↑

Properties

Label 5.32.8.1.2
Class number $1$
Dimension $5$
Determinant $32$
Level $8$

Downloads

Learn more

Lattice Invariants

Dimension:$5$
Determinant:$32$
Level:$8$
Density:$0.164493406684822643647241516664\dots$
Group order:$192$
Hermite number:$1.00000000000000000000000000000\dots$
Minimal vector length:$2$
Kissing number:$14$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$, $(0, 1, -1, 0, 0)$, $(0, 1, 0, -1, 0)$, $(0, 1, 0, 0, 0)$, $(0, 0, 1, -1, 0)$, $(0, 0, 1, 0, 0)$, $(0, 0, 0, 1, 0)$
Download this list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 14 q^{2} \) \(\mathstrut +\mathstrut 32 q^{4} \) \(\mathstrut +\mathstrut 64 q^{6} \) \(\mathstrut +\mathstrut 122 q^{8} \) \(\mathstrut +\mathstrut 144 q^{10} \) \(\mathstrut +\mathstrut 192 q^{12} \) \(\mathstrut +\mathstrut 256 q^{14} \) \(\mathstrut +\mathstrut 264 q^{16} \) \(\mathstrut +\mathstrut 350 q^{18} \) \(\mathstrut +\mathstrut 448 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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