A formula for Fourier coefficients of certain eta-quotients and their expansions as Eisenstein series

We give a list of [Formula: see text] holomorphic eta-quotients of integral weight ([Formula: see text] of which are primitive) and provide a uniform closed formula for their Fourier coefficients [Formula: see text] where [Formula: see text] with some fixed [Formula: see text]. The proof involves Wohlfahrt’s extension of Hecke operators and a dimension formula for spaces of modular forms of general multiplier system. We further provide the expansions of these eta-quotients as linear combinations of standard Eisenstein series.