Properties

Label 3.16.16.1.2
Class number $1$
Dimension $3$
Determinant $16$
Level $16$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$16$
Level:$16$
Density:$0.370240244846530520584656749171\dots$
Group order:$8$
Hermite number:$0.793700525984099737375852819636\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
Download this vector for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 4 q^{3} \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 8 q^{5} \) \(\mathstrut +\mathstrut 4 q^{6} \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 12 q^{11} \) \(\mathstrut +\mathstrut 8 q^{12} \) \(\mathstrut +\mathstrut 8 q^{13} \) \(\mathstrut +\mathstrut 8 q^{14} \) \(\mathstrut +\mathstrut 6 q^{16} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut 12 q^{19} \) \(\mathstrut +\mathstrut 8 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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