Congruences for modular forms

We investigate congruences for Fourier coefficients of modular forms of integral and half integral weight. We prove that any cusp form, having a half integral weight which is at least 5/2, will be a "good form". For weight 3/2, we prove that any cusp form of such weight which is not a linear combination of theta-series will be a "good form". We use the notion of "good form" in the sense of Ken Ono and Christopher Skinner, as defined in their Annals of Mathematics paper "Fourier coefficients of half integral weight forms modulo l". Our results give an almost complete proof of the conjecture stated in the above mentioned paper. The main tools used in the proof are Ribet's theory of modular forms with complex multiplication and Atkin and Lehner's theory of new forms.;We next prove that under very weak hypotheses for a cusp form, if its Fourier coefficients in a "block" form a periodic sequence, then the "block" will be all zero. By a "block" of coefficients we mean a sequence of coefficients of the form a( t), a(4t),...a( tn2),... where t is some fixed positive integer and n runs through the set of positive integers. The main tool used in the proof is Shimura's lifting theorem.;Following the ideas of Serre and Swinnerton-Dyer we give a complete description of the space of Gamma0(4)-modular forms modulo a prime l. The main tool used in the proof is the theory of the ∂-operator.