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