On twisting operators and newforms of half-integral weight

Abstract

The theory of newforms is very important and useful for arithmetical study of modular forms of integral weight. It is natural to try to extend this theory into the case of modular forms of half-integral weight Until now, several authors have attempted to find a theory of newforms of half-integral weight (cf. [She], [N], [K], [M-R-V], [She-W]). But complete results have not been obtained yet.