Sur les repr\'esentations $p$-adiques g\'eom\'etriques de conducteur 1 et de dimension 2 de $G_{\text{Q}}$

We prove that there is no geometric $p$-adic representation of the Galois group of $\text{Q}$ which is irreducible, of dimension 2, of conductor 1 and low weight, according to a conjecture of Fontaine and Mazur.