  Given a Hilbert cuspidal newform $g$ we construct a family of modular forms
of half-integral weight whose Fourier coefficients give the central values of
the twisted $L$-series of $g$ by fundamental discriminants.
  The family is parametrized by quadratic conditions on the primes dividing the
level of $g$, where each form has coefficients supported on the discriminants
satisfying the conditions. These modular forms are given as generalized theta
series and thus their coefficients can be effectively computed.
  Our construction works over arbitrary totally real number fields, except that
in the case of odd degree the square levels are excluded. It includes all
discriminants except those divisible by primes whose square divides the level.
