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Properties

Label 5.8.4.1.2
Class number $1$
Dimension $5$
Determinant $8$
Level $4$

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Lattice Invariants

Dimension:$5$
Determinant:$8$
Level:$4$
Density:$0.0581572016636573294513130078014\dots$
Group order:$384$
Hermite number:$0.659753955386447129687000985614\dots$
Minimal vector length:$1$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q \) \(\mathstrut +\mathstrut 10 q^{2} \) \(\mathstrut +\mathstrut 24 q^{3} \) \(\mathstrut +\mathstrut 40 q^{4} \) \(\mathstrut +\mathstrut 56 q^{5} \) \(\mathstrut +\mathstrut 80 q^{6} \) \(\mathstrut +\mathstrut 80 q^{7} \) \(\mathstrut +\mathstrut 90 q^{8} \) \(\mathstrut +\mathstrut 124 q^{9} \) \(\mathstrut +\mathstrut 112 q^{10} \) \(\mathstrut +\mathstrut 184 q^{11} \) \(\mathstrut +\mathstrut 240 q^{12} \) \(\mathstrut +\mathstrut 200 q^{13} \) \(\mathstrut +\mathstrut 320 q^{14} \) \(\mathstrut +\mathstrut 272 q^{15} \) \(\mathstrut +\mathstrut 200 q^{16} \) \(\mathstrut +\mathstrut 368 q^{17} \) \(\mathstrut +\mathstrut 250 q^{18} \) \(\mathstrut +\mathstrut 328 q^{19} \) \(\mathstrut +\mathstrut 560 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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