Let $p\geq 3$ be a prime, $f\geq 1$ an integer and $\Q_{p^f}$ the unramified
extension of $\Q_p$ of degree $f$. After Breuil and Paskunas, to a generic
semi-simple continue representation $\Gal(\bQp/\Q_{p^f})\ra\GL_2(\bFp)$, we can
associate a parameterized family of smooth admissible representations of
$\GL_2(\Q_{p^f})$ with coefficients in $\bFp$. In this article, we prove that
there are more parameters than those known.