Periods and quasiperiods of modular forms and the mirror quintic at the conifold

We review the theory of periods of modular forms and extend it to quasiperiods. General motivic conjectures predict a relation between periods and quasiperiods of certain weight 4 Hecke eigenforms associated to hypergeometric one-parameter families of Calabi-Yau threefolds. We verify this prediction and discuss some of its implications on D-brane masses at the conifold on the corresponding mirrors.