Eta-quotients and embeddings of $$X_0(N)$$ X 0 ( N ) in the projective plane

Abstract

In this paper, we find projective plane models of the modular curves $$X_0(N)$$ by constructing maps from $$X_0(N)$$ to the projective plane using modular forms. We use eta-quotients of weight 12. We find those eta-quotients in $$M_{12}(\varGamma _0(N))$$ which have maximal order of vanishing at infinity.