Abstract
In this paper, we study congruence properties of modular forms in various ways. By proving a weight-dependent congruence property of modular forms, we give some sufficient conditions, in terms of the weights of modular forms, for a modular form to be non- p-ordinary. As applications of our main theorem we derive a linear relation among coefficients of new forms. Furthermore, congruence relations among special values of Dedekind zeta functions of real quadratic fields are derived.
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