Let $N$ and $p$ be relatively prime integers with $p$ a prime. Suppose $f$ is a weight $k=2$ (normalized, cuspidal, etc) newform of level $\Gamma\_1(N) \cap \Gamma\_0(p)$. I seem to recall the existence of a theorem to the following effect:



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> Let $\rho\_{f,p}: G\_{\mathbf{Q}\_p} \to \mathrm{GL}\_2(\bar{\mathbf{F}}\_p)$ be the mod $p$ $p$-adic representation associated to $f$ (and some prime ${\frak{p}} \mid p$). Suppose $\rho\_{f,p}$ is irreducible and finite flat. Then there exists a newform $g$ of weight $k=2$ and level $\Gamma\_1(N)$ which is congruent to $f$ mod $p$. 
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Does such a theorem actually exist? The content I'm looking for is the ability to simultaneously **remove $p$ from the level** while also **remaining in weight $k=2$.**


Theorem 2.1 of [these notes](http://math.stanford.edu/~conrad/vigregroup/vigre05/edixhoven4.pdf) attributes a similar theorem to Mazur, but it is required that $f$ be of level $\Gamma\_0(Np)$. Can this be strengthened to allow nontrivial nebentype away from $p$?



Level-Lowering in Weight 2
The answer is yes. This result (and more) is contained in Theorem 6.4 of Diamond's "The refined conjecture of Serre".


