It's called the congruence topology, and is (obviously) always at least as coarse as the profinite topology.  If your group has the Congruence Subgroup Property (the modular group doesn't, but $SL_n(\mathbb{Z})$ does for $n>2$) then it's the same as the profinite topology.

A google search found, for instance, [Section 7.3][1] of *Algebraic theory of the Bianchi groups* by Benjamin Fine.


  [1]: http://books.google.com/books?id=1D6crOEoRFEC&pg=PA200&lpg=PA200&dq=congruence+topology&source=bl&ots=d-mel58Uo0&sig=Lxim14zcfsKZdMxgO2gU9otjPGY&hl=en&ei=TZx2TN3sGIW-sQPjktCgDQ&sa=X&oi=book_result&ct=result&resnum=11&ved=0CFEQ6AEwCg#v=onepage&q=congruence%2520topology&f=false