On the modular forms of weight 1/2 over algebraic number fields

[摘要] Serre and Stark succeeded in deciding a basis of the space of modular forms of weight 1/2 over the rational number field. Achimescu and Saha generalized their result to the case of modular forms of weight 1/2 over totally real algebraic number fields. Gove also solved this problem in the case of modular forms of weight 1/2 over imaginary quadratic fields. In this paper, we determine an explicit basis of the space of modular forms of weight 1/2, level c and character psi over algebraic number fields. We prove our assertion using their arguments and Shimura's transformation formula of theta series over algebraic number fields. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Theta series;Forms of half-integer weight;Automorphic forms on GL(2)