Explicit families of congruences for the overpartition function

In this article we exhibit new explicit families of congruences for the overpartition function, making effective the existence results given previously by Treneer. We give infinite families of congruences modulo m for \(m = 3, 5, 7, 11\) $m=3,5,7,11$ , and finite families for \(m = 13, 17, 19\) $m=13,17,19$ .