Properties

Label 9.16777216.8.1.1
Class number $1$
Dimension $9$
Determinant $16777216$
Level $8$

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Lattice Invariants

Dimension:$9$
Determinant:$16777216$
Level:$8$
Density:$0.000805300025082692106782740845641\dots$
Group order:$11612160$
Hermite number:$0.629960524947436582383605303639\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(0, 1, 0, 0, 0, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 4 q^{5} \) \(\mathstrut +\mathstrut 116 q^{13} \) \(\mathstrut +\mathstrut 242 q^{16} \) \(\mathstrut +\mathstrut 480 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrrrrrr} 5 & -2 & 1 & -1 & 1 & 1 & 1 & 1 & -1 \\ -2 & 4 & -2 & 2 & -2 & -2 & -2 & -2 & 2 \\ 1 & -2 & 13 & -5 & 5 & -3 & -3 & -3 & 3 \\ -1 & 2 & -5 & 13 & -5 & -5 & -5 & -5 & 5 \\ 1 & -2 & 5 & -5 & 13 & 5 & -3 & 5 & -5 \\ 1 & -2 & -3 & -5 & 5 & 13 & 5 & 5 & -5 \\ 1 & -2 & -3 & -5 & -3 & 5 & 13 & 5 & -5 \\ 1 & -2 & -3 & -5 & 5 & 5 & 5 & 13 & -5 \\ -1 & 2 & 3 & 5 & -5 & -5 & -5 & -5 & 13 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrrrrrr} 4 & -2 & 2 & 2 & -2 & -2 & -2 & -2 & 2 \\ -2 & 5 & -1 & -1 & 1 & 1 & 1 & 1 & -1 \\ 2 & -1 & 13 & 5 & 3 & 3 & -5 & -5 & -3 \\ 2 & -1 & 5 & 13 & -5 & -5 & -5 & -5 & -3 \\ -2 & 1 & 3 & -5 & 13 & 5 & 5 & -3 & -5 \\ -2 & 1 & 3 & -5 & 5 & 13 & -3 & 5 & 3 \\ -2 & 1 & -5 & -5 & 5 & -3 & 13 & -3 & -5 \\ -2 & 1 & -5 & -5 & -3 & 5 & -3 & 13 & 3 \\ 2 & -1 & -3 & -3 & -5 & 3 & -5 & 3 & 13 \end{array}\right)$
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