  Working over an algebraically closed field of characteristic zero, we compute
the cohomology of the subalgebra A(2) of the motivic Steenrod algebra that is
generated by Sq^1, Sq^2, and Sq^4. The method of calculation is a motivic
version of the May spectral sequence.
  Speculatively assuming that there is a "motivic modular forms" spectrum with
certain properties, we use an Adams-Novikov spectral sequence to compute the
homotopy of such a spectrum at the prime 2.
