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Properties

Label 6.4.2.1.1
Class number $1$
Dimension $6$
Determinant $4$
Level $2$

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Lattice Invariants

Dimension:$6$
Determinant:$4$
Level:$2$
Density:$0.0403727560941403908534847852436\dots$
Group order:$9216$
Hermite number:$0.793700525984099737375852819636\dots$
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

\(1 \) \(\mathstrut +\mathstrut 4 q \) \(\mathstrut +\mathstrut 28 q^{2} \) \(\mathstrut +\mathstrut 96 q^{3} \) \(\mathstrut +\mathstrut 124 q^{4} \) \(\mathstrut +\mathstrut 104 q^{5} \) \(\mathstrut +\mathstrut 288 q^{6} \) \(\mathstrut +\mathstrut 576 q^{7} \) \(\mathstrut +\mathstrut 508 q^{8} \) \(\mathstrut +\mathstrut 292 q^{9} \) \(\mathstrut +\mathstrut 728 q^{10} \) \(\mathstrut +\mathstrut 1440 q^{11} \) \(\mathstrut +\mathstrut 1056 q^{12} \) \(\mathstrut +\mathstrut 680 q^{13} \) \(\mathstrut +\mathstrut 1728 q^{14} \) \(\mathstrut +\mathstrut 2496 q^{15} \) \(\mathstrut +\mathstrut 2044 q^{16} \) \(\mathstrut +\mathstrut 1160 q^{17} \) \(\mathstrut +\mathstrut 2044 q^{18} \) \(\mathstrut +\mathstrut 4320 q^{19} \) \(\mathstrut +\mathstrut 3224 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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