This survey paper exposes in a systematic way results on local newforms for representations of GL(2) over a non-archimedean local field. The author collects several formulas for the local newform for different types of representations and various models. He computes the action of intertwining operators and Whittaker functionals on local newforms and obtains a list of conductors for supercuspidal, special and principal series representations.
For the representation \(\pi\) with trivial central character, the author considers the Atkin-Lehner involution acting on the one-dimensional space of newvectors and proves that the sign attached to \(\pi\) by the Atkin-Lehner involution coincides with the sign defined by the \(\epsilon\)-factor.