Properties

Label 3.208.416.5.3
Class number 5
Dimension 3
Determinant 208
Level 416

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Lattice Invariants

Dimension:$3$
Determinant:$208$
Level:$416$
Label:$3.208.416.5.3$
Density:$0.102686168233423677485465537571\dots$
Group order:$4$
Hermite number:$0.337553190589581834018929384547\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 8 & 4 \\ 1 & 4 & 16 \end{array}\right)$

Genus Structure

Class number:$5$
 
Genus representatives: $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 8 & 4 \\ 1 & 4 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & -1 \\ 0 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 1 \\ 0 & 1 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -2 \\ -1 & 8 & -1 \\ -2 & -1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & 3 \\ 2 & 6 & 1 \\ 3 & 1 & 8 \end{array}\right)$
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Comments

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