Vol. 274, No. 1, 2015

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Theory of newforms of half-integral weight

Murugesan Manickam, Jaban Meher and Balakrishnan Ramakrishnan

Vol. 274 (2015), No. 1, 125–139
Abstract

We set up the theory of newforms of half-integral weight on Γ0(8N) and Γ0(16N), where N is odd and squarefree. Further, we extend the definition of the Kohnen plus space in general for trivial character and also study the theory of newforms in the plus spaces on Γ0(8N), Γ0(16N), where N is odd and squarefree. Finally, we show that the Atkin–Lehner W-operator W4 acts as the identity operator on S2knew(4N), where N is odd and squarefree. This proves that S2k(4) = S2k(4).

Keywords
modular forms of half-integral weight, theory of newforms, Kohnen plus space
Mathematical Subject Classification 2010
Primary: 11F37
Secondary: 11F11, 11F32
Milestones
Received: 24 April 2014
Revised: 22 August 2014
Accepted: 28 August 2014
Published: 2 March 2015
Authors
Murugesan Manickam
Kerala School of Mathematics
Kunnamangalam P.O.
Kozhikode 673 571
India
Jaban Meher
Inspire Fellow, Department of Mathematics
Indian Institute of Science
Bangalore 560 012
India
Balakrishnan Ramakrishnan
Harish-Chandra Research Institute
Chhatnag Road, Jhunsi
Allahabad 211 019
India