Properties

Label 3.198.396.5.1
Class number 5
Dimension 3
Determinant 198
Level 396

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Lattice Invariants

Dimension:$3$
Determinant:$198$
Level:$396$
Label:$3.198.396.5.1$
Density:$0.105247313899942548492181597980\dots$
Group order:$8$
Hermite number:$0.343142832800059541532272933723\dots$
Minimal vector length:$2$
Kissing Number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 6 & 0 \\ 0 & 0 & 18 \end{array}\right)$

Genus Structure

Class number:$5$
 
Genus representatives: $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 6 & 0 \\ 0 & 0 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & -1 \\ 0 & -1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 10 & -4 \\ 1 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & -1 \\ -3 & 6 & -1 \\ -1 & -1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 2 \\ -1 & 6 & 1 \\ 2 & 1 & 10 \end{array}\right)$
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Comments

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