This is a report on recent work, with Wen-Ching Winnie Li and Ling Long. In that work explicit formulas are given, involving hypergeometric character sums, for the traces of Hecke operators $T_p$ acting spaces of cusp forms $S_k(\Gamma)$ of weight $k$ for certain arithmetically defined Fuchsian subgroups $\Gamma\subset \mathrm{ SL}_2 (\mathbf{ R})$. In particular we consider the groups attached to the quaternion division algebra $B_6$ over $\mathbf{ Q}$ of discriminant 6.
Categories: math.NT