This question already has an answer here:

- Modular forms of fractional weight 3 answers

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.