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Properties

Label 3.66.132.3.3
Class number $3$
Dimension $3$
Determinant $66$
Level $132$

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Lattice Invariants

Dimension:$3$
Determinant:$66$
Level:$132$
Density:$0.515604431706781356122931955656\dots$
Group order:$4$
Hermite number:$0.989795206319905505771296988096\dots$
Minimal vector length:$4$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 8 q^{6} \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 4 q^{12} \) \(\mathstrut +\mathstrut 8 q^{14} \) \(\mathstrut +\mathstrut 8 q^{16} \) \(\mathstrut +\mathstrut 10 q^{18} \) \(\mathstrut +\mathstrut 4 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 4 & 2 \\ 2 & 2 & 6 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$3$
 
$\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 4 & 2 \\ 2 & 2 & 6 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 2 & 0 \\ 0 & 0 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 6 & 0 \\ 0 & 0 & 6 \end{array}\right)$
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Comments

This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.