As part of ongoing research in student use of math in upper-division physics, we examine student understanding of Fourier analysis. Fourier series are used in a variety of physics contexts and provide the first example of non-Euclidian vector spaces for many students. This study extends previous work in which we highlighted the procedural and conceptual difficulties students have when thinking about Fourier series. Using the concept image framework, as described by Tall and Vinner, we probe how students think about the constant coefficient in front of the Fourier series representation of a function and what it means when graphing the series. We also investigate whether students use the odd or even properties of a function to eliminate terms in the Fourier series. Data were collected at a large four-year university, including nine years of written data from an intermediate-level Math Methods course as well as several interviews.