On degrees in family of maps constructed via modular forms

This paper is a continuation of our previous works (see Mui'c in Monatsh. Math. 180, no. 3, 607–629, (2016)) and (Mui'c, Kodrnja in Ramanujan J. 55, no. 2, 393–420, (2021)) where we have studied maps from $X_0(N)$ into $\mathbb P^2$ (and more general) constructed via modular forms of the same weight. In this short note we study how degrees of the maps and degrees of the resulting curve change when we let modular forms vary.