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Properties

Label 7.320.10.1.1
Class number $1$
Dimension $7$
Determinant $320$
Level $10$

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Lattice Invariants

Dimension:$7$
Determinant:$320$
Level:$10$
Density:$0.0964983159728844068221463957339\dots$
Group order:$46080$
Hermite number:$1.31595999318561227299141258835\dots$
Minimal vector length:$3$
Kissing number:$32$
Normalized minimal vectors: $(1, -1, -1, 1, 0, 1, 0)$, $(1, -1, 0, 0, 0, 1, 0)$, $(1, -1, 0, 0, 1, 0, 0)$, $(1, -1, 0, 1, 0, 0, 0)$, $(1, 0, -1, 0, 0, 1, 0)$, $(1, 0, -1, 1, -1, 1, 0)$, $(1, 0, -1, 1, 0, 0, 0)$, $(1, 0, 0, 0, 0, 0, 0)$, $(0, 1, -1, 0, -1, 0, 0)$, $(0, 1, 0, 0, 0, 0, 0)$, $(0, 0, 1, -1, 1, 0, 0)$, $(0, 0, 1, 0, 0, 0, 0)$, $(0, 0, 1, 0, 1, -1, 0)$, $(0, 0, 0, 1, 0, 0, 0)$, $(0, 0, 0, 0, 1, 0, 0)$ ...
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 32 q^{3} \) \(\mathstrut +\mathstrut 60 q^{4} \) \(\mathstrut +\mathstrut 216 q^{7} \) \(\mathstrut +\mathstrut 316 q^{8} \) \(\mathstrut +\mathstrut 800 q^{11} \) \(\mathstrut +\mathstrut 928 q^{12} \) \(\mathstrut +\mathstrut 1456 q^{15} \) \(\mathstrut +\mathstrut 1980 q^{16} \) \(\mathstrut +\mathstrut 3360 q^{19} \) \(\mathstrut +\mathstrut 3226 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrrrr} 3 & 1 & 1 & -1 & -1 & -1 & -1 \\ 1 & 3 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 3 & 1 & -1 & 1 & -1 \\ -1 & 1 & 1 & 3 & 1 & 1 & 1 \\ -1 & 1 & -1 & 1 & 3 & 1 & 1 \\ -1 & 1 & 1 & 1 & 1 & 3 & 1 \\ -1 & 1 & -1 & 1 & 1 & 1 & 7 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrrrr} 3 & -1 & 1 & 1 & -1 & -1 & -1 \\ -1 & 3 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 3 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 3 & -1 & 1 & -1 \\ -1 & 1 & 1 & -1 & 3 & 1 & 1 \\ -1 & 1 & 1 & 1 & 1 & 3 & 1 \\ -1 & 1 & 1 & -1 & 1 & 1 & 7 \end{array}\right)$
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