Sparse matrix-vector multiplication (SpMV) multiplies a sparse matrix with a dense vector. SpMV plays a crucial role in many applications, from graph analytics to deep learning. The random memory accesses of the sparse matrix make accelerator design challenging. However, high bandwidth memory (HBM) based FPGAs are a good fit for designing accelerators for SpMV. In this paper, we present Serpens, an HBM based accelerator for general-purpose SpMV, which features memory-centric processing engines and index coalescing to support the efficient processing of arbitrary SpMVs. From the evaluation of twelve large-size matrices, Serpens is 1.91x and 1.76x better in terms of geomean throughput than the latest accelerators GraphLiLy and Sextans, respectively. We also evaluate 2,519 SuiteSparse matrices, and Serpens achieves 2.10x higher throughput than a K80 GPU. For the energy/bandwidth efficiency, Serpens is 1.71x/1.99x, 1.90x/2.69x, and 6.25x/4.06x better compared with GraphLily, Sextans, and K80, respectively. After scaling up to 24 HBM channels, Serpens achieves up to 60.55 GFLOP/s (30,204 MTEPS) and up to 3.79x over GraphLily. The code is available at https://github.com/UCLA-VAST/Serpens.