What is the reletion between level and conductor of a supercuspidal representation of $GL_2(\mathbb{Q}_p)$ for some prime $p$?

The proposition 3.4 in [this](https://arxiv.org/pdf/1008.2796.pdf) paper is referring to [this](https://www.imo.universite-paris-saclay.fr/~breuil/PUBLICATIONS/multiplicite.pdf) paper which I am unable to understand because of the language.

Can someone help me to understand this?

Thanks in advance.