Slopes of modular forms and the Ghost conjecture

Abstract: We give an algorithm to compute the slope sequence of modular forms with fixed Galois components from its first few entries, which is a refined version of the conjecture of [Buz05]. We use the results of arXiv:2302.07697 on the ghost conjecture from axXiv:1710.01572. These symmetries in slope sequences have potential implication to unexplained symmetries in many Coleman-Mazur eigencurves.