  It is known that the automorphism group of any projective K3 surface is
finitely generated [24]. In this paper, we consider a certain kind of K3
surfaces with Picard number 3 whose automorphism groups are isomorphic to
congruence subgroups of the modular group $PSL_2(\mathbb{Z})$. In particular,
we show that a free group of arbitrarily large rank appears as the automorphism
group of such a K3 surface.
