Whittaker newforms for archimedean representations of GL(2)

We present a unified characterization of Whittaker newforms for infinite-dimensional admissible representations π of GL(2,R) and GL(2,C). We connect this problem with that of finding test vectors for toric linear forms on the representation space of π. This method allows us to treat in the same way the real and complex fields, thus identifying Whittaker newforms in all cases, including those previously unavailable in the literature.