  We prove a conjecture of Udo Riese about the minimal ring of definition for
principal series Weil characters of $\text{SL}_2(\mathbb{F}_p)$, for $p$ an odd
prime. More precisely, we show that the $(p+1)/2$-dimensional Weil characters
can be realized over the ring of integers of $\mathbb{Q}(\sqrt{\varepsilon
p})$, where $\varepsilon =(-1)^{(p-1)/2}$, and we provide explicit integral
models over these quadratic rings. We do so by studying the Galois action on
the integral models of Weil characters recently discovered by Yilong Wang.
