Obstruction criteria for modular deformation problems.

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