Local Newforms for GSp(4) describes a theory of new- and
oldforms for representations of GSp(4) over a non-archimedean local
field. This theory considers vectors fixed by the paramodular
groups, and singles out certain vectors that encode canonical
information, such as L-factors and epsilon-factors, through their
Hecke and Atkin-Lehner eigenvalues. While there are analogies to
the GL(2) case, this theory is novel and unanticipated by the
existing framework of conjectures. An appendix includes extensive
tables about the results and the representation theory of
GSp(4).
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