TY - JOUR
T1 - Newforms of Half-integral Weight
T2 - The Minus Space Counterpart
AU - Baruch, Ehud Moshe
AU - Purkait, Soma
N1 - Publisher Copyright:
© 2019 Canadian Mathematical Society.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - 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(γ0(4M)), M odd and square-free. In [9] Manickam, Ramakrishnan, and Vasudevan defined the new space of Sk+1/2(γ0(4M)) that maps Hecke isomorphically onto the space of newforms of S2k(γ0(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.
AB - 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(γ0(4M)), M odd and square-free. In [9] Manickam, Ramakrishnan, and Vasudevan defined the new space of Sk+1/2(γ0(4M)) that maps Hecke isomorphically onto the space of newforms of S2k(γ0(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.
KW - Hecke algebra
KW - Kohnen plus space
KW - Niwa isomorphism
KW - half-integral weight form
UR - http://www.scopus.com/inward/record.url?scp=85083069955&partnerID=8YFLogxK
U2 - 10.4153/S0008414X19000233
DO - 10.4153/S0008414X19000233
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AN - SCOPUS:85083069955
SN - 0008-414X
VL - 72
SP - 326
EP - 372
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
IS - 2
ER -