Modular symbols for Γ1(N) and elliptic curves with everywhere good reduction

Abstract. The modular symbols method developed by the author in [4] for the computation of cusp forms for Γ0(N) and related elliptic curves is here extended to Γ1(N). Two applications are given: the verification of a conjecture of Stevens [14] on modular curves parametrised by Γ1(N); and the study of certain elliptic curves with everywhere good reduction over real quadratic fields of prime discriminant, introduced by Shimura and related to Pinch’s thesis [10]. 1