Give the values of one row of the character table of $D_{10}$ corresponding to a character of degree $2$
I know the conjugacy classes of $D_{10}$, the dimensions of the irreducible representations and the number of irreps of each dimension.
Also the character of a representation $\pi$ is $\chi(g)=tr(g\pi)$.
Can I use this information to connstruct the table? I am really stuck on this one.
Also, does a degree 2 character mean that the vector space is of dimension $2$?
Thanks