On minima of theta and Epstein zeta functions in dimension four

Let the theta and Epstein zeta functions be $Θ(α,L)=\sum_{v\in L}e^{-πα|v|^2}$ for $α>0$ and $E(L,s)=\sum_{v\in L\setminus\{0\}}{|v|^{-2s}}$ for $s>2$, respectively. We consider full-rank lattices $L\subset\mathbb R^4$. Let the covolume of $L$ be one, and let $\mathcal D_4=2^{-1/4}D_4$ be the root l