On degrees in family of maps constructed via modular forms

TL;DR

This paper investigates how the degrees of maps from modular curves into projective spaces, constructed via modular forms, vary when the modular forms themselves are varied, extending previous work on these mappings.

Contribution

It analyzes the behavior of degrees of modular form-induced maps and resulting curves as the modular forms vary, providing new insights into their geometric properties.

Findings

Degree of maps varies with modular forms

Degrees of resulting curves change under modular form variation

Extended understanding of modular form-induced mappings

Abstract

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.