Title: Generalised Hecke eigenvalues




Abstract: Eigenforms for the Hecke operators and their associated systems of Hecke eigenvalues encode rich arithmetic information, notably the frobenius traces of two dimensional Galois representations. In settings where suitable spaces of modular forms fail to be  semisimple over the Hecke algebra,  generalised eigenspaces are also related to a plethora of invariants related to  extension classes of Galois representations and (higher) Chow groups. We will illustrate this principle by discussing two examples, arising in the space of p-adic overconvergent modular forms of weight one and in the space of mod p modular forms of weight two. This is an account of joint works with Alice Pozzi and Jan Vonk.


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