Where does a modulation from the home key to the new key in the exposition of the sonata form take place?

In the exposition of the sonata form, the modulation from the home key to the new key typically occurs at the transition or bridge section, which follows the first theme. This transition prepares for the introduction of the second theme, which is usually presented in a contrasting key, often the dominant key in major works. This modulation is crucial for establishing the tonal framework for the development section that follows.