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Properties

Label 7.1.2.1.1
Class number $1$
Dimension $7$
Determinant $1$
Level $2$

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Lattice Invariants

Dimension:$7$
Determinant:$1$
Level:$2$
Density:$0.0369122341432140716374718036513\dots$
Group order:$645120$
Hermite number:$1.00000000000000000000000000000\dots$
Minimal vector length:$1$
Kissing number:$14$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0, 0)$, $(0, 0, 1, 0, 0, 0, 0)$, $(0, 0, 0, 1, 0, 0, 0)$, $(0, 0, 0, 0, 1, 0, 0)$, $(0, 0, 0, 0, 0, 1, 0)$, $(0, 0, 0, 0, 0, 0, 1)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 14 q \) \(\mathstrut +\mathstrut 84 q^{2} \) \(\mathstrut +\mathstrut 280 q^{3} \) \(\mathstrut +\mathstrut 574 q^{4} \) \(\mathstrut +\mathstrut 840 q^{5} \) \(\mathstrut +\mathstrut 1288 q^{6} \) \(\mathstrut +\mathstrut 2368 q^{7} \) \(\mathstrut +\mathstrut 3444 q^{8} \) \(\mathstrut +\mathstrut 3542 q^{9} \) \(\mathstrut +\mathstrut 4424 q^{10} \) \(\mathstrut +\mathstrut 7560 q^{11} \) \(\mathstrut +\mathstrut 9240 q^{12} \) \(\mathstrut +\mathstrut 8456 q^{13} \) \(\mathstrut +\mathstrut 11088 q^{14} \) \(\mathstrut +\mathstrut 16576 q^{15} \) \(\mathstrut +\mathstrut 18494 q^{16} \) \(\mathstrut +\mathstrut 17808 q^{17} \) \(\mathstrut +\mathstrut 19740 q^{18} \) \(\mathstrut +\mathstrut 27720 q^{19} \) \(\mathstrut +\mathstrut 34440 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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