Generators of the ring of weakly holomorphic modular functions for $$Gamma _1(N)$$

For a positive integer N divisible by 4, 5, 6, 7 or 9, let (mathcal {O}_{1,N}(mathbb {Q})) be the ring of weakly holomorphic modular functions for the congruence subgroup (Gamma _1(N)) with rational Fourier coefficients. We present explicit generators of the ring (mathcal {O}_{1,N}(mathbb {Q})) over (mathbb {Q}) by making use of modular units which have infinite product expansions.