Binary quadratic forms of odd class number

Let -D be a fundamental discriminant. We express the number of representations of an integer by a positive definite binary quadratic form of discriminant -D with an odd class number h (-D) as a rational linear expression involving the Kronecker symbol (-D. ) and the Fourier coefficients of certain cusp forms. We prove these cusp forms have eta quotient representations only if D=23. This provides, using theta functions, a generalization of a result of F. van der Blij from 1952 for binary quadratic forms of discriminant -23 to the case of forms of discriminant -D with odd h (-D). We also study the eta quotient representations of some related theta functions.