Subjectivity of siegelΦ-operator for square free level and small weight

摘要

We show the subjectivity of the (global) Siegel Φ-operator for modular forms for certain congruence subgroups of Sp(2,Z) and weight k = 4, where the standard techniques (Poincare series or Klingen-Eisenstein series) are no longer available. Our main tools are theta series and genus versions of basis problems.