We prove that there exist at least 15 pairs of measures for which the two normalized Frobenius traces on modular Abelian surfaces are equidistributed. Under an assumption about stochastic independence, we prove that there are exactly 18 such pairs of measures. Moreover, we describe all of them by giving their moments and distributions.
Gonzalez, J. The Frobenius traces distribution for modular Abelian surfaces. "Rmanujan journal", Febrer 2014, vol. 33, núm. 2, p. 247-261.