$TMF_0(3)$ Characteristic classes for String bundles
  We compute the completed $TMF_0(3)$ cohomology of the 7-connective cover $BString$ of $BO$. We use cubical structures on line bundles over elliptic curves to construct an explicit class which together with the Pontryagin classes freely generates the cohomology ring. 
Gerd Laures and Martin Olbermann
math.AT