice Invariants

Dimension:$5$
Determinant:$2$
Level:$4$
Density:$0.116314403327314658902626015603\dots$
Group order:$768$
Hermite number:$0.870550563296124139136270017480\dots$
Minimal vector length:$1$
Kissing number:$8$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0)$, $(0, 0, 1, 0, 0)$, $(0, 0, 0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 8 q \) \(\mathstrut +\mathstrut 26 q^{2} \) \(\mathstrut +\mathstrut 48 q^{3} \) \(\mathstrut +\mathstrut 72 q^{4} \) \(\mathstrut +\mathstrut 112 q^{5} \) \(\mathstrut +\mathstrut 144 q^{6} \) \(\mathstrut +\mathstrut 160 q^{7} \) \(\mathstrut +\mathstrut 218 q^{8} \) \(\mathstrut +\mathstrut 248 q^{9} \) \(\mathstrut +\mathstrut 240 q^{10} \) \(\mathstrut +\mathstrut 368 q^{11} \) \(\mathstrut +\mathstrut 432 q^{12} \) \(\mathstrut +\mathstrut 400 q^{13} \) \(\mathstrut +\mathstrut 576 q^{14} \) \(\mathstrut +\mathstrut 544 q^{15} \) \(\mathstrut +\mathstrut 456 q^{16} \) \(\mathstrut +\mathstrut 736 q^{17} \) \(\mathstrut +\mathstrut 650 q^{18} \) \(\mathstrut +\mathstrut 656 q^{19} \) \(\mathstrut +\mathstrut 1008 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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