Fourier series of a class of eta quotients

The sum of divisors function σ(m) is defined by σ(m) = {∑d d∈ℕ d|m if m ∈ ℕ, 0 if m ∈ ℚ, m ∉ ℕ. Let H denote the upper half of the complex plane. Let η(z)(z ∈ H) be the Dedekind eta function. A class C of eta quotients is given for which the Fourier series of each member of C can be given explicitly. One example is η 2(2z)η 4(4z)η 6(6z)/ η 2(z)η 2(3z)η 4(12z)= 1+∑ ∞ n=1c(n)e 2πinz, z ∈ H, where c(n)=2σ(n)-3 σ(n/2) +4σ(n/4)+9σ(n/6)-36σ(n/ 12), n ∈ ℕ