Nonhomogeneous $G$-spaces of compact Lie groups

The group $A(K)/N$ is computed, where $A(K)$ is the group of points of a Tate curve over a local field while $N$ is the group of universal norms from the group of points over a $\Gamma$-extension. As an application, the Mazur $l$-modulus of modular elliptic curves is computed for values of $l$ dividing the denominator of the absolute invariant.