  To every $n$-dimensional lens space $L$, we associate a congruence lattice
$\mathcal L$ in $\mathbb Z^m$, 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 $\|\cdot\|_1$-length in $\mathcal L$. 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 $\|\cdot\|_1$-isospectral (resp.\
$\|\cdot\|_1$-isospectral plus a geometric condition). Using this fact, we
give, for every dimension $n\ge 5$, infinitely many examples of Riemannian
manifolds that are isospectral on every level $p$ and are not strongly
isospectral.
