Modular forms for the Weil representation induced from isotropic subgroups

Abstract

For an isotropic subgroup H of a discriminant form D there exists a lift from modular forms for the Weil representation of the discriminant form $H^{\perp }/H$ to modular forms for the Weil representation of D. We determine a set of discriminant forms such that all modular forms for any discriminant form are induced from the discriminant forms in this set. Furthermore for any discriminant form in this set there exist modular forms that are not induced from smaller discriminant forms.