Computing isogeny covariant differential modular forms

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