  For an optimal modular parametrization $J_0(n) \twoheadrightarrow E$ of an
elliptic curve $E$ over $\mathbb{Q}$ of conductor $n$, Manin conjectured the
agreement of two natural $\mathbb{Z}$-lattices in the $\mathbb{Q}$-vector space
$H^0(E, \Omega^1)$. Multiple authors generalized his conjecture to higher
dimensional newform quotients. We prove the Manin conjecture for semistable
$E$, give counterexamples to all the proposed generalizations, and prove
several semistable special cases of these generalizations. The proofs establish
general relations between the integral $p$-adic etale and de Rham cohomologies
of abelian varieties over $p$-adic fields and exhibit a new exactness result
for Neron models.
