Explicit families of congruences for the overpartition function

Abstract 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 $$m = 3, 5, 7, 11$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>7</mml:mn> <mml:mo>,</mml:mo> <mml:mn>11</mml:mn> </mml:mrow> </mml:math> , and finite families for $$m = 13, 17, 19$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> <mml:mo>,</mml:mo> <mml:mn>17</mml:mn> <mml:mo>,</mml:mo> <mml:mn>19</mml:mn> </mml:mrow> </mml:math> .