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Properties

Label 6.16.8.1.2
Class number $1$
Dimension $6$
Determinant $16$
Level $8$

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Lattice Invariants

Dimension:$6$
Determinant:$16$
Level:$8$
Density:$0.0201863780470701954267423926218\dots$
Group order:$4608$
Hermite number:$0.629960524947436582383605303639\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 24 q^{2} \) \(\mathstrut +\mathstrut 48 q^{3} \) \(\mathstrut +\mathstrut 28 q^{4} \) \(\mathstrut +\mathstrut 52 q^{5} \) \(\mathstrut +\mathstrut 192 q^{6} \) \(\mathstrut +\mathstrut 288 q^{7} \) \(\mathstrut +\mathstrut 124 q^{8} \) \(\mathstrut +\mathstrut 146 q^{9} \) \(\mathstrut +\mathstrut 624 q^{10} \) \(\mathstrut +\mathstrut 720 q^{11} \) \(\mathstrut +\mathstrut 288 q^{12} \) \(\mathstrut +\mathstrut 340 q^{13} \) \(\mathstrut +\mathstrut 1152 q^{14} \) \(\mathstrut +\mathstrut 1248 q^{15} \) \(\mathstrut +\mathstrut 508 q^{16} \) \(\mathstrut +\mathstrut 580 q^{17} \) \(\mathstrut +\mathstrut 1752 q^{18} \) \(\mathstrut +\mathstrut 2160 q^{19} \) \(\mathstrut +\mathstrut 728 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrrr} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 2 & 1 & -1 & -1 & 0 \\ 0 & 1 & 2 & 0 & 0 & 0 \\ 0 & -1 & 0 & 2 & 0 & 0 \\ 0 & -1 & 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 4 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrrr} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 2 & 1 & -1 & -1 & 0 \\ 0 & 1 & 2 & 0 & 0 & 0 \\ 0 & -1 & 0 & 2 & 0 & 0 \\ 0 & -1 & 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 4 \end{array}\right)$
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