Properties

Label 7.64.4.1.1
Class number $1$
Dimension $7$
Determinant $64$
Level $4$

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Lattice Invariants

Dimension:$7$
Determinant:$64$
Level:$4$
Density:$0.00461402926790175895468397545642\dots$
Group order:$92160$
Hermite number:$0.552044756836906168824752693812\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 12 q^{2} \) \(\mathstrut +\mathstrut 24 q^{3} \) \(\mathstrut +\mathstrut 62 q^{4} \) \(\mathstrut +\mathstrut 120 q^{5} \) \(\mathstrut +\mathstrut 184 q^{6} \) \(\mathstrut +\mathstrut 320 q^{7} \) \(\mathstrut +\mathstrut 372 q^{8} \) \(\mathstrut +\mathstrut 506 q^{9} \) \(\mathstrut +\mathstrut 632 q^{10} \) \(\mathstrut +\mathstrut 648 q^{11} \) \(\mathstrut +\mathstrut 1048 q^{12} \) \(\mathstrut +\mathstrut 1208 q^{13} \) \(\mathstrut +\mathstrut 1584 q^{14} \) \(\mathstrut +\mathstrut 2240 q^{15} \) \(\mathstrut +\mathstrut 2110 q^{16} \) \(\mathstrut +\mathstrut 2544 q^{17} \) \(\mathstrut +\mathstrut 2820 q^{18} \) \(\mathstrut +\mathstrut 2376 q^{19} \) \(\mathstrut +\mathstrut 3720 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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