2 problems

Local Ohno–Nakagawa duality conjecture. The Fourier dual, as a function of $L$, satisfies

Let $K$ be a $2$-adic local field and let $0\leq t\leq s\leq e=v_K(2)$. Let $C_1\subseteq C_2$ be orders in a cubic $K$-algebra $R$ with $C_2/C_1\cong\mathcal{O}_K/\pi^{s-t}$ cycli…