To every n-dimensional lens space L, we associate a congruence lattice
L in Zm, with n=2m−1 and we prove a formula relating
the multiplicities of Hodge-Laplace eigenvalues on L with the number of
lattice elements of a given ∥⋅∥1​-length in L. As a
consequence, we show that two lens spaces are isospectral on functions (resp.\
isospectral on p-forms for every p) if and only if the associated
congruence lattices are ∥⋅∥1​-isospectral (resp.\
∥⋅∥1​-isospectral plus a geometric condition). Using this fact, we
give, for every dimension n≥5, infinitely many examples of Riemannian
manifolds that are isospectral on every level p and are not strongly
isospectral.Comment: Accepted for publication in IMR