For a maximal ideal $\mathfrak m$ of some anemic Hecke algebra $\mathbb{T}^S$, associated to an irreducible Galois $\overline{\mathbb F}_l$-representation of dimension $d$, on can also define a Galois $\mathbb{F}_{\mathfrak m}^S$-representation $\rho_{\mathfrak m}$. The length of $\rho_{\mathfrak m} \otimes_{\overline{\mathbb Z}_l} \overline{\mathbb F}_l$ is equal to the number of prime ideals $\widetilde{\mathfrak m} \subset \mathfrak m$ and we try to translate some of the properties of $\bigl \{ \widetilde{\mathfrak m} \subset \mathfrak m \bigr \}$ into those of $\rho_{\mathfrak m} \otimes_{\overline{\mathbb Z}_l} \overline{\math bb F}_l$. For example the level raising (or lowering) property is encoded by the non semi-simplicity of $\rho_{\mathfrak m} \otimes_{\overline{\mathbb Z}_l} \overline{\mathbb F}_l$.