Bounds for the coefficients of cusp forms for Gamma(0)(3)

Abstract

We give bounds of the coefficients of cusp forms f for Gamma(0)(3) in terms of its first d(k) numbers of coefficients off and f vertical bar W-k(3), where W-3 is the Fricke involution of level 3, and d(k) is the dimension of the space S-k (Gamma(0) (3)) of weight k cusp forms for Gamma(0)(3). In particular, we find bounds of the coefficients of cusp forms for Gamma(+)(0)(3). (C) 2018 Elsevier Inc. All rights reserved.