Abstract
Let $F$ be a totally real Galois number field. We prove the existence of base change relative to the extension $F/\mathbb{Q}$ for every holomorphic newform of weight at least $2$ and odd level, under simple local assumptions on the field $F$.
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@book {AC, MRKEY = {1007299},
AUTHOR = {Arthur, James and Clozel, Laurent},
TITLE = {Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula},
SERIES = {Ann. of Math. Stud.},
VOLUME = {120},
PUBLISHER = {Princeton Univ. Press},
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ISBN = {0-691-08517-X; 0-691-08518-8},
MRCLASS = {22E55 (11F70 11F72 11R39)},
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ZBLNUMBER = {0682.10022},
} -
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ARXIV= {math.NT/0406576},
}