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(Qₚ) and translate the generators and relations to classical operators on the space Sk+1/2([STIX]x1D6E4₀(4M)) , M odd and square-free. In [9] Manickam, Ramakrishnan, and Vasudevan defined the new space of Sk+1/2([STIX]x1D6E4₀(4M)) that maps Hecke isomorphically onto the space of newforms of S₂ₖ([STIX]x1D6E4₀(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.