  In this article, we study two important properties of ${\rm{sym}}^3$
transfers of the automorphic representation $\pi$ associated to a modular form.
First we compute the conductor of ${\rm{sym}}^3(\pi)$. Then we detect the types
of local automorphic representations at bad primes by the variation of the
epsilon factors of symmetric cube transfer of the representation $\pi$ attached
to a cusp form $f$. Here we twist the modular forms by a specific quadratic
character. From this variation number, for each prime $p$, we classify all
possible types of symmetric cube transfers of the local representations
$\pi_p$. For ${\rm{sym}}^3$ transfer, the most difficult prime is $p=3$.
