This paper introduces HINER, a novel neural representation for compressing HSI and ensuring high-quality downstream tasks on compressed HSI. HINER fully exploits inter-spectral correlations by explicitly encoding of spectral wavelengths and achieves a compact representation of the input HSI sample through joint optimization with a learnable decoder. By additionally incorporating the Content Angle Mapper with the L1 loss, we can supervise the global and local information within each spectral band, thereby enhancing the overall reconstruction quality. For downstream classification on compressed HSI, we theoretically demonstrate the task accuracy is not only related to the classification loss but also to the reconstruction fidelity through a first-order expansion of the accuracy degradation, and accordingly adapt the reconstruction by introducing Adaptive Spectral Weighting. Owing to the monotonic mapping of HINER between wavelengths and spectral bands, we propose Implicit Spectral Interpolation for data augmentation by adding random variables to input wavelengths during classification model training. Experimental results on various HSI datasets demonstrate the superior compression performance of our HINER compared to the existing learned methods and also the traditional codecs. Our model is lightweight and computationally efficient, which maintains high accuracy for downstream classification task even on decoded HSIs at high compression ratios. Our materials will be released at https://github.com/Eric-qi/HINER.