Adams spectral sequence of ${\mathrm{tmf}}\wedge {\mathbb {RP}}^\infty$$v_2$-periodic classes

# 2 $v_2$-periodic classes

We next look at the five brown classes. There is not much interesting to say about them. They have no periodicity apart from $v_2^8$. For degree reasons, only $x_{16, 3}$ can potentially hit something, but the target is $v_1$ periodic while this is not. Note however that $v_2^8$ multiples of these need not be permanent, and indeed they will not be.