↑

Properties

Label 7.32.16.1.1
Class number $1$
Dimension $7$
Determinant $32$
Level $16$

Downloads

Learn more

Lattice Invariants

Dimension:$7$
Determinant:$32$
Level:$16$
Density:$0.0738244682864281432749436073025\dots$
Group order:$2880$
Hermite number:$1.21901365420447544091169100259\dots$
Minimal vector length:$2$
Kissing number:$32$
Normalized minimal vectors: $(1, -1, 0, 0, 0, 0, 0)$, $(1, 0, -1, 0, 0, 0, 0)$, $(1, 0, 0, 0, -1, 0, 0)$, $(1, 0, 0, 0, 0, 0, 0)$, $(1, 0, 0, 1, 0, 0, 0)$, $(0, 1, -1, 0, 0, 0, 0)$, $(0, 1, 0, 0, -1, 0, 0)$, $(0, 1, 0, 0, 0, 0, 0)$, $(0, 1, 0, 1, 0, 0, 0)$, $(0, 0, 1, 0, -1, 0, 0)$, $(0, 0, 1, 0, 0, 0, 0)$, $(0, 0, 1, 1, 0, 0, 0)$, $(0, 0, 0, 1, 0, 0, 0)$, $(0, 0, 0, 1, 1, 0, 0)$, $(0, 0, 0, 0, 1, 0, 0)$ ...
Download the complete list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 32 q^{2} \) \(\mathstrut +\mathstrut 180 q^{4} \) \(\mathstrut +\mathstrut 512 q^{6} \) \(\mathstrut +\mathstrut 1086 q^{8} \) \(\mathstrut +\mathstrut 1920 q^{10} \) \(\mathstrut +\mathstrut 2760 q^{12} \) \(\mathstrut +\mathstrut 4096 q^{14} \) \(\mathstrut +\mathstrut 6516 q^{16} \) \(\mathstrut +\mathstrut 8096 q^{18} \) \(\mathstrut +\mathstrut 9480 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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