We prove an algebraic property of the elements defining Hecke operators on
period polynomials associated with modular forms, which implies that the
pairing on period polynomials corresponding to the Petersson scalar product of
modular forms is Hecke equivariant. As a consequence of this proof, we derive
two indefinite theta series identities which can be seen as analogues of
Jacobi's formula for the theta series associated with the sum of four squares.Comment: 11 pages. Published version. Forum Math., published online February
201
