In the page 458 of his paper(A tameness criterion for Galois representations associated to modular forms), Gross wrote the following

"A detailed analysis of $U_p(Af)+V_p(<p>f)$ shows that it vanishes at each supersingular point", (where $f$ is a mod p modular form of weight 1, $U_p$ is the Hecke operator on mod $p$ modular forms of weight p, $A$ is the Hasse invariant, $V_p$ is the $p$-power map, and $<p>$ is the diamond operator.)

Can someone explain how to do analysis of this section at supersingular points?

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. Also, it would be nice to include the full citation of the paper; in particular, there are several mathematicians named Gross (and at least two number theorists). – Nate Eldredge Nov 26 '13 at 16:43