I was trying to read through some note by Kowalski (see https://people.math.ethz.ch/~kowalski/ik-ant-exp-sums.pdf). I was interested in trying to understand the following. The author states on page 313 that "One can also think this way about the real character sums with cubic polynomials; they are coefficients of a cusp form associated with an elliptic curve..." I assume that the author is referring to real-valued sums of the form $$\sum_{t\in (\mathbb{F}_q)^{\times}} \psi \big(f(t)\big),$$ where $\psi$ is an additive character on $\mathbb{F}_q$ (field with $q$ elements) and $f(t)\in \mathbb{F}_q[t]$ is a polynomial of degree 3.
First off, I'm sorry about the vague question. I really don't much about this subject, and I'm just curious. I would like if somebody gave a short (if possible) explanation how one can think of these sums as the coefficients of a cusp form. Or point me to a reference. Thanks!