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Properties

Label 6.3.6.1.2
Class number $1$
Dimension $6$
Determinant $3$
Level $6$

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Lattice Invariants

Dimension:$6$
Determinant:$3$
Level:$6$
Density:$0.0466184431977581174454346948350\dots$
Group order:$4608$
Hermite number:$0.832683177655604319608786362509\dots$
Minimal vector length:$1$
Kissing number:$8$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0)$, $(0, 0, 1, 0, 0, 0)$, $(0, 0, 0, 0, 0, 1)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 8 q \) \(\mathstrut +\mathstrut 30 q^{2} \) \(\mathstrut +\mathstrut 80 q^{3} \) \(\mathstrut +\mathstrut 168 q^{4} \) \(\mathstrut +\mathstrut 240 q^{5} \) \(\mathstrut +\mathstrut 246 q^{6} \) \(\mathstrut +\mathstrut 400 q^{7} \) \(\mathstrut +\mathstrut 750 q^{8} \) \(\mathstrut +\mathstrut 728 q^{9} \) \(\mathstrut +\mathstrut 576 q^{10} \) \(\mathstrut +\mathstrut 1200 q^{11} \) \(\mathstrut +\mathstrut 1680 q^{12} \) \(\mathstrut +\mathstrut 1360 q^{13} \) \(\mathstrut +\mathstrut 1500 q^{14} \) \(\mathstrut +\mathstrut 1968 q^{15} \) \(\mathstrut +\mathstrut 2472 q^{16} \) \(\mathstrut +\mathstrut 2880 q^{17} \) \(\mathstrut +\mathstrut 2190 q^{18} \) \(\mathstrut +\mathstrut 2896 q^{19} \) \(\mathstrut +\mathstrut 5040 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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