  The existence of a strong spectral gap for lattices in semi-simple Lie groups
is crucial in many applications. In particular, for arithmetic lattices it is
useful to have bounds for the strong spectral gap that are uniform in the
family of congruence covers. When the lattice is itself a congruence group,
there are uniform and very good bounds for the spectral gap coming from the
known bounds toward the Ramanujan-Selberg conjectures. In this note, we
establish a uniform bound for the strong spectral gap for congruence covers of
an irreducible co-compact lattice $\Gamma$ in $PSL(2,R)^d$ with $d\geq 2$,
which is the simplest and most basic case where the congruence subgroup
property is not known.
