  We have used the PIBETA large acceptance detector for a precise measurement
of the $\pi^+ \to e^+\nu\gamma$ radiative decay at rest, with broad phase space
coverage. Using the CVC value for the pion vector form factor, $F_V =
0.0259(5)$, we have obtained a new value of the pion axial-vector form factor
$\gamma = F_A/F_V = 0.429(14)$. However, significant deviations from the SM
predictions are evident in our data. The discrepancy can be accounted for by
introducing a pion tensor form factor of $F_T = -0.0016(3)$. The question of
the true nature of the observed deviations remains open pending further
theoretical and experimental study.
