Quadratic Twists and the Coefficients of Weakly Holomorphic Modular Forms

Linear congruences have been shown to exist for the partition function and for several other arithmetic functions that are generated by weakly holomorphic modular forms. In previous work, the author showed that such congruences exist for the Fourier coefficients of any weakly holomorphic modular form in a large class. In this paper, quadratic twists are used to produce new congruences for the coefficients of these forms. To demonstrate our main theorems, we give new congruences for overpartitions, and extend a result of Penniston regarding congruences for ℓ-regular partitions.