  In this paper, motivated by the work of Mahlburg, we find congruences for a
large class of modular forms. Moreover, we generalize the generating function
of the Andrews-Garvan-Dyson crank on partition and establish several new
infinite families of congruences. In this framework, we showed that both the
birank of an ordered pair of partitions introduced by Hammond and Lewis, and
$k$-crank of $k$-colored partition introduced by Fu and Tang process the same
as the partition function and crank.
