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Properties

Label 5.8.16.1.1
Class number $1$
Dimension $5$
Determinant $8$
Level $16$

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Lattice Invariants

Dimension:$5$
Determinant:$8$
Level:$16$
Density:$0.0581572016636573294513130078014\dots$
Group order:$192$
Hermite number:$0.659753955386447129687000985614\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 12 q^{2} \) \(\mathstrut +\mathstrut 36 q^{3} \) \(\mathstrut +\mathstrut 32 q^{4} \) \(\mathstrut +\mathstrut 28 q^{5} \) \(\mathstrut +\mathstrut 80 q^{6} \) \(\mathstrut +\mathstrut 120 q^{7} \) \(\mathstrut +\mathstrut 122 q^{8} \) \(\mathstrut +\mathstrut 62 q^{9} \) \(\mathstrut +\mathstrut 96 q^{10} \) \(\mathstrut +\mathstrut 276 q^{11} \) \(\mathstrut +\mathstrut 192 q^{12} \) \(\mathstrut +\mathstrut 100 q^{13} \) \(\mathstrut +\mathstrut 320 q^{14} \) \(\mathstrut +\mathstrut 408 q^{15} \) \(\mathstrut +\mathstrut 264 q^{16} \) \(\mathstrut +\mathstrut 184 q^{17} \) \(\mathstrut +\mathstrut 300 q^{18} \) \(\mathstrut +\mathstrut 492 q^{19} \) \(\mathstrut +\mathstrut 448 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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