UCLA

For a quaternion algebra B over a totally real field F unramified at every finite place and ramified most at infinite places of F, we prove that the space of Z[1/E]$-integral Hilbert modular forms of weight 2 and of level 1 is spanned over Z[1/E] by the theta series of the norm form of B. Here E is an explicit constant given by the product of 6, the discriminant of F and the value at -1 of Hecke L-functions of conductor 1.