Properties

Label 4.1.2.1.1
Class number 1
Dimension 4
Determinant 1
Level 2

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Lattice Invariants

Dimension:$4$
Determinant:$1$
Level:$2$
Label:$4.1.2.1.1$
Density:$0.308425137534042456838577843746\dots$
Group order:$384$
Hermite number:$1.00000000000000000000000000000\dots$
Minimal vector length:$1$
Kissing number:$8$
Normalized minimal vectors: $(1, 0, 0, 0)$, $(0, 1, 0, 0)$, $(0, 0, 1, 0)$, $(0, 0, 0, 1)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 8q \) \(\mathstrut +\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 32q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 48q^{5} \) \(\mathstrut +\mathstrut 96q^{6} \) \(\mathstrut +\mathstrut 64q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 104q^{9} \) \(\mathstrut +\mathstrut 144q^{10} \) \(\mathstrut +\mathstrut 96q^{11} \) \(\mathstrut +\mathstrut 96q^{12} \) \(\mathstrut +\mathstrut 112q^{13} \) \(\mathstrut +\mathstrut 192q^{14} \) \(\mathstrut +\mathstrut 192q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 144q^{17} \) \(\mathstrut +\mathstrut 312q^{18} \) \(\mathstrut +\mathstrut 160q^{19} \) \(\mathstrut +\mathstrut 144q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right)$

Genus Structure

Class number:$1$
 
Genus representatives: $\left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right)$
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