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We extend the modularity lifting result of the arXiv:1111.2804 to allowGalois representations with some ramification at p. We also prove modularitymod 2 and 5 of certain Galois representations. We use these results to provemany new cases of the strong Artin conjecture over totally real fields in which5 is unramified. As an ingredient of the proof, we provide a general result onthe automatic analytic continuation of overconvergent p-adic Hilbert modularforms of finite slope which substantially generalizes a similar result inarXiv:1111.2804.

Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case