Unitary PSL2 CM fields and the Colmez conjecture

We study certain unitary CM fields whose Galois closure has Galois group PSL2(Fq)×Z/2Z. After investigating the CM types of these fields, we turn towards Colmez's conjectural formula on the Faltings heights of CM abelian varieties. We explicitly calculate the class functions appearing in the statement of the conjecture and then apply refinements of the recently proven average version to establish Colmez's conjecture in this case.