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We consider rigid Calabi--Yau threefolds defined over $\QQ$ and the questionof whether they admit quadratic twists. We give a precise geometric definitionof the notion of a quadratic twists in this setting.  Every rigid Calabi--Yau threefold over $\QQ$ is modular so there is attachedto it a certain newform of weight 4 on some $\Gamma_0(N)$. We show thatquadratic twisting of a threefold corresponds to twisting the attached newformby quadratic characters and illustrate with a number of obvious and not soobvious examples.  The question is motivated by the deeper question of which newforms of weight4 on some $\Gamma_0(N)$ and integral Fourier coefficients arise from rigidCalabi--Yau threefolds defined over $\QQ$.

Quadratic twists of rigid Calabi-Yau threefolds over $\QQ$