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We consider the fourteen families $W$ of Calabi-Yau threefolds with onecomplex structure parameter and Picard-Fuchs equation of hypergeometric type,like the mirror of the quintic in $\mathbb{P}^4$. Mirror symmetry identifiesthe masses of even--dimensional D--branes of the mirror Calabi-Yau $M$ withfour periods of the holomorphic $(3,0)$-form over a symplectic basis of$H_3(W,\mathbb{Z})$. It was discovered by Chad Schoen that the singular fiberat the conifold of the quintic gives rise to a Hecke eigenform of weight fourunder $\Gamma_0(25)$, whose Hecke eigenvalues are determined by the Hasse-Weilzeta function which can be obtained by counting points of that fiber overfinite fields. Similar features are known for the thirteen other cases. In twocases we further find special regular points, so called rank two attractorpoints, where the Hasse-Weil zeta function gives rise to modular forms ofweight four and two. We numerically identify entries of the period matrix atthese special fibers as periods and quasiperiods of the associated modularforms. In one case we prove this by constructing a correspondence between theconifold fiber and a Kuga-Sato variety. We also comment on simpler applicationsto local Calabi-Yau threefolds.

D-brane masses at special fibres of hypergeometric families of Calabi-Yau threefolds, modular forms, and periods