We give a criterion for an irreducible, admissible, supercuspidal representation π of GL(2, K), where K is a p-adic field, to become a principal series representation under every quadratic base change. We determine all such π that have trivial central character and conductor 2, and explain their relevance for the theory of elliptic curves.
In this appendix, we attached a sample reading on Integration by Parts and the associated reading quiz from Implementation I. Similarly, we attached a sample reading on Cross Product and the associated reading HW from Implementation II. Additionally, we have 4 charts with captions to expand on our quantitative data.
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