Let denote the number of overpartitions of . In this paper, we establish an infinite family of congruences , where , is an arbitrary odd prime and is a nonnegative integer such that . In this way, we find various congruences for modulo such as and . Furthermore, by studying the generating function of modulo 9 and applying the fact that is a Hecke eigenform, we obtain another infinite family of congruences , where is a prime with , and is a nonnegative integer such that . This leads to lots of congruences for modulo such as .
"New congruences for overpartitions modulo and ." Rocky Mountain J. Math. 51 (6) 2269 - 2273, December 2021. https://doi.org/10.1216/rmj.2021.51.2269