Published online by Cambridge University Press: 15 June 2022
We use a linear algebra interpretation of the action of Hecke operators on Drinfeld cusp forms to prove that when the dimension of the
$\mathbb {C}_\infty $
-vector space
$S_{k,m}(\mathrm {{GL}}_2(\mathbb {F}_q[t]))$
is one, the Hecke operator
$\mathbf {T}_t$
is injective on
$S_{k,m}(\mathrm {{GL}}_2(\mathbb {F}_q[t]))$
and
$S_{k,m}(\Gamma _0(t))$
is a direct sum of oldforms and newforms.