  We show that the Eigenvariety attached to Hilbert modular forms over a
totally real field $F$ is smooth at the points corresponding to certain
classical weight one theta series and we give a precise criterion for etaleness
over the weight space at those points. In the case where the theta series has
real multiplication, we construct a non-classical overconvergent generalised
eigenform and compute its Fourier coefficients in terms of $p$-adic logarithms
of algebraic numbers. Our approach uses deformations and pseudo-deformations of
Galois representations.
