To be specific, do the weights have some geometric meanings? A modular form $f$ satisfies $f(\frac{az+b}{cz+d})(cz+d)^{-2k}=f(z)$, where $z\in \mathbb{C}$. $k$ or $2k$ is called the weight of $f$.
Are there any interpretations for the weights of modular forms?
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number-theory
complex-analysis
modular-forms