# Properties

 Label 1.4.2.4.2a Name $$F_{a,b}$$ Weight 1 Degree 4 Real dimension 2 Components 4 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{U}(1)\times\mathrm{U}(1)$$ Component group $$C_2^2$$

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## Invariants

 Weight: $1$ Degree: $4$ $\mathbb{R}$-dimension: $2$ Components: $4$ Contained in: $\mathrm{USp}(4)$ Rational: $\mathrm{True}$

## Identity Component

 Name: $\mathrm{U}(1)\times\mathrm{U}(1)$ Index: $4$ $\mathbb{R}$-dimension: $2$ Description: $\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}: A,B\in \mathrm{U}(1)\right\}$

## Component Group

 Name: $C_2^2$ Order: $4$ Abelian: $\mathrm{True}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $12$ $0$ $110$ $0$ $1260$ $0$ $16002$ $0$ $213906$
$a_2$ $1$ $2$ $5$ $14$ $49$ $202$ $944$ $4720$ $24553$ $130658$ $705880$ $3855040$ $21232468$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{1}{4}$ $\mathrm{P}[a_2=2]=\frac{3}{4}$