+1 for a diagram chase through history. Very nice.

Ah, great. Thanks for coming to the rescue, Jack -- I was getting pretty turned around.

I don't think you had to torch the whole thing -- I think the 2007 article you linked to claims to answer the question affirmatively, as you said.

Ah, no, it's a little more complicated, since you could have products and powers forming a complete set of conjugates. And whatever theorem comes out of this line of thinking might not be easy to implement algorithmically.

You mean Z[f_1,f_2,...f_n], not Z[f_1f_2...f_n], right? I suspect it's if and only if your f_i's contains a set of Galois conjugate polynomials up to constant multiples, or something to that effect.

@Lucas: Ah, nice point. I'd been 2-focused on 2-forms to notice the 1-form relation. @Will: Ah, yes, I'd heard that name as a reference as well. Thanks for the references. I'll go check them out. (Or if you or anyone else can explain the tie-in, I'd be happy to accept the answer, even if it doesn't fully finish off the question.)

Oh, sure. I meant that the ability to learn about Maass forms by playing with already-working code would be a nice primer, not that your document would be a polished introduction to the topic.

+1 for a clever use of MO. What language is the code in? I would personally find a primer to Maass forms via documented (or at least clear) SAGE code very appealing!

Thanks. Should be fixed up now -- anything dumb left is more likely ignorance than a typo.