Computing isogeny covariant differential modular forms

Abstract

We present the computation modulo p 2 p^2 and explicit formulas for the unique isogeny covariant differential modular form of order one and weight χ − p − 1 , − p \chi _{-p-1,-p} called f j e t f_{\mathrm {jet}} , an isogeny covariant differential modular form of order two and weight χ − p 2 − p , − 1 , − 1 \chi _{-p^2-p,-1,-1} denoted by f j e t h j e t f_{\mathrm {jet}}h_{\mathrm {jet}} , and an isogeny covariant differential modular form h j e t h_{\mathrm {jet}} of order two and weight χ 1 − p 2 , 0 , − 1 \chi _{1-p^2,0,-1} .