Suppose $(V,N)$ is an $n$-dimensional semisimple $WD$ representation of $W_{mathbb{Q}_p}$. This corresponds under local Langlands to an admissable representation $pi$ of $GL_n(mathbb{Q}_p)$. Is there some simple way to "read off" the conductor of $pi$ from the corresponding $WD$ represention $(V,N)$?
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