Monstrous Moonshine of higher weight 
C. Dong, G. Mason 

Abstract: We determine the space of 1-point correlation functions associated 
with the Moonshine module: they are precisely those modular forms of 
non-negative integral weight which are holomorphic in the upper half plane, 
have a pole of order at most 1 at infinity, and whose Fourier expansion has 
constant 0. There are Monster-equivariant analogues in which one naturally 
associates to each element in the Monster a modular form of fixed weight k, 
the case k=0 corresponding to the original ``Moonshine'' of Conway and Norton.