The topological modular forms of RP2$\mathbb {R}P boolean AND 2$ and RP2 boolean AND CP2$\mathbb {R}P boolean AND 2 \wedge \mathbb {C}P boolean AND 2$

We study the elliptic spectral sequence computing tmf*(RP2)$tmf_*(\mathbb {R}P<^>2)$ and tmf*(RP2 perpendicular to CP2)$tmf_* (\mathbb {R} P<^>2 \wedge \mathbb {C} P<^>2)$. Specifically, we compute all differentials and resolve exotic extensions by 2, eta$\eta$, and nu$\nu$. For tmf*(RP2 perpendicular to CP2)$tmf_* (\mathbb {R} P<^>2 \wedge \mathbb {C} P<^>2)$, we also compute the effect of the v1$v_1$-self maps of RP2 perpendicular to CP2$\mathbb {R} P<^>2 \wedge \mathbb {C} P<^>2$ on tmf$tmf$-homology.