  Let F be a number field and N an integral ideal in its ring of integers. Let
f be a modular newform over F of level Gamma0(N) with rational Fourier
coefficients. Under certain additional conditions, Guitart-Masdeu-Sengun
constructed a p-adic lattice which is conjectured to be the Tate lattice of an
elliptic curve E whose L-function equals that of f. The aim of this note is to
generalize this construction when the Hecke eigenvalues of f generate a number
field of degree d >= 1, in which case the geometric object associated to f is
expected to be, in general, an abelian variety A of dimension d. We also
provide numerical evidence supporting the conjectural construction in the case
of abelian surfaces.
