With the explosive growth of data, tensor processing has emerged as a pivotal component of the next generation of artificial intelligence (AI) algorithms. Current photonic convolutional processors transform tensor convolutions into multi-channel general matrix multiplication (GeMM), which follows the path of electronic counterparts, leading to data replication and hardware complexity. In this study, we experimentally and theoretically demonstrate a photonic tensor processing unit (PTPU) with a single modulator, which offers a more concise approach for multi-channel standard tensor convolution processing, different from the channel-wise convolution method. By executing multi-tensor parallel computing instead of multi-channel parallel computing, PTPU can directly produce feature tensors without clock synchronization and delay compensation between multiple channels and allows more release of physical hardware resources. Furthermore, an integrated array of semiconductor optical amplifiers (SOAs) are used to be photonic synapses for programmable weight bank, demonstrating record-high precision of 9.2 bits for weights. In the proof-of-concept experiment, we extracted features from a 3-channel (RGB) image in horizontal and vertical directions, using integrated multi-wavelength photonic tensor kernels. We then built a 3D convolutional neural network to predict the presence of COVID-19 based on computer tomography (CT) scan data consisting of 64-channel tensors.