# Properties

 Label 6.16.8.1.1 Class number 1 Dimension 6 Determinant 16 Level 8

## Lattice Invariants

Dimension:$6$
Determinant:$16$
Level:$8$
Label:$6.16.8.1.1$
Density:$0.0201863780470701954267423926218\dots$
Group order:$1536$
Hermite number:$0.629960524947436582383605303639\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0)$
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## Theta Series

$$1$$ $$\mathstrut +\mathstrut 2q$$ $$\mathstrut +\mathstrut 8q^{2}$$ $$\mathstrut +\mathstrut 48q^{3}$$ $$\mathstrut +\mathstrut 92q^{4}$$ $$\mathstrut +\mathstrut 52q^{5}$$ $$\mathstrut +\mathstrut 64q^{6}$$ $$\mathstrut +\mathstrut 288q^{7}$$ $$\mathstrut +\mathstrut 380q^{8}$$ $$\mathstrut +\mathstrut 146q^{9}$$ $$\mathstrut +\mathstrut 208q^{10}$$ $$\mathstrut +\mathstrut 720q^{11}$$ $$\mathstrut +\mathstrut 800q^{12}$$ $$\mathstrut +\mathstrut 340q^{13}$$ $$\mathstrut +\mathstrut 384q^{14}$$ $$\mathstrut +\mathstrut 1248q^{15}$$ $$\mathstrut +\mathstrut 1532q^{16}$$ $$\mathstrut +\mathstrut 580q^{17}$$ $$\mathstrut +\mathstrut 584q^{18}$$ $$\mathstrut +\mathstrut 2160q^{19}$$ $$\mathstrut +\mathstrut 2392q^{20}$$ $$\mathstrut +\mathstrut O(q^{21})$$

## Gram Matrix

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

## Genus Structure

 Class number: $1$ Genus representatives: $\left(\begin{array}{rrrrrr} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 1 & -1 \\ 0 & 0 & 2 & 0 & -1 & 1 \\ 0 & 0 & 0 & 2 & 1 & -1 \\ 0 & 1 & -1 & 1 & 3 & -2 \\ 0 & -1 & 1 & -1 & -2 & 3 \end{array}\right)$ Download this matrix for gp, magma, sage