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Properties

Label 6.2.4.1.1
Class number $1$
Dimension $6$
Determinant $2$
Level $4$

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Lattice Invariants

Dimension:$6$
Determinant:$2$
Level:$4$
Density:$0.0570956992187143648821809232224\dots$
Group order:$7680$
Hermite number:$0.890898718140339304740226205591\dots$
Minimal vector length:$1$
Kissing number:$10$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0)$, $(0, 0, 1, 0, 0, 0)$, $(0, 0, 0, 1, 0, 0)$, $(0, 0, 0, 0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 10 q \) \(\mathstrut +\mathstrut 42 q^{2} \) \(\mathstrut +\mathstrut 100 q^{3} \) \(\mathstrut +\mathstrut 170 q^{4} \) \(\mathstrut +\mathstrut 272 q^{5} \) \(\mathstrut +\mathstrut 420 q^{6} \) \(\mathstrut +\mathstrut 544 q^{7} \) \(\mathstrut +\mathstrut 682 q^{8} \) \(\mathstrut +\mathstrut 910 q^{9} \) \(\mathstrut +\mathstrut 1040 q^{10} \) \(\mathstrut +\mathstrut 1220 q^{11} \) \(\mathstrut +\mathstrut 1700 q^{12} \) \(\mathstrut +\mathstrut 1904 q^{13} \) \(\mathstrut +\mathstrut 2080 q^{14} \) \(\mathstrut +\mathstrut 2720 q^{15} \) \(\mathstrut +\mathstrut 2730 q^{16} \) \(\mathstrut +\mathstrut 2900 q^{17} \) \(\mathstrut +\mathstrut 3822 q^{18} \) \(\mathstrut +\mathstrut 3620 q^{19} \) \(\mathstrut +\mathstrut 4112 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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