Integral magneticity of the level-two K3 packet: CM theta lifts and a 2-isogeny trace contraction

Bönisch, Duhr, and Maggio introduced three meromorphic modular forms $C_4,C_{6a},C_{6b}$ on ${\mathrm{\Gamma }}_0(2)$, arising from a hypergeometric K3 family, and conjectured that they are magnetic of depths $1,2,2$. Writing $$C_4=\sum _{n\ge 1}{c}_4(n)q^n,C_{6a}=\sum _{n\ge 1}{c}_{6a}(n)q^n,C_{6b}=\sum _{n\ge 1}{c}_{6b}(n)q^n,$$ we prove the stronger denominator-one statements $$\frac{c_4(n)}{n},\frac{c_{6a}(n)}{n^2},\frac{c_{6b}(n)}{n^2}\in \mathbb{Z}(n\ge 1)\mathrm{.}$$ The weight-four case is reduced to a termwise binomial divisibility by a hypergeometric change of Hauptmodul. For weight six we identify the two forms with canonical level-two CM forms of discriminants $-8$ and $-4$: $$f_{3,-8,0,1,1}=-64C_{6a},f_{3,-4,2,1,1}=32C_{6b}\mathrm{.}$$ An explicit pair of vector-valued weakly holomorphic forms of weight $-3\mathrm{/}2$ then gives the full odd-prime divisibility through the higher-level theta-lift coefficient formula of Löbrich–Schwagenscheidt. The prime $2$ is treated independently. If $t=(\eta (2\tau )\mathrm{/}\eta (\tau ){)}^{24}$, $H=\eta (\tau {)}^4\mathrm{/}\eta (2\tau {)}^2$, $J=2E_2(2\tau )-E_2(\tau )$, $u=64t$, and $\mathcal{T}=H^{4}J$, we prove the infinite-family contraction $$U_2(\mathcal{T}t{\mathbb{Z}}_2[[u]])\subseteq 2^5\mathcal{T}t{\mathbb{Z}}_2[[u]]\mathrm{.}$$ Consequently $v_2(c_{6\bullet }(2^{r}m))\ge 5r$, which is stronger than the slope $2r$ required for double magneticity. Thus the complete level-two K3 packet is magnetic with global denominator one.