Abstract. To every n-dimensional lens space L, we associate a congruence lattice L in Z m , 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.

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