  Given a one-dimensional formal group of height 2, let E be the Morava
E-theory spectrum associated to its universal deformation over the Lubin-Tate
ring. By computing with moduli spaces of elliptic curves, we give an
explicitation for an algebra of Hecke operators acting on E-cohomology. This
leads to a vanishing result for Rezk's logarithmic cohomology operation on the
units of E. It identifies a family of elements in the kernel with meromorphic
modular forms whose Serre derivative is zero. Our calculation finds a
connection to logarithms of modular units. In particular, we work out an action
of Hecke operators on certain "logarithmic" q-series, in the sense of Knopp and
Mason, that agrees with our vanishing result and extends the classical Hecke
action on modular forms.
