  We construct almost holomorphic and holomorphic modular forms by considering
theta series for quadratic forms of signature $(n-1,1)$. We include homogeneous
and spherical polynomials in the definition of the theta series (generalizing a
construction of the second author) to obtain holomorphic, almost holomorphic
and modular theta series. We give a criterion for these series to coincide,
enabling us to construct almost holomorphic and holomorphic cusp forms on
congruence subgroups of the modular group. Further, we provide numerous
explicit examples.
