Some notes on the genus of modular curve X_ (N)

We estimate the genus g(N) of modular curve $X_0^0(N)$ and show that g(N) = 0 if and only if $1 \leq N \leq 5$.

Mathematical Notes v.40 Elliptic Curves Knapp, A.W.
Modular Forms Miyake, T.
Modular Forms and Functions Rankin, R.
Elliptic Modular Functions Schoeneberg, B.
Publ. Math. Soc. Japan no.11 Introduction to the Arithmetic Theory of Automorphic Functions Shimura, G.