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May 14, 2014 at 13:10 comment added Joël Thanks @tkr et TSG. The claim mentioned by TSG is probably the one I remembered.
May 14, 2014 at 5:29 comment added TSG There was a preprint a few years ago, not by a former student of R. Taylor, but by a former student of someone closely associated, that claimed such a result, but it had a mistake. This might be what you're thinking of; the BLGGT/PT results are the best I know of for general n.
May 13, 2014 at 22:33 comment added tkr There is a density result for general n, and in the more general CM situation, in the paper "Automorphy and irreducibility of some $\ell$-adic representations" of Patrikis and Taylor (available on R. Taylor website, see Theorem D). I suspect this is not the result you believe you once heard, though.
May 13, 2014 at 17:58 history asked Joël CC BY-SA 3.0