  This paper studies a covering map phi from the upper half plane to the
complex plane with a triangular lattice excised. This map is interesting as it
factorises Klein's J invariant. Its derivative has properties which are a
slight generalisation of modular functions, and (phi')^6 is a modular function
of weight 12. There is a homomorphism from the modular group Gamma to the
affine transformations of the complex plane which preserve the excised lattice.
With respect to this action phi is a map of Gamma-sets. Identification of the
excised lattice with the root lattice of sl_3(C) allows functions familiar from
the study of modular functions to be expressed in terms of standard
constructions on representations of sl_3(C).
