Let denote the number of overpartitions of . We show that for and for by using a relation of the generating function of modulo and elementary dissection manipulations. Furthermore, by studying a 4-dissection formula of the generating function of modulo 3 and iterating the above two congruence relations, we derive that for . Moreover, applying the fact that is a Hecke eigenform in , we obtain an infinite family of congruences , where and is a prime such that and . In this way, we find various Ramanujan-type congruences for modulo such as , and for .
Li Zhang. "Ramanujan-type congruences for overpartitions modulo $3$." Rocky Mountain J. Math. 50 (6) 2257 - 2264, December 2020. https://doi.org/10.1216/rmj.2020.50.2257