Hecke Base Change, Semisimplicity, and Deformation — Examples

Compute the rank-one regular-trace determinant and repeated-root nonsemisimple case; compare symmetrizing and regular trace forms. Illustrate the formal lifting theorem on a two-dimensional algebra and locate the exact exceptional parameter.

These are planned worked examples and counterexamples for hecke-base-change-semisimplicity-and-deformation, with empty item lists pending normal authoring and proof review. Each example must calculate from the stated hypotheses, and each counterexample must verify both its premises and the failed conclusion. This companion is a dependency leaf and supplies no theorem to another page.