On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5

Abstract

After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the Fourier coefficients of weakly holomorphic modular forms of weight 3/2 on the congruence subgroups of higher genus by using the Bruinier-Funke modular traces. Extending their work, we construct real-valued class invariants by using the singular values of the generalized Weber functions of level 5 and prove that their Galois traces are Fourier coefficients of a harmonic weak Maass form of weight 3/2 by using Shimura’s reciprocity law.

Keywords

• modular forms
• modular traces
• galois traces
• class field theory
• primary 11f37
• secondary 11f30
• 11g15
• 11r27
• 11r37