Benedict Gross's paper on companion forms

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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Welcome to MathOverflow! You can use $\LaTeX$ syntax for math here; just enclose it in \$. 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
Nate, who are the two Gross number theorists? –  Joël Dec 3 '13 at 15:02
A search of MathSciNet for Author: Gross and MR Primary: 10 or 11 yields Samuel, Benedict, Robert, Warren, Christian, Herbert, Kenneth, and Oliver (but mostly Benedict). –  Gerry Myerson Dec 3 '13 at 22:44
@NateEldredge Thank you very much! –  Tom Dec 5 '13 at 13:24