Affiliation:
1. The Institute of Mathematical Sciences A CI of Homi Bhabha National Institute Chennai India
Abstract
AbstractIn 2008, Soundararajan showed that there exists a normalized Hecke eigenform of weight and level one such that
for sufficiently large . In this note, we show that for any and for all sufficiently large , the number of normalized Hecke eigenforms of weight and level one for which
is . For an odd fundamental discriminant , let be the set of all cuspidal normalized Hecke eigenforms of weight and level dividing . When the real primitive Dirichlet character satisfies , we investigate the number of for which takes extremal values.