Recently, the interaction between Fourier transform and deep learning has opened new avenues for long-term time series forecasting (LTSF). However, most of the existing studies do not provide sufficient interpretation of frequency domain features, resulted from inappropriate designs such as independent channels for real and imaginary parts. Rethinking the Fourier transform from a pure basis perspective, the real and imaginary parts of the frequency spectrum can be interpreted as the coefficients of cosine and sine basis functions over tiered frequency levels, respectively. This indicates that crucial information is associated with the amplitude and arctangent of the real and imaginary values rather than the values themselves. The amplitude controls the energy and the arctangent determines the starting cycle. Further, the ambiguity of actual frequency arises when the mapping is conducted in the frequency space without recognizing the distinct interpretations of input and output spectrums due to the differences between their series lengths. Accordingly, a Fourier basis mapping model FBM addresses these issues differently from existing approaches. FBM (i) embeds the discrete Fourier transform with basis functions, and then (ii) introduces a linear or nonlinear mapping network to replace the inverse discrete Fourier transform. FBM captures implicit frequency features while preserving temporal characteristics. It outperforms the Fourier and Transformer based methods with the state-of-the-art LTSF results on eight real-world datasets.