Bounding the free spectrum of nilpotent algebras of prime power order

Let A be a finite nilpotent algebra in a congruence modular variety with finitely many fundamental operations. If A is of prime power order, then it is known that there is a polynomial p such that for every n ∈ N, every n-generated algebra in the variety generated by A has at most 2^p(n) elements. We present a bound on the degree of this polynomial.