  We make the subconvex exponent for $\mathrm{GL}_2$ cuspidal representation in
the work of Michel \& Venkatesh explicit. The result depends on an effective
dependence on the `fixed' $\mathrm{GL}_2$ representation in our former work on
the subconvex bounds for twists by Hecke characters, which in turn depends on
the $\mathrm{L}^4$-norm of the test function.
