Finance vs. Economics & CS

I am currently a sophomore at a non-Ivy target school, and my main interests are finance and tech. I have not declared a major at this time, because that is done after the second year at my school. I have already taken some business/lower-level finance classes, some economics classes, and have some background in programming. Ideally, I would prefer to double-major in finance and computer science, but due to the classes that each of these majors require and some other factors, I am not able to double-major in these two areas. However, it is possible to major in economics and CS.

My dilemma becomes: do I major in finance alone, do I pursue the economics/CS double-major?

While I could take another CS class or two as a finance major, I would not have the CS background I would need to be able to put it on a resume or do anything very meaningful with it in the corporate world.

On the other hand, I am afraid that if I do not pursue a major in finance that I will miss out on specific classes about debt, equity, modeling, and other things that I will not take as an economics major.

I have already had internships in private wealth management and business valuation, but the main job fields that I am looking into at this point are investment banking, private equity, and venture capital. I know that IB is a great gateway into PE and VC, so I am looking into internships in IB this summer and next (like thousands of other students in my situation).

I know that BBs like to see technical backgrounds like CS and physics, so I think that a CS degree could help, but I also know that many of the interns they hire are finance majors. What do you guys think would be the best route to take?