  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.

Number Theory;Representation Theory