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The isotropy of multiples of Pfister forms is studied. In particular, animproved lower bound on the value of their first Witt index is obtained. Thisresult and certain of its corollaries are applied to the study of the weakisotropy index (or equivalently, the sublevel) of arbitrary quadratic forms.The relationship between this invariant and the level of the (quadratic) formis investigated. The problem of determining the set of values of the weakisotropy index of a form with respect to field extensions is addressed, withboth admissible and inadmissible integers being determined. The analogousinvestigation with respect to the level of a form is also undertaken, with somequestions asked by Berhuy, Grenier-Boley and Mahmoudi being resolved. Anexamination of the weak isotropy index and the level of round and Pfister formsconcludes this article.

Isotropy of multiples of Pfister forms and weak isotropy of forms over field extensions