  We outline a numerical procedure to incorporate the crystal symmetries in the
Helmholtz Fermi-surface harmonics basis set, which are the solutions of the
Helmholtz equation defined on the Fermi surface. This improvement allows for an
optimal representation of anisotropic quantities defined on the Fermi surface
in terms of few symmetric elements of the set. We demonstrate the general
validity of our approach by identifying the fully symmetric Helmholtz
Fermi-surface harmonics subset for several representative systems with
different crystal structures, namely, FCC-Cu, HEX-MgB$_2$, and BCC-YH$_6$.
Furthermore, we illustrate the potential of the method applied to the
electron-phonon problem, showing that the anisotropic electron-phonon
mass-enhancement parameter $\lambda_{\bf k}$ can be represented to high
accuracy by a handful of coefficients. This works as an effective filter,
paving the way for a reduction of several orders of magnitude in the
computation of superconductivity, impurity problems, or any other Fermi surface
dependent property of metals from first principles.

Materials Science;Computational Physics