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Properties

Label 6.16.8.1.4
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:$512$
Hermite number:$0.629960524947436582383605303639\dots$
Minimal vector length:$1$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q \) \(\mathstrut +\mathstrut 8 q^{2} \) \(\mathstrut +\mathstrut 32 q^{3} \) \(\mathstrut +\mathstrut 92 q^{4} \) \(\mathstrut +\mathstrut 104 q^{5} \) \(\mathstrut +\mathstrut 64 q^{6} \) \(\mathstrut +\mathstrut 192 q^{7} \) \(\mathstrut +\mathstrut 380 q^{8} \) \(\mathstrut +\mathstrut 292 q^{9} \) \(\mathstrut +\mathstrut 208 q^{10} \) \(\mathstrut +\mathstrut 480 q^{11} \) \(\mathstrut +\mathstrut 800 q^{12} \) \(\mathstrut +\mathstrut 680 q^{13} \) \(\mathstrut +\mathstrut 384 q^{14} \) \(\mathstrut +\mathstrut 832 q^{15} \) \(\mathstrut +\mathstrut 1532 q^{16} \) \(\mathstrut +\mathstrut 1160 q^{17} \) \(\mathstrut +\mathstrut 584 q^{18} \) \(\mathstrut +\mathstrut 1440 q^{19} \) \(\mathstrut +\mathstrut 2392 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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