Properties

Label 4.16.8.1.2
Class number $1$
Dimension $4$
Determinant $16$
Level $8$

Downloads

Learn more

Lattice Invariants

Dimension:$4$
Determinant:$16$
Level:$8$
Density:$0.308425137534042456838577843746\dots$
Group order:$64$
Hermite number:$1.00000000000000000000000000000\dots$
Minimal vector length:$2$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0, 0)$, $(0, 0, 1, 0)$
Download this list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{2} \) \(\mathstrut +\mathstrut 16 q^{3} \) \(\mathstrut +\mathstrut 8 q^{4} \) \(\mathstrut +\mathstrut 16 q^{6} \) \(\mathstrut +\mathstrut 32 q^{7} \) \(\mathstrut +\mathstrut 24 q^{8} \) \(\mathstrut +\mathstrut 24 q^{10} \) \(\mathstrut +\mathstrut 48 q^{11} \) \(\mathstrut +\mathstrut 32 q^{12} \) \(\mathstrut +\mathstrut 32 q^{14} \) \(\mathstrut +\mathstrut 96 q^{15} \) \(\mathstrut +\mathstrut 24 q^{16} \) \(\mathstrut +\mathstrut 52 q^{18} \) \(\mathstrut +\mathstrut 80 q^{19} \) \(\mathstrut +\mathstrut 48 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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