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Properties

Label 6.8.16.1.1
Class number $1$
Dimension $6$
Determinant $8$
Level $16$

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Lattice Invariants

Dimension:$6$
Determinant:$8$
Level:$16$
Density:$0.0285478496093571824410904616112\dots$
Group order:$768$
Hermite number:$0.707106781186547524400844362105\dots$
Minimal vector length:$1$
Kissing number:$6$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0)$, $(0, 0, 1, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q \) \(\mathstrut +\mathstrut 16 q^{2} \) \(\mathstrut +\mathstrut 40 q^{3} \) \(\mathstrut +\mathstrut 106 q^{4} \) \(\mathstrut +\mathstrut 176 q^{5} \) \(\mathstrut +\mathstrut 160 q^{6} \) \(\mathstrut +\mathstrut 192 q^{7} \) \(\mathstrut +\mathstrut 426 q^{8} \) \(\mathstrut +\mathstrut 546 q^{9} \) \(\mathstrut +\mathstrut 384 q^{10} \) \(\mathstrut +\mathstrut 488 q^{11} \) \(\mathstrut +\mathstrut 1060 q^{12} \) \(\mathstrut +\mathstrut 1232 q^{13} \) \(\mathstrut +\mathstrut 768 q^{14} \) \(\mathstrut +\mathstrut 960 q^{15} \) \(\mathstrut +\mathstrut 1706 q^{16} \) \(\mathstrut +\mathstrut 1740 q^{17} \) \(\mathstrut +\mathstrut 1456 q^{18} \) \(\mathstrut +\mathstrut 1448 q^{19} \) \(\mathstrut +\mathstrut 2576 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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