Put $B_p := \left\{ \begin{pmatrix} a & b \\ 0 & c \end{pmatrix} \in GL_2(Q_p) : a, b, c \in Q_p \right\}$ the subgroup of upper triangular matrices in $GL_2(Q_p)$, $Q_p$ denoting the $p$-adic rationals. I have already figured out that the modularity function is
$\Delta \begin{pmatrix} a & b \\ 0 & c \end{pmatrix} = (|a|/|c|)^\lambda$ i.e. if $\mu$ is the Haar measure on $B_p$ and $M$ is a measurable set then for any $x \in B_p$, $\mu(Mx)=\Delta(x)\mu(M)$
Does anybody know how to figure out that $\lambda=1$?
Cheers,
Fabian Werner