ABSTRACT
In this article, we present a heuristic model that describes the asymptotic behavior of the number of primes p such that the pth coefficient of a given eigenform is a rational integer. We treat the case of a weight 2 eigenform with quadratic coefficient field without inner twists. Moreover, we present numerical data which agree with our model and the assumptions we made to obtain it.
Acknowledgments
I wish to express my sincere gratitude to Jan Tuitman and Gabor Wiese for suggesting to me this problem, for our discussions, for their enthusiasm and for their guidance. I would also like to thank Andrew Sutherland and the anonymous referee for useful comments.