Slopes of modular forms and the Ghost conjecture

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.