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Properties

Label 6.16.8.1.5
Class number $1$
Dimension $6$
Determinant $16$
Level $8$

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Lattice Invariants

Dimension:$6$
Determinant:$16$
Level:$8$
Density:$0.161491024376561563413939140974\dots$
Group order:$7680$
Hermite number:$1.25992104989487316476721060728\dots$
Minimal vector length:$2$
Kissing number:$40$
Normalized minimal vectors: $(1, -1, 0, 0, 0, 0)$, $(1, -1, 0, 0, 1, 0)$, $(1, -1, 0, 1, 1, 0)$, $(1, -1, 1, 0, 1, 0)$, $(1, 0, -1, 0, 0, 0)$, $(1, 0, 0, -1, 0, 0)$, $(1, 0, 0, 0, 0, 0)$, $(1, 0, 0, 0, 1, 0)$, $(0, 1, -1, -1, -1, 0)$, $(0, 1, -1, 0, -1, 0)$, $(0, 1, -1, 0, 0, 0)$, $(0, 1, 0, -1, -1, 0)$, $(0, 1, 0, -1, 0, 0)$, $(0, 1, 0, 0, 0, 0)$, $(0, 0, 1, -1, 0, 0)$, $(0, 0, 1, 0, 0, 0)$, $(0, 0, 1, 0, 1, 0)$, $(0, 0, 0, 1, 0, 0)$ ...
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 40 q^{2} \) \(\mathstrut +\mathstrut 92 q^{4} \) \(\mathstrut +\mathstrut 320 q^{6} \) \(\mathstrut +\mathstrut 380 q^{8} \) \(\mathstrut +\mathstrut 1040 q^{10} \) \(\mathstrut +\mathstrut 800 q^{12} \) \(\mathstrut +\mathstrut 1920 q^{14} \) \(\mathstrut +\mathstrut 1532 q^{16} \) \(\mathstrut +\mathstrut 2920 q^{18} \) \(\mathstrut +\mathstrut 2392 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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