We study several aspects of nonvanishing Fourier coefficients of elliptic modular forms mod , partially answering a question of Bellaïche-Soundararajan concerning the asymptotic formula for the count of the number of Fourier coefficients upto x which do not vanish mod . We also propose a precise conjecture as a possible answer to this question. Further, we prove several results related to the nonvanishing of arithmetically interesting (e.g., primitive or fundamental) Fourier coefficients mod of a Siegel modular form with integral algebraic Fourier coefficients provided is large enough. We also make some efforts to make this "largeness" of effective.