Most approaches to emotion analysis of social media, literature, news, and other domains focus exclusively on basic emotion categories as defined by Ekman or Plutchik. However, art (such as literature) enables engagement in a broader range of more complex and subtle emotions. These have been shown to also include mixed emotional responses. We consider emotions in poetry as they are elicited in the reader, rather than what is expressed in the text or intended by the author. Thus, we conceptualize a set of aesthetic emotions that are predictive of aesthetic appreciation in the reader, and allow the annotation of multiple labels per line to capture mixed emotions within their context. We evaluate this novel setting in an annotation experiment both with carefully trained experts and via crowdsourcing. Our annotation with experts leads to an acceptable agreement of k = .70, resulting in a consistent dataset for future large scale analysis. Finally, we conduct first emotion classification experiments based on BERT, showing that identifying aesthetic emotions is challenging in our data, with up to .52 F1-micro on the German subset. Data and resources are available at https://github.com/tnhaider/poetry-emotion.