Newforms are a type of mathematical structure that generalizes the concept of modular forms. They arise in the study of number theory and algebraic geometry, particularly in the context of modular forms associated with elliptic curves. Newforms are often used to understand the properties of L-functions and their connections to automorphic forms. In essence, newforms can be thought of as a special class of modular forms that have certain symmetries and properties. They are typically expressed in terms of Fourier coefficients and play a crucial role in various areas of mathematics, including representation theory and the proof of the Taniyama-Shimura-Weil conjecture.