Counting irreducible representations of a finite abelian group over a finite field

Let [Formula: see text] be a finite abelian group and let [Formula: see text] be a positive integer. In this paper, we find a formula for the number of irreducible representations of [Formula: see text] of dimension [Formula: see text] over a given finite field, up to equivalence. We also provide a formula for such [Formula: see text] using the prime decomposition of the exponent of [Formula: see text] and an algorithm to compute the irreducible degrees and their multiplicities.