  The Garsia--Haiman module is a bigraded $\mathfrak{S}_n$-module whose
Frobenius image is a Macdonald polynomial. The method of orbit harmonics
promotes the $\mathfrak{S}_n$-set $X$ to a graded polynomial ring. The orbit
harmonics can be applied to prove cyclic sieving phenomena which is a notion
that encapsulates the fixed-point structure of finite cyclic group action on a
finite set. By applying this idea to the Garsia--Haiman module, we provide
cyclic sieving results regarding the enumeration of matrices that are invariant
under certain cyclic row and column rotation and translation of entries.
