  Previous work constructed a generalized truncated Brown-Peterson spectrum of
chromatic height 2 at the prime 2 as an E_infinity-ring spectrum, based on the
study of elliptic curves with level-3 structure. We show that the natural map
forgetting this level structure induces an E_infinity-ring map from the
spectrum of topological modular forms to this truncated Brown-Peterson
spectrum, and that this orientation fits into a diagram of E_infinity-ring
spectra lifting a classical diagram of modules over the mod-2 Steenrod algebra.
In an appendix we document how to organize Morava's forms of K-theory into a
sheaf of E_infinity-ring spectra.
