Lower Bounds for Slopes of Overconvergent Eigenforms

Let p ≥ 3 be a prime and suppose G is a form of a reductive group, that is compact at infinity and splits at p. Under these assumptions, we can estimate the slopes in the corresponding eigenvariety by finding the lower bound of the Newton polygon of the compact Hecke operator in the spirit of the 2017 paper of Liu, Wan and Xiao. In case GSp₄, we obtain a sharper estimate.