Critical points of modular forms

We count the number of critical points of a modular form with real Fourier coefficients in a [Formula: see text]-translate of the standard fundamental domain [Formula: see text] (with [Formula: see text]). Whereas by the valence formula the (weighted) number of zeros of this modular form in [Formula: see text] is a constant only depending on its weight, we give a closed formula for this number of critical points in terms of those zeros of the modular form lying on the boundary of [Formula: see text], the value of [Formula: see text] and the weight. More generally, we indicate what can be said about the number of zeros of a quasimodular form.