Summary: The author studies an analog over an imaginary quadratic field \(K\) of Serre’s conjecture for modular forms. Given a continuous irreducible representation \(\rho:\text{Gal} (\overline \mathbb{Q}/K)\to \text{GL}_2 (\overline \mathbb{F}_l)\) he asks if \(\rho\) is modular. He gives three examples of representations \(\rho\) obtained by restriction of even representations of \(\text{Gal} (\overline\mathbb{Q}/ \mathbb{Q})\). 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.