At the DeKalb conference on Hilbert's problems, John Tate gave a masterly survey of Problem 9, the General Reciprocity Law. He ends with a discussion of the Langlands Programme, especially the case of odd Artin representations $R$ of degree $2$. Let me quote from the final paragraph of the written version of his talk :

Another reason for the relationship's eluding Artin and Hecke may be the fact that explicit non-dihedral numerical examples are hard to find. Indeed at the time of the DeKalb conference, none was known ! I concluded the oral presentation of the paper there by explaining that, in the hope of finding one, I had looked for non-dihedral $R$'s of low conductor, $N$, and had found an $R$ with $N=133=7\cdot19$ which I hoped might be amenable to computation. After the talk, Atkin suggested that the labor involved might be considerably reduced by systematic use of $w_7$ and $w_{19}$. Armed with his theory of the $w$'s, four Harvard students, D. Flath, R. Kottwitz, J. Tunnell, J. Weisinger and I succeeded in the next month in proving (by relatively easy hand computation) the existence of the corresponding new form $f_R$ of weight $1$ and level $133$ predicted by Langlands.

My first question is : what was $R$ ? The second question is : how would you verify today (on a computer) the existence of $f_R$, without invoking any of the theorems which have been proved in the meantime ?