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Consider the Shimura datum $(GSp_{2g},\mathcal{H}_g)$. Let $G$ be a reductive $\mathbb{Q}$-subgroup of $Sp_{2g}$. I want to know under what condition there exists a point $x\in\mathcal{H}_g$ such that ...

This is the opposite to my last question case. Let $F$ be a totally real number field, $R$ is a quaternion algebra over $F$ unramified in at least one infinite place of $F$. Let $\mathcal{O}⊂R$ be an ...