Patterns of primes in joint Sato--Tate distributions

A. Anas Chentouf, Catherine Cossaboom, Samuel Goldberg +1

For $j=1,2$, let $f_j(z)={\sum }_{n=1}^{\infty }{a}_j(n)e^{2\pi inz}$ be a holomorphic, non-CM cuspidal newform of even weight $k_j\ge 2$ with trivial nebentypus. For each prime $p$…