Joint equidistribution of newforms

I will introduce a new equidistribution problem that generalises quantum unique ergodicity in the level aspect. More precisely, the conjecture states that the mass of newforms on $X_0(q)$, viewed as the Hecke correspondence inside $X_0(1) \times X_0(1)$, equidistributes with respect to the uniform product measure as $q$ tends to infinity. I will point to analogies with the mixing conjecture of Michel—Venkatesh. Finally, I will present a new result in joint work with Asbjørn Nordentoft: we prove the conjecture, in a variant for compact hyperbolic surfaces with prime level, assuming GRH.