[1][2] In the classical elliptic modular form theory, the Hecke operators Tn with n coprime to the level acting on the space of cusp forms of a given weight are self-adjoint with respect to the Petersson inner product.
[3] Therefore, the spectral theorem implies that there is a basis of modular forms that are eigenfunctions for these Hecke operators.
[4][5] In the case treated by Mordell, the space of cusp forms of weight 12 with respect to the full modular group is one-dimensional.
[8][9][10] It was introduced by Peter Schneider in 2015 who, together with Rachel Ollivier, used them to study the p-adic Langlands correspondence.
[8][9][10][11] It is the subject of several conjectures on the cohomology of arithmetic groups by Akshay Venkatesh and his collaborators.