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Properties

Label 3.15.30.1.1
Class number $1$
Dimension $3$
Determinant $15$
Level $30$

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Lattice Invariants

Dimension:$3$
Determinant:$15$
Level:$30$
Density:$0.382382480636365096122443120483\dots$
Group order:$8$
Hermite number:$0.810960266076453357986459333032\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 6 q^{3} \) \(\mathstrut +\mathstrut 4 q^{5} \) \(\mathstrut +\mathstrut 8 q^{6} \) \(\mathstrut +\mathstrut 4 q^{7} \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 10 q^{10} \) \(\mathstrut +\mathstrut 4 q^{11} \) \(\mathstrut +\mathstrut 6 q^{12} \) \(\mathstrut +\mathstrut 4 q^{13} \) \(\mathstrut +\mathstrut 4 q^{14} \) \(\mathstrut +\mathstrut 20 q^{15} \) \(\mathstrut +\mathstrut 14 q^{18} \) \(\mathstrut +\mathstrut 8 q^{19} \) \(\mathstrut +\mathstrut 4 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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