Properties

Label 6.16.8.1.1
Class number 1
Dimension 6
Determinant 16
Level 8

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Lattice Invariants

Dimension:$6$
Determinant:$16$
Level:$8$
Label:$6.16.8.1.1$
Density:$0.0201863780470701954267423926218\dots$
Group order:$1536$
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

\(1 \) \(\mathstrut +\mathstrut 2q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 48q^{3} \) \(\mathstrut +\mathstrut 92q^{4} \) \(\mathstrut +\mathstrut 52q^{5} \) \(\mathstrut +\mathstrut 64q^{6} \) \(\mathstrut +\mathstrut 288q^{7} \) \(\mathstrut +\mathstrut 380q^{8} \) \(\mathstrut +\mathstrut 146q^{9} \) \(\mathstrut +\mathstrut 208q^{10} \) \(\mathstrut +\mathstrut 720q^{11} \) \(\mathstrut +\mathstrut 800q^{12} \) \(\mathstrut +\mathstrut 340q^{13} \) \(\mathstrut +\mathstrut 384q^{14} \) \(\mathstrut +\mathstrut 1248q^{15} \) \(\mathstrut +\mathstrut 1532q^{16} \) \(\mathstrut +\mathstrut 580q^{17} \) \(\mathstrut +\mathstrut 584q^{18} \) \(\mathstrut +\mathstrut 2160q^{19} \) \(\mathstrut +\mathstrut 2392q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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