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In this article we present a heuristic model that describes the asymptoticbehaviour of the number of primes p such that the p-th coefficient of a giveneigenform is a rational integer. We treat the case of a weight 2 eigenform withquadratic coefficient field without inner twists. Moreover we present numericaldata which agrees with our model and the assumptions we made to obtain it.

On the Distribution of Frobenius of Weight 2 Eigenforms with Quadratic Coefficient Field