↑

Properties

Label 3.14.28.1.1
Class number $1$
Dimension $3$
Determinant $14$
Level $28$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$14$
Level:$28$
Density:$0.395803470574575316261541765983\dots$
Group order:$8$
Hermite number:$0.829826533366243441000991496950\dots$
Minimal vector length:$2$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
Download this list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{2} \) \(\mathstrut +\mathstrut 8 q^{4} \) \(\mathstrut +\mathstrut 8 q^{6} \) \(\mathstrut +\mathstrut 8 q^{8} \) \(\mathstrut +\mathstrut 16 q^{10} \) \(\mathstrut +\mathstrut 8 q^{12} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 24 q^{16} \) \(\mathstrut +\mathstrut 20 q^{18} \) \(\mathstrut +\mathstrut 8 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 4 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 4 \end{array}\right)$
Download this matrix for gp, magma, sage

Comments

This is the digonal C Bravais lattice of even holotype. Also called the orthorhombic C Bravais lattice..