Properties

Label 5.20.40.1.1
Class number $1$
Dimension $5$
Determinant $20$
Level $40$

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Lattice Invariants

Dimension:$5$
Determinant:$20$
Level:$40$
Density:$0.208069530081762638801450214161\dots$
Group order:$192$
Hermite number:$1.09856054330611775221957169077\dots$
Minimal vector length:$2$
Kissing number:$14$
Normalized minimal vectors: $(1, -1, 0, 0, 0)$, $(1, -1, 1, 0, 0)$, $(1, 0, 0, 0, 0)$, $(1, 0, 1, 0, 0)$, $(0, 1, 0, 0, 0)$, $(0, 0, 1, 0, 0)$, $(0, 0, 0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 14 q^{2} \) \(\mathstrut +\mathstrut 54 q^{4} \) \(\mathstrut +\mathstrut 68 q^{6} \) \(\mathstrut +\mathstrut 182 q^{8} \) \(\mathstrut +\mathstrut 106 q^{10} \) \(\mathstrut +\mathstrut 312 q^{12} \) \(\mathstrut +\mathstrut 268 q^{14} \) \(\mathstrut +\mathstrut 438 q^{16} \) \(\mathstrut +\mathstrut 350 q^{18} \) \(\mathstrut +\mathstrut 664 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 2 & 1 & -1 & 0 & -1 \\ 1 & 2 & 0 & 0 & -1 \\ -1 & 0 & 2 & 0 & 1 \\ 0 & 0 & 0 & 2 & -1 \\ -1 & -1 & 1 & -1 & 4 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 2 & 1 & -1 & 0 & -1 \\ 1 & 2 & 0 & 0 & -1 \\ -1 & 0 & 2 & 0 & 1 \\ 0 & 0 & 0 & 2 & -1 \\ -1 & -1 & 1 & -1 & 4 \end{array}\right)$
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