We will begin by describing the notion of nonabelian level structures for elliptic curves, which are roughly given by a G-Galois cover of the curve, ramified only above the origin. Afterwards, we will describe some questions surrounding this notion and applications to the arithmetic of the Fourier coefficients of noncongruence modular forms.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246