Sequence of families of lattice polarized K3 surfaces, modular forms and degrees of complex reflection groups

We introduce a sequence of families of lattice polarized K3 surfaces. This sequence is closely related to complex reflection groups of exceptional type. Namely, we obtain modular forms coming from the inverse correspondences of the period mappings attached to our sequence. We study a non-trivial relation between our modular forms and invariants of complex reflection groups. Especially, we consider a family concerned with the Shephard-Todd group No.34 based on arithmetic properties of lattices and algebro-geometric properties of the period mappings.