I am reading about the modular method and I have a question about Ribet's Level Lowering Theorem.
In its simplest form, it says that if an elliptic curve $E$ of conductor $N$ has no $p$-isogenies, there exists a newform $f$ of level $N_p$ (the Artin conductor of $E$) such that the modulo $p$ Galois representation of $E$ arises from the newform $f$. My question is: is this $f$ unique?