Thank you! Do you know of a reference for the SL(3, Z) case?

You're right that the term I used is shaky, but let's say anything non-holomorphic. For example, in the case of GSp4 we could refer to modular forms associated to generic representations gsp4.org/cat-browser.php?categoryID=199 Thanks for the response so far!

Thanks, I got blindsighted by the fact it was hosted on his website.

Isn't the transpose its own inverse?

For a while, I thought Piatetski-Shapiro...

I assume you mean on the whole complex plane. The power series coefficients come from C, so there are very few meromorphic functions with integer coefficients. Certainly 1/z^k * f(z) for f(z) = e(z), sin(z), cos(z), but it's hard to say something specific. Can you expound on your question?

i.e. geometry without specifying a base

Seems like a homework problem. You may have more luck posting this on math.stackexchange