For KHT-free Hecke maximal ideals, the nilpotency partition of local monodromy at v agrees modulo l with the characteristic-zero partition, so level lowering at v is impossible.
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Level lowering: a Mazur principle in higher dimension
For KHT-free Hecke maximal ideals, the nilpotency partition of local monodromy at v agrees modulo l with the characteristic-zero partition, so level lowering at v is impossible.