A child's environment is thought to be composed of different levels that interact with their individual genetic propensities. However, studies have not tested this theory comprehensively across multiple environmental levels. Here, we quantify the contributions of child, parent, school, neighbourhood, district, and municipality factors to achievement, and investigate interactions between polygenic indices for educational attainment (EA-PGI) and environmental levels. We link population-wide administrative data on children's standardised test results, schools and residential identifiers to the Norwegian Mother, Father, and Child Cohort Study (MoBa), which includes >23,000 genotyped parent-child trios. We test for gene-environment interactions using multilevel models with interactions between EA-PGI and random effects for school and residential environments (thus remaining agnostic to specific features of environments). We use parent EA-PGI to control for gene-environment correlation. We found an interaction between students' EA-PGI and schools suggesting compensation: higher-performing schools can raise overall achievement without leaving children with lower EA-PGI behind. Differences between schools matter more for students with lower EA-PGI, explaining 4 versus 2% of the variance in achievement for students 2 SD below versus 2 SD above the mean EA-PGI. Neighbourhood, district, and municipality variation contribute little to achievement (<2% of the variance collectively), and do not interact with children's individual EA-PGI. Policy to reduce social inequality in achievement in Norway should focus on tackling unequal support across schools for children with difficulties.