Fundamental Data

• Level q = 2089


• (q,∞)-Quaternion Algebra D = Q[I,J] with I² = -2089, J² = -7, K = IJ = -JI


• Class Number H = 174, Type Number T = 98


• A Maximal Order O in D :
  O = (1/14) < 7+0I+1J+10K, 7I+0J+7K, 2J+6K, 14K >


• Group Order e_j of the Unit Group of O_j :
  e_j = 2 ( 1 <= j <= H )

Further Data ( Text Files )

• Factorization of the Characteristic Polynomial of the Hecke Operator T(2), T(3) on S₂⁺(Γ₀(q)) and on M₂^-(Γ₀(q)) ( Including the Eisenstein Series )


• The eigenvalues of B(3) and the common eigenvectors v_j ( j = 1, ..., H ) of B(n)'s ( 523KB )
  • The j-th line of this text file indicates the associated eigenvalue and the transposed vector of v_j = ( v_ij ), i.e., those data are stored in the order
         for j = 1 to H
             the eigenvalue, v_1j, v_2j, ... , v_H,j


• Representatives { A_j } _{j = 1,...,H} of Left O-Ideal Classes


• Maximal Orders O_j = (A_j)^-1(A_j)


• Isomorphic Relations Among O_j's


• Representatives { A_ij } _{i = 1,...,H} of Left O_j-Ideal Classes ( 1.2MB )


• The data size of the theta series is too large to show.