Algebraicity of weakly holomorphic modular functions at divisors of meromorphic modular forms for certain Fuchsian groups

We show that the values of a certain basis of weakly holomorphic modular functions on Γ₀⁺(N) at points of the divisors of any meromorphic modular form of weight k on Γ₀⁺(N) with algebraic Fourier coefficients are algebraic. We also find the basis of an Eisenstein space of weight 2 on Γ₀⁺(N). As an application, we show that a certain eta quotient has only single zeros on the fundamental domain. Moreover, we give a number field containing all the values of the certain basis of M₀#() at the zeros of this certain eta quotient. 2010 Mathematics Subject Classification: 11F03, 11F12, 11F25, 11F30, 11G30, 11R04