↑

Properties

Label 3.14.28.1.2
Class number $1$
Dimension $3$
Determinant $14$
Level $28$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$14$
Level:$28$
Density:$0.139937659030226164954352612261\dots$
Group order:$4$
Hermite number:$0.414913266683121720500495748475\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
Download this vector for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q \) \(\mathstrut +\mathstrut 2 q^{3} \) \(\mathstrut +\mathstrut 6 q^{4} \) \(\mathstrut +\mathstrut 2 q^{5} \) \(\mathstrut +\mathstrut 6 q^{6} \) \(\mathstrut +\mathstrut 8 q^{7} \) \(\mathstrut +\mathstrut 6 q^{9} \) \(\mathstrut +\mathstrut 6 q^{10} \) \(\mathstrut +\mathstrut 4 q^{11} \) \(\mathstrut +\mathstrut 6 q^{12} \) \(\mathstrut +\mathstrut 6 q^{13} \) \(\mathstrut +\mathstrut 12 q^{14} \) \(\mathstrut +\mathstrut 4 q^{15} \) \(\mathstrut +\mathstrut 6 q^{16} \) \(\mathstrut +\mathstrut 4 q^{17} \) \(\mathstrut +\mathstrut 10 q^{19} \) \(\mathstrut +\mathstrut 6 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 3 & 1 \\ 0 & 1 & 5 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 3 & 1 \\ 0 & 1 & 5 \end{array}\right)$
Download this matrix for gp, magma, sage