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?