The base change L-function for modular forms and Beyond Endoscopy

Following ideas of Langlands and Sarnak on Beyond Endoscopy, we introduce a method to study the base change L-function of a modular form via the trace formula. We complete the analysis in the case of quadratic base change for real fields, to deduce a new proof of the analytic continuation of the base change L-function to the left of the line R(s)=1.