We prove an explicit formula for the conductor of an irreducible, admissible representation of $\operatorname{GL} _{n}(F)$ twisted by a character of $F^{\times} $ where the field $F$ is local and non-archimedean. As a consequence, we quantify the number of character twists of such a representation of fixed conductor.
Rocky Mountain J. Math.
49(4):
1093-1110
(2019).
DOI: 10.1216/RMJ-2019-49-4-1093
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