  We prove two results on arithmetic quantum chaos for dihedral Maass forms,
both of which are manifestations of Berry's random wave conjecture: Planck
scale mass equidistribution and an asymptotic formula for the fourth moment.
For level $1$ forms, these results were previously known for Eisenstein series
and conditionally on the generalised Lindelof hypothesis for Hecke-Maass
eigenforms. A key aspect of the proofs is bounds for certain mixed moments of
$L$-functions that imply hybrid subconvexity.
