SENATUS POPULUSQUE ROMANUS - S.P.Q.R.
The abbreviation S.P.Q.R. is always used correctly, but its full name is quite often mispelt or incorrectly written or spoken. I have come across all sorts of incorrect case combinations. The last one that I came across today, and which prompted me to write this page, was written as: "populis romanirorum". Now then, the word "populis" is the dative case of populus hence its spelling is correct, but grammatically incorrect as in this instance we want the nomivative case and not the dative. In the context of the specific example I referred to the error is likely to be a spelling error as the text was part of the transcript of a video lecture in practical philosophy given by Prof. Luke T. Johnson of Emory University (USA). In his speech he did say "populus" and not "populis". Also, the second word "romanirorum" is another mis-pelling by the person conducting the transliteration. The correct term should be "romanorum" if one needs the genitive case. But, in this expression you do not need the genitive but the simple nominative case, hence "romanus". Thus, the proper and correct expression is simply the one shown in large capitals above and which I repeat hereafter for the sake of closure of this statement: Senatus Populusque Romanus which translates as The Senate and the People of Rome. The conjuction "que" is added to the word "pupulus" as explained in Lesson 3/Conjunctions.
In conclusion the correct term to use is always Senatus Populusque Romanus, S.P.Q.R. Don't ask why in the abbreviation we have P.Q. and not simply PQ. This is a convention. Some advanced scholars suggest that S.P.Q.R. can also stand for "Senatus Populus Quiritium Romanus" which translates as "The Senate and the Roman People of the Quirites". But, unless you know how to explain your way out of Quiris, which means Roman citizen, I suggest you forget about this second and academic definition which is both true and false! The existing epigraphic evidence and the literature points always to Senatus Populusque Romanus.
Here is an image of the epigraphic inscription at the base of Trajan's Column in Rome. Note the first line - Senatus Populusque Romanus - written in full rather than as an abbreviation. The abbreviation SPQR can be seen on the Arch of Constantine in Rome, and of course, in many other epigraphic inscriptions.
A better image and full text can be seen on this recommended link: