Vector-valued Eisenstein series of congruence types and their products
Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
Fourier expansion of modular forms
products of Eisenstein series
vector-valued modular forms
Pascal-salen, Matematiska vetenskaper, Chalmers tvärgata 3, Chalmers
Opponent: Associate Professor, Daniel Persson, Department of Mathematical Sciences, Chalmers University of Technology, Sweden