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Serre's strong conjecture, now a theorem of Khare and Wintenberger, statesthat every two-dimensional continuous, odd, irreducible mod $p$ Galoisrepresentation $\rho$ arises from a modular form of a specific minimal weight$k(\rho)$, level $N(\rho)$ and character $\epsilon(\rho)$. In this short paperwe show that the minimal weight $k(\rho)$ is equal to a notion of minimalweight inspired by the recipe for weights introduced by Buzzard, Diamond andJarvis. Moreover, using the Breuil-M\'{e}zard conjecture we show that bothweight recipes are equal to the smallest $k \geq 2$ such that $\rho$ has acrystalline lift of Hodge-Tate type $(0,k-1)$.

Serre weights and the Breuil-M\'{e}zard conjecture for modular forms