On the trace and norm maps from Γ0(p) to GL2(A)

Let f be a Drinfeld modular form for Γ0(p). From such a form, one can obtain two forms for the full modular group GL2(A): by taking the trace or the norm from Γ0(p) to GL2(A). In this paper we show some connections between the arithmetic modulo p of the coefficients of the u-series expansion of f and those of a form closely related to its trace, and of the coefficients of f and those of its norm.