Properties

Label 5.16.32.1.1
Class number $1$
Dimension $5$
Determinant $16$
Level $32$

Downloads

Learn more

Lattice Invariants

Dimension:$5$
Determinant:$16$
Level:$32$
Density:$0.232628806654629317805252031205\dots$
Group order:$240$
Hermite number:$1.14869835499703500679862694678\dots$
Minimal vector length:$2$
Kissing number:$20$
Normalized minimal vectors: $(1, -1, 0, 0, 0)$, $(1, 0, -1, 0, 0)$, $(1, 0, 0, 0, 0)$, $(1, 0, 0, 1, 0)$, $(0, 1, -1, 0, 0)$, $(0, 1, 0, 0, 0)$, $(0, 1, 0, 1, 0)$, $(0, 0, 1, 0, 0)$, $(0, 0, 1, 1, 0)$, $(0, 0, 0, 1, 0)$ ...
Download the complete list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 20 q^{2} \) \(\mathstrut +\mathstrut 40 q^{4} \) \(\mathstrut +\mathstrut 120 q^{6} \) \(\mathstrut +\mathstrut 120 q^{8} \) \(\mathstrut +\mathstrut 280 q^{10} \) \(\mathstrut +\mathstrut 160 q^{12} \) \(\mathstrut +\mathstrut 400 q^{14} \) \(\mathstrut +\mathstrut 410 q^{16} \) \(\mathstrut +\mathstrut 620 q^{18} \) \(\mathstrut +\mathstrut 320 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 2 & 1 & 1 & -1 & -1 \\ 1 & 2 & 1 & -1 & -1 \\ 1 & 1 & 2 & -1 & -1 \\ -1 & -1 & -1 & 2 & 1 \\ -1 & -1 & -1 & 1 & 4 \end{array}\right)$

Genus Structure

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