Computing Central Values of Twisted $L$-Series: The Case of Composite Levels

Abstract

We describe a general method to compute weight-$\frac32$ modular forms ``associated'' with a given weight-$2$ modular form $f$ of level $N$, and relate its Fourier coefficients to central values of quadratic twists (real and imaginary) of $L(f,s)$. We will focus on examples for levels $N = 27$, $N = 15$, and $N=75$.