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}
.