  In this paper we study special bases of certain spaces of half-integral
weight weakly holomorphic modular forms. We establish a criterion for the
integrality of Fourier coefficients of such bases. By using recursive relations
between Hecke operators, we derive relations of Fourier coefficients of each
basis element and obtain congruences of the Fourier coefficients, which extend
known congruences for traces of singular moduli.
