Abstract
For a cuspidal newform [Formula: see text] of weight [Formula: see text] and a prime [Formula: see text] of [Formula: see text], the deformation problem for its associated mod [Formula: see text] Galois representation is unobstructed for all primes outside some finite set. Previous results gave an explicit bound on this finite set for [Formula: see text] of squarefree level; we modify this bound and remove the squarefree hypothesis. We also show that if the [Formula: see text]-adic deformation problem for [Formula: see text] is unobstructed, then [Formula: see text] is not congruent mod [Formula: see text] to a newform of lower level.
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