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How can I prove that:

  • For a given natural number $k$ the dimension space of modular forms of weight $2k$ is $\lfloor{\frac{k}{6}\rfloor}+1$ if $k \not\equiv 1 \: (\text{mod}\ 6)$ and $\lfloor{\frac{k}{6}\rfloor}$ if $k \equiv 1 \: (\text{mod}\ 6)$
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This presumably means of level 1. Where are you learning about modular forms? Most introductory books that have this statement also prove it... –  Matt Apr 28 '12 at 19:59
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1 Answer 1

This is a very standard argument, see e.g. Corollary 2.16 of William Stein's book "Modular Forms: A Computational Approach". This is available as a free e-book; the relevant section is here:

http://modular.math.washington.edu/books/modform/modform/level_one.html#structure-theorem-for-level-1-modular-forms

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