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I need a good reference about the connection between modular forms and line bundles. I found only Milne's note that treats briefly this argument. I've already checked, but without finding anything, many books such as:

  • "A first course in modular forms - F. Diamond, J. Shurman"
  • "Elliptic curves and modular forms - N.Koblitz"
  • "Modular Forms - Miyake"
  • "A course in arithmetic - J.P.Serre" (the last chapter)
  • "Complex analysis - E.Freitag, R.Busam"
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    ... more likely, a "non-modular" reading that treats "line bundles" might provide some illumination of _that_ general idea. In fact, you should read about "vector bundles", to better understand the simplest case, "line bundles". Sources on algebraic geometry, even "just" analytic geometry, such as Griffiths-Harris, discuss vector bundles (and line bundles) at great length. Looking at such sources you will see that, in the basic complex-analytic context, saying "line bundle" adds little to the discussion of modular forms.2012-09-25

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