The space of test functions of the space $\mathcal S'^{(M_\alpha)}$ of tempered ultradisributions of Beurling type [4] is determined by several equivalent families of norms. Two representation theorems of the space $\mathcal S'^{(M_\alpha)}$ are proved. The operations of differentiation, ultradifferentiation and multiplication on $\mathcal S'^{(M_\alpha)}$ are investigated and the space of multipliers of the space $\mathcal S'^{(M_\alpha)}$ is determined.