Social norms regulate actions in artificial societies, steering collective behavior towards desirable states. In real societies, social norms can solve cooperation dilemmas, constituting a key ingredient in systems of indirect reciprocity: reputations of agents are assigned following social norms that identify their actions as good or bad. This, in turn, implies that agents can discriminate between the different actions of others and that the behaviors of each agent are known to the population at large. This is only possible if the agents report their interactions. Reporting constitutes, this way, a fundamental ingredient of indirect reciprocity, as in its absence cooperation in a multiagent system may collapse. Yet, in most studies to date, reporting is assumed to be cost-free, which collides with many life situations, where reporting can easily incur a cost (costly reputation building). Here we develop a new model of indirect reciprocity that allows reputation building to be costly. We show that only two norms can sustain cooperation under costly reputation building, a feature that requires agents to be able to anticipate the reporting intentions of their opponents, depending sensitively on both the cost of reporting and the accuracy level of reporting anticipation.