Geodesic
Newforms of Half-integral Weight: The Minus Space Counterpart
Canadian journal of mathematics, Tome 72 (2020) no. 2, pp. 326-372

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DOI

We study genuine local Hecke algebras of the Iwahori type of the double cover of $\operatorname{SL}_{2}(\mathbb{Q}_{p})$ and translate the generators and relations to classical operators on the space $S_{k+1/2}(\unicode[STIX]{x1D6E4}_{0}(4M))$, $M$ odd and square-free. In [9] Manickam, Ramakrishnan, and Vasudevan defined the new space of $S_{k+1/2}(\unicode[STIX]{x1D6E4}_{0}(4M))$ that maps Hecke isomorphically onto the space of newforms of $S_{2k}(\unicode[STIX]{x1D6E4}_{0}(2M))$. 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.
DOI : 10.4153/S0008414X19000233
Mots-clés : Hecke algebra, half-integral weight form, Niwa isomorphism, Kohnen plus space 
Baruch, Ehud Moshe; Purkait, Soma. Newforms of Half-integral Weight: The Minus Space Counterpart. Canadian journal of mathematics, Tome 72 (2020) no. 2, pp. 326-372. doi: 10.4153/S0008414X19000233
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     title = {Newforms of {Half-integral} {Weight:} {The} {Minus} {Space} {Counterpart}},
     journal = {Canadian journal of mathematics},
     pages = {326--372},
     year = {2020},
     volume = {72},
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     doi = {10.4153/S0008414X19000233},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000233/}
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