in this question counterexample: degree of representation $\leq$ index of normal subgroup there was the answer (in the second comment under the answer), that the dihedral group $D_5$ hat exactly 3 irreducible representations over $\mathbb{F}_3$ (or $\mathbb{F}_{13}$): Two with dimension 1 and one faithful irreducible with dimension 4. But according to Wedderburn I should have $ 10 = dim_{\mathbb{F}_3} \mathbb{F}_3 [D_5] = 2 \cdot 1 + 1 \cdot 4 $ (two 1-dimensional and one 4-dimensional). Where is my mistake?
Khanna