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Properties

Label 6.48.6.1.3
Class number $1$
Dimension $6$
Determinant $48$
Level $6$

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Lattice Invariants

Dimension:$6$
Determinant:$48$
Level:$6$
Density:$0.0116546107994395293613586737087\dots$
Group order:$2880$
Hermite number:$0.524557531710824092763760744844\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 20 q^{3} \) \(\mathstrut +\mathstrut 72 q^{4} \) \(\mathstrut +\mathstrut 60 q^{5} \) \(\mathstrut +\mathstrut 100 q^{7} \) \(\mathstrut +\mathstrut 270 q^{8} \) \(\mathstrut +\mathstrut 182 q^{9} \) \(\mathstrut +\mathstrut 300 q^{11} \) \(\mathstrut +\mathstrut 720 q^{12} \) \(\mathstrut +\mathstrut 340 q^{13} \) \(\mathstrut +\mathstrut 492 q^{15} \) \(\mathstrut +\mathstrut 936 q^{16} \) \(\mathstrut +\mathstrut 720 q^{17} \) \(\mathstrut +\mathstrut 724 q^{19} \) \(\mathstrut +\mathstrut 2160 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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