Introduction

In this note we apply a theorem of Sturm [S] to prove a bound on the number of Hecke operators needed to generate the Hecke algebra as a $\mathbb{Z}$-module. This bound was observed by to Ken Ribet, but has not been written down. In section 2 we record our notation and some standard theorems. In section 3 we state Sturm's theorem and use it to deduce a bound on the number of generators of the Hecke algebra.