  Deformed states in $^{40}$Ca are investigated with a method of
antisymmetrized molecular dynamics. Above the spherical ground state,
rotational bands arise from a normal deformation and a superdeformation as well
as an oblate deformation. The calculated energy spectra and $E2$ transition
strengths in the superdeformed band reasonably agree to the experimental data
of the superdeformed band starting from the $0^+_3$ state at 5.213 MeV. By the
analysis of single-particle orbits, it is found that the superdeformed state
has particle-hole nature of an $8p$-$8h$ configuration. One of new findings is
parity asymmetric structure with $^{12}$C+$^{28}$Si-like clustering in the
superdeformed band. We predict that $^{12}$C+$^{28}$Si molecular bands may be
built above the superdeformed band due to the excitation of inter-cluster
motion. They are considered to be higher nodal states of the superdeformed
state. We also suggest negative-parity bands caused by the parity asymmetric
deformation.
