Properties

Label 3.13.26.2.1
Class number $2$
Dimension $3$
Determinant $13$
Level $26$

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Lattice Invariants

Dimension:$3$
Determinant:$13$
Level:$26$
Density:$0.410744672933694709941862150283\dots$
Group order:$4$
Hermite number:$0.850580740565980329457283811243\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 6 q^{3} \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 4 q^{5} \) \(\mathstrut +\mathstrut 4 q^{7} \) \(\mathstrut +\mathstrut 10 q^{8} \) \(\mathstrut +\mathstrut 2 q^{9} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 12 q^{11} \) \(\mathstrut +\mathstrut 10 q^{12} \) \(\mathstrut +\mathstrut 6 q^{14} \) \(\mathstrut +\mathstrut 8 q^{15} \) \(\mathstrut +\mathstrut 8 q^{16} \) \(\mathstrut +\mathstrut 6 q^{17} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut 8 q^{19} \) \(\mathstrut +\mathstrut 12 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

Genus representatives:
Class number:$2$
 
$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 3 & 1 \\ 0 & 1 & 3 \end{array}\right)$, $\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 7 \end{array}\right)$
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Comments

This is the monoclinic C Bravais lattice of classical holotype.