Hecke operators on differential modular forms mod p

A description is given of all primitive δ-series mod p of order 1 which are eigenvectors of all the Hecke operators nTκ(n), “pTκ(p)”, (n,p)=1, and which are δ-Fourier expansions of δ-modular forms of arbitrary order and weight w with deg(w)=κ⩾0; this set of δ-series is shown to be in a natural one-to-one correspondence with the set of series mod p (of order 0) which are eigenvectors of all the Hecke operators Tκ+2(n), Tκ+2(p), (n,p)=1 and which are Fourier expansions of (classical) modular forms of weight ≡κ+2 mod p−1.