We will discuss some results and problems on the geometry and arithmetic of the SL(2, C) Hitchin system on a modular curve. In particular, we will demonstrate a natural action of the classical Hecke operators on this Hitchin system and study some of the arithmetic properties of their action. We will also show that the spectral curves of the Hitchin system are motives for weight four cuspidal modular forms associated with the modular curve.