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Properties

Label 7.2.4.1.1
Class number $1$
Dimension $7$
Determinant $2$
Level $4$

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Lattice Invariants

Dimension:$7$
Determinant:$2$
Level:$4$
Density:$0.0261008910714122810889969934731\dots$
Group order:$92160$
Hermite number:$0.905723664263906671594172873215\dots$
Minimal vector length:$1$
Kissing number:$12$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0, 0)$, $(0, 0, 1, 0, 0, 0, 0)$, $(0, 0, 0, 1, 0, 0, 0)$, $(0, 0, 0, 0, 1, 0, 0)$, $(0, 0, 0, 0, 0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 12 q \) \(\mathstrut +\mathstrut 62 q^{2} \) \(\mathstrut +\mathstrut 184 q^{3} \) \(\mathstrut +\mathstrut 372 q^{4} \) \(\mathstrut +\mathstrut 632 q^{5} \) \(\mathstrut +\mathstrut 1048 q^{6} \) \(\mathstrut +\mathstrut 1584 q^{7} \) \(\mathstrut +\mathstrut 2110 q^{8} \) \(\mathstrut +\mathstrut 2820 q^{9} \) \(\mathstrut +\mathstrut 3720 q^{10} \) \(\mathstrut +\mathstrut 4472 q^{11} \) \(\mathstrut +\mathstrut 5704 q^{12} \) \(\mathstrut +\mathstrut 7464 q^{13} \) \(\mathstrut +\mathstrut 8512 q^{14} \) \(\mathstrut +\mathstrut 10160 q^{15} \) \(\mathstrut +\mathstrut 12660 q^{16} \) \(\mathstrut +\mathstrut 13552 q^{17} \) \(\mathstrut +\mathstrut 15686 q^{18} \) \(\mathstrut +\mathstrut 18984 q^{19} \) \(\mathstrut +\mathstrut 19592 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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