Explicit calculations with Eisenstein series Academic Article uri icon


  • © 2018 Elsevier Inc. We find explicit change-of-basis formulas between Eisenstein series attached to cusps, and newform Eisenstein series attached to pairs of primitive Dirichlet characters. As a consequence, we prove a Bruggeman–Kuznetsov formula for newforms of square-free level and trivial nebentypus. We also derive, in explicit form, the Fourier expansion, Hecke eigenvalues, Atkin–Lehner pseudo-eigenvalues, and other data associated to these Eisenstein series, with arbitrary integer weight, level, and nebentypus.

author list (cited authors)

  • Young, M. P.

citation count

  • 9

publication date

  • June 2019