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Properties

Label 5.16.8.1.3
Class number $1$
Dimension $5$
Determinant $16$
Level $8$

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Lattice Invariants

Dimension:$5$
Determinant:$16$
Level:$8$
Density:$0.0411233516712056609118103791662\dots$
Group order:$128$
Hermite number:$0.574349177498517503399313473389\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 4 q^{2} \) \(\mathstrut +\mathstrut 24 q^{3} \) \(\mathstrut +\mathstrut 42 q^{4} \) \(\mathstrut +\mathstrut 16 q^{5} \) \(\mathstrut +\mathstrut 24 q^{6} \) \(\mathstrut +\mathstrut 96 q^{7} \) \(\mathstrut +\mathstrut 104 q^{8} \) \(\mathstrut +\mathstrut 50 q^{9} \) \(\mathstrut +\mathstrut 56 q^{10} \) \(\mathstrut +\mathstrut 168 q^{11} \) \(\mathstrut +\mathstrut 208 q^{12} \) \(\mathstrut +\mathstrut 80 q^{13} \) \(\mathstrut +\mathstrut 80 q^{14} \) \(\mathstrut +\mathstrut 288 q^{15} \) \(\mathstrut +\mathstrut 346 q^{16} \) \(\mathstrut +\mathstrut 96 q^{17} \) \(\mathstrut +\mathstrut 124 q^{18} \) \(\mathstrut +\mathstrut 456 q^{19} \) \(\mathstrut +\mathstrut 368 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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