# Properties

 Name A14 Label 14.15.15.9.1 Class number 9 Dimension 14 Determinant 15 Level 15

## Lattice Invariants

Dimension:$14$
Determinant:$15$
Level:$15$
Label:$14.15.15.9.1$
Density:$0.00120882371980846561842974135302\dots$
Group order:$2615348736000$
Hermite number:$1.64825149055779494991198141680\dots$
Minimal vector length:$2$
Kissing number:$210$
Normalized minimal vectors: $(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0)$ ...

## Theta Series

$$1$$ $$\mathstrut +\mathstrut 210q$$ $$\mathstrut +\mathstrut 8190q^{2}$$ $$\mathstrut +\mathstrut 102830q^{3}$$ $$\mathstrut +\mathstrut 570780q^{4}$$ $$\mathstrut +\mathstrut 2140866q^{5}$$ $$\mathstrut +\mathstrut 6527430q^{6}$$ $$\mathstrut +\mathstrut 16213080q^{7}$$ $$\mathstrut +\mathstrut 36584730q^{8}$$ $$\mathstrut +\mathstrut 73035900q^{9}$$ $$\mathstrut +\mathstrut 139912500q^{10}$$ $$\mathstrut +\mathstrut 243455940q^{11}$$ $$\mathstrut +\mathstrut 417269580q^{12}$$ $$\mathstrut +\mathstrut 664812330q^{13}$$ $$\mathstrut +\mathstrut 1050179130q^{14}$$ $$\mathstrut +\mathstrut 1567036926q^{15}$$ $$\mathstrut +\mathstrut 2347625490q^{16}$$ $$\mathstrut +\mathstrut 3315827970q^{17}$$ $$\mathstrut +\mathstrut 4752128290q^{18}$$ $$\mathstrut +\mathstrut 6479581290q^{19}$$ $$\mathstrut +\mathstrut 8930870676q^{20}$$ $$\mathstrut +\mathstrut O(q^{21})$$

## Gram Matrix

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

## Genus Structure

 Class number: $9$ Genus representatives: $\left(\begin{array}{rrrrrrrrrrrrrr} 2 & 0 & -1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 1 & 1 & -1 & -1 \\ 0 & 2 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 \\ -1 & 0 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 2 & 1 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 1 & 1 & 2 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & -1 & 0 & 0 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 2 & 1 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 2 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 2 & -1 & -1 & 1 & 1 \\ 1 & 0 & -1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 2 & 1 & -1 & -1 \\ 1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 2 & -1 & -1 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 2 & 1 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 2 \end{array}\right)$, $\left(\begin{array}{rrrrrrrrrrrrrr} 2 & 1 & 1 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ 1 & 2 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ 1 & 0 & 2 & -1 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ 0 & 0 & -1 & 2 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & -1 & -1 & 1 & 0 & -1 \\ 1 & 1 & 1 & 0 & 0 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ -1 & -1 & -1 & 1 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 1 & -1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & -1 & 0 & 0 & 0 & -1 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & -1 & 2 & 1 & -1 & 0 & 1 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 1 & 2 & -1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 & -1 & 2 & 0 & -1 \\ -1 & -1 & -1 & 1 & 0 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 2 & -1 \\ 1 & 1 & 1 & -1 & -1 & 1 & -1 & 0 & -1 & 1 & 1 & -1 & -1 & 4 \end{array}\right)$ ... Download the complete list for gp, magma, sage