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We find formal and holomorphic normal forms for a class of meromorphicconnections (the so-called $(TE)$-structures) over the irreducible$2$-dimensional globally nilpotent $F$-manifold germ $\mathcal N_{2}$. We findnormal forms for Euler fields on $\mathcal N_{2}$ and we characterize the Eulerfields on $\mathcal N_{2}$ which are induced by a $(TE)$-structure.

(TE)-structures over the irreducible 2-dimensional globally nilpotent F-manifold germ