BLOCH model wave functions and pseudopotentials for all fractional Chern insulators. 
We introduce a Bloch-like basis in a C-component lowest Landau level fractional quantum Hall (FQH) effect, which entangles the real and internal degrees of freedom and preserves an N(x)×N(y) full lattice translational symmetry.  We implement the Haldane pseudopotential Hamiltonians in this new basis.  Their ground states are the model FQH wave functions, and our Bloch basis allows for a mutatis mutandis transcription of these model wave functions to the fractional Chern insulator of arbitrary Chern number C, obtaining wave functions different from all previous proposals.  For C>1, our wave functions are related to color-dependent magnetic-flux inserted versions of Halperin and non-Abelian color-singlet states.  We then provide large-size numerical results for both the C = 1 and C = 3 cases.  This new approach leads to improved overlaps compared to previous proposals.  We also discuss the adiabatic continuation from the fractional Chern insulator to the FQH in our Bloch basis, both from the energy and the entanglement spectrum perspectives.