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Properties

Label 5.22.44.1.1
Class number $1$
Dimension $5$
Determinant $22$
Level $44$

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Lattice Invariants

Dimension:$5$
Determinant:$22$
Level:$44$
Density:$0.198386512894871064941805259936\dots$
Group order:$96$
Hermite number:$1.07781806771272591316292780453\dots$
Minimal vector length:$2$
Kissing number:$14$
Normalized minimal vectors: $(1, 0, 0, -1, 0)$, $(1, 0, 0, 0, 0)$, $(1, 1, 0, -1, 0)$, $(0, 1, 0, -1, 0)$, $(0, 1, 0, 0, 0)$, $(0, 0, 1, 0, 0)$, $(0, 0, 0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 14 q^{2} \) \(\mathstrut +\mathstrut 46 q^{4} \) \(\mathstrut +\mathstrut 84 q^{6} \) \(\mathstrut +\mathstrut 126 q^{8} \) \(\mathstrut +\mathstrut 184 q^{10} \) \(\mathstrut +\mathstrut 224 q^{12} \) \(\mathstrut +\mathstrut 264 q^{14} \) \(\mathstrut +\mathstrut 414 q^{16} \) \(\mathstrut +\mathstrut 434 q^{18} \) \(\mathstrut +\mathstrut 412 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 2 & 1 & -1 & 0 & 1 \\ 1 & 2 & -1 & 0 & 1 \\ -1 & -1 & 2 & 0 & -1 \\ 0 & 0 & 0 & 2 & 1 \\ 1 & 1 & -1 & 1 & 4 \end{array}\right)$
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