  It is known that there is an one-to-one correspondence among the space of
cusp forms, the space of homogeneous period polynomials and the space of
Dedekind symbols with polynomial reciprocity laws. We add one more space, the
space of quantum modular forms with polynomial period functions, to extend
results from Fukuhara. Also, we consider Hecke operators on the space of
quantum modular forms and construct new quantum modular forms.
