On the modularity of three Calabi-Yau threefolds with bad reduction at 11

The modularity of rigid Calabi-Yau threefolds over Q has recently been established for a huge class of manifolds (cf. [DM]). However, the number of explicit examples of modular (rigid and non-rigid) Calabi-Yau threefolds is still quite small (cf. [Y]). As a consequence, only a few primes of bad reduction, combining to the level of the associated newform, have appeared in those examples which cannot be derived from others by a change of coordinates. To my knowledge these primes are 2,3,5,7,17,73. Hence I found it worth investigating the modularity of three nodal Calabi-Yau threefolds which turn out to have bad reduction at 11.