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I know that theta series are modular forms of weight 1/2 and I have read about modular forms of other fractional weights. Does anybody have an explicit example of a modular form of weight e. g. 1/3 or 1/4?
I thought that in analogy with theta series one could define for example $\sum_{n\in \mathbb Z}q^{n^4}$, but I don't know how to continue.

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marked as duplicate by abx, Henry.L, Community Sep 4 '17 at 19:22

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  • $\begingroup$ @abx Thisone is a little too theoretical for most people. Is there a simple case to look at, with say $\prod_{\sigma} f^{\sigma}$ a well-known modular form ? $\endgroup$ – reuns Sep 4 '17 at 19:04

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