In their work, Serre and Swinnerton-Dyer study the congruence properties of the Fourier coefficients of modular forms. We will examine similar congruence properties, but for the Taylor series coefficients of modular forms about a CM point τ . These coefficients can be shown to be the product of a power of a constant transcendental factor and an algebraic integer. In our work, we give a condition on τ and a prime number p that, if satisfied, implies that p m divides all the Taylor coefficients

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... f of sufficiently high degree. We also give effective bounds on the largest n such that p m does not divide the n th Taylor coefficient of f at τ that are sharp under certain additional hypotheses.