Wavetable synthesis generates quasi-periodic waveforms of musical tones by interpolating a list of waveforms called wavetable. Studies in wavetable generation with invertible architecture have arisen recently. However, it is still challenging to generate wavetables with detailed controls within the latent representation. In response, we present Wavespace, a framework for wavetable generation that empowers users with enhanced parameter controls. Our model allows users to apply timbral conditions to the output wavetables. Users handle a latent space factorized by each timbral group called style. Then they adjust timbral details with descriptors. This way, users can create wavetables by manipulating timbral parameters step by step. Our framework is efficient enough for practical use; we prototyped an oscillator plug-in for real-time integration of Wavespace within digital audio workspaces (DAWs).