TITLE: Corollaries of the halo conjecture that do not involve the eigencurve
QUESTION [6 upvotes]: In the theory of p-adic modular forms there is a certain construction called the Coleman-Mazur eigencurve. The spectral halo conjecture roughly states that if you remove a closed subdisc of the weight space, the eigencurve is an infinite disjoint union of finite flat covers of what remains of the weight space.
For a person who does not intrinsically care about the eigencurve, what interest does the halo conjecture pose? What corollaries does it have that do not directly involve the eigencurve?

REPLY [3 votes]: There was just a paper posted by Newton and Thorne (https://arxiv.org/abs/1912.11261) on automorphy of symmetric powers of eigenforms that might be something you care about. See also a recent blog post here: https://www.galoisrepresentations.com/2019/12/30/new-results-in-modularity-christmas-update-ii/. 
Of course, you might also not care about that thing. Perhaps someone can answer you more usefully if you describe more carefully what you actually care about?