We study p-adic families of cohomological automorphic forms for GL(2) over imaginary quadratic fields and prove that interpolating a Zariski-dense set classical cuspidal only occur under very restrictive conditions. show how to computationally determine when this is not the case establish concrete examples finitely many Bianchi modular forms.

Abstract. Let f(z) = q ∏∞ n=1(1−q) be a modular form on SL2(Z). Formal logarithmic differentiation of f yields a q-series g(z) := h −∞n=1 ∑ d|n c(d)dq n whose coefficients are uniquely determined by the exponents of the original form. We provide a formula, due to Bruinier, Kohnen, and Ono for g(z) in terms of the values of the classical j-function at the zeros and poles of f(z). Further, we giv...

Let F be a totally real field and ρ : Gal(F/F )→ GL2(Fp) a Galois representation whose restriction to a decomposition group at some place dividing p is irreducible. Suppose that ρ is modular of some weight σ. We specify a set of weights, not containing σ, such that ρ is modular for at least one weight in this set. Let F be a totally real field and p a prime, and consider a Galois representation...

The theory of overconvergent modular symbols was created by Glenn Stevens over 20 years ago, and since then the subject has had many generalizations and applications central to modern number theory (e.g. overconvergent cohomology, eigenvarieties of reductive groups, families of p-adic L-functions, just to name a few). In these notes, rather than give a systematic development of the general theo...