Atkin–Lehner signs

An Atkin–Lehner sign is an eigenvalue $+1$ or $-1$ of an Atkin–Lehner involution acting on the newform in question, with the normalization and local hypotheses specified in the paper. These local signs are related to the sign in its functional equation.

The LMFDB explains the classical Atkin–Lehner involution; conjecture 40 studies the analogous local signs for Hilbert newforms.