Newforms of Half-integral Weight: The Minus Space Counterpart

We study genuine local Hecke algebras of the Iwahori type of the double cover of SL2 (Q(p)) and translate the generators and relations to dassical operators on the space Sk+1/2 (Gamma(0) (4M)), M odd and square-free. In [9] Manickam, Ramakrishnan, and Vasudevan defined the new space of Sk+1/2 (Gamma(0) (4M)) that maps Hecke isomorphically onto the space of newforms of S-2k (Gamma(0) (2M)). We characterize this newspace as a common-1-eigenspace of a certain pair of conjugate operators that come from local Hecke algebras. We use the classical Hecke operators and relations that we obtain to give a new proof of the results in [9] and to prove our characterization result.