The transformer architecture has catalyzed revolutionary advances in language modeling. However, recent architectural recipes, such as state-space models, have bridged the performance gap. Motivated by this, we examine the benefits of Convolution-Augmented Attention (CAT) layer for recall, copying, and length generalization tasks. CAT incorporates convolutional filters in the K/Q/V embeddings of an attention layer. Through CAT, we show that the locality of the convolution synergizes with the global view of the attention. Unlike existing architectures such as Mamba or transformer, CAT can provably solve the associative recall(AR) and copying tasks using a single layer while also enjoying guaranteed length generalization. Evaluations on real datasets corroborate our findings and demonstrate that CAT and its more sophisticated variations indeed enhance the language modeling performance.