Properties

Name A3*, D3*
Label 3.128.8.1.1
Class number 1
Dimension 3
Determinant 128
Level 8

Learn more about

Lattice Invariants

Dimension:$3$
Determinant:$128$
Level:$8$
Label:$3.128.8.1.1$
Density:$0.680174761587831693972779346617\dots$
Group order:$48$
Hermite number:$1.19055078897614960606377922945\dots$
Minimal vector length:$6$
Kissing Number:$8$
Normalized minimal vectors: $(1, 0, 0)$, $(1, 1, 1)$, $(0, 1, 0)$, $(0, 0, 1)$
Download this list for gp, magma, sage

Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 6 & -2 & -2 \\ -2 & 6 & -2 \\ -2 & -2 & 6 \end{array}\right)$

Genus Structure

Class number:$1$
 
Genus representatives: $\left(\begin{array}{rrr} 6 & -2 & -2 \\ -2 & 6 & -2 \\ -2 & -2 & 6 \end{array}\right)$
Download this matrix for gp, magma, sage

Comments

This integral lattice is the A3*, D3* lattice.

This is the cubic I Bravais lattice of even holotype. This is the body centered cubic lattice.