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Properties

Label 5.27.6.1.1
Class number $1$
Dimension $5$
Determinant $27$
Level $6$

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Lattice Invariants

Dimension:$5$
Determinant:$27$
Level:$6$
Density:$0.0316567708764669798421166163915\dots$
Group order:$192$
Hermite number:$0.517281857971786558091115045172\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 16 q^{3} \) \(\mathstrut +\mathstrut 10 q^{4} \) \(\mathstrut +\mathstrut 24 q^{5} \) \(\mathstrut +\mathstrut 70 q^{6} \) \(\mathstrut +\mathstrut 28 q^{7} \) \(\mathstrut +\mathstrut 30 q^{8} \) \(\mathstrut +\mathstrut 134 q^{9} \) \(\mathstrut +\mathstrut 68 q^{10} \) \(\mathstrut +\mathstrut 36 q^{11} \) \(\mathstrut +\mathstrut 144 q^{12} \) \(\mathstrut +\mathstrut 104 q^{13} \) \(\mathstrut +\mathstrut 108 q^{14} \) \(\mathstrut +\mathstrut 196 q^{15} \) \(\mathstrut +\mathstrut 74 q^{16} \) \(\mathstrut +\mathstrut 156 q^{17} \) \(\mathstrut +\mathstrut 402 q^{18} \) \(\mathstrut +\mathstrut 84 q^{19} \) \(\mathstrut +\mathstrut 120 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 2 & 1 & 0 & 0 \\ 0 & 1 & 2 & 0 & 0 \\ 0 & 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 2 & 1 & 0 & 0 \\ 0 & 1 & 2 & 0 & 0 \\ 0 & 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right)$
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