  We consider here a manifestly covariant quark model of the nucleon and the
Delta, where one quark is off-shell and the other two quarks form an on-shell
diquark pair. Using this model, we have shown previously that the nucleon form
factors and the dominant form factor for the gamma N -> Delta transition (the
magnetic dipole (M1) form factor) can be well described by nucleon and Delta
wave functions with S-state components only. In this paper we show that
non-vanishing results for the small electric (E2) and Coulomb (C2) quadrupole
form factors can be obtained if D-state components are added to the Delta
valence quark wave function. We present a covariant definition of these
components and compute their contributions to the form factors. We find that
these components cannot, by themselves, describe the data. Explicit pion cloud
contributions must also be added and these contributions dominate both the E2
and the C2 form factors. By parametrizing the pion cloud contribution for the
transition electric and Coulomb form factors in terms of the neutron electric
form factor, we estimate that the contributions of the Delta D-state coupled to
quark core spin of 3/2 is of the order of 1%, and the contributions of the
Delta D-state coupled to quark core spin 1/2 is of the order of 4%.
