A simple example of modular forms as tau-functions for integrable equations

We show how classical modular forms and functions appear as tau-functions for a certain integrable reduction of the self-dual Yang–Mills equations obtained by S. Chakravarty, M. Ablowitz, and P. Clarkson [6]. We discuss possible consequences of this novel phenomenon in integrable systems which indicate deep connections between integrable equations, group representations, modular forms, and moduli spaces.