Serre‘s Conjecture for Imaginary Quadratic Fields
We study an analog over an imaginary quadratic field K of Serre‘s conjecture for modular forms. Given a continuous irreducible representation ρ:Gal(Q/K) [rightward arrow]GL$_2$(F$_l$) we ask if ρ is modular. We give three examples of representations ρ obtained by restriction of even representations of Gal(Q/Q). These representations appear to be modular when viewed as representations over K, as shown by the computer calculations described at the end of the paper.
Key Words: modular forms; Serre‘s conjecture.; ; ; .