For the measurement of social status, many studies rely on a one-dimensional operationalization, even though the theoretical background that is typically referred to -- Bourdieu's theory of capital (1986) -- suggests doing otherwise. A multi-dimensional empirical representation of social status is challenging because the indicators that are typically used in educational research cannot easily be attributed to only one form of capital. In this paper, we test a new scale for the separate measurement of economic and cultural capital. It consists of a list of socially desirable resources and activities for which respondents are asked to state whether they have/do them. In TIMSS 2015 Germany, the scale was implemented for the first time in a large-scale assessment study. Using multi-dimensional scaling, we identify two dimensions: economic and cultural capital. Conducting latent class analyses, we are able to group answers to the scale into four classes, which differ by the amount of economic (low/high) and cultural capital (low/high) students' parents possess. In multivariate analyses with student achievement, the scale shows additional explanatory power. Overall, our analyses show that economic and cultural capital can be measured separately and that social status is a multi-layered construct that requires a multi-dimensional operationalization.