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Ternary quadratic forms and half-integral weight modular forms

Part of: Forms and linear algebraic groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 December 2012

Alia Hamieh
Alia Hamieh*
Affiliation:
Department of Mathematics, University of British Columbia, Room 121, 1984 Mathematics Road Vancouver, British Columbia, V6T 1Z2, Canada (email: [email protected])

Abstract

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Let k be a positive integer such that k≡3 mod 4, and let N be a positive square-free integer. In this paper, we compute a basis for the two-dimensional subspace Sk/2(Γ0(4N),F) of half-integral weight modular forms associated, via the Shimura correspondence, to a newform F∈Sk−1(Γ0(N)), which satisfies . This is accomplished by using a result of Waldspurger, which allows one to produce a basis for the forms that correspond to a given F via local considerations, once a form in the Kohnen space has been determined.

MSC classification

Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11E20: General ternary and quaternary quadratic forms; forms of more than two variables
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 418 - 435
Copyright
© The Author(s) 2012

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