Abstract
Let f be a modular form of weight k for a congruence subgroup Γ ⊂ SL2(Z), and t a weight 0 modular function for Γ. Assume that near t = 0, we can write f = ∑n≥0bn tn, bn ∈ Z. Let ℓ(z) be a weight k + 2 modular form with q-expansion ∑γnqn, such that the Mellin transform of ℓ can be expressed as an Euler product. Then we show that if for some integers ai, di, then the congruence relation bmprpbmpr-1 + εppk+1bmpr-2 ≡ 0 (mod pr) holds. We give a number of examples of this phenomena.

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