Fundamental Data

• Level q = 151


• (q,∞)-Quaternion Algebra D = Q[ I, J ] with I² = -1, J² = -151, K = IJ = -JI


• Class Number H = 13, Type Number T = 10


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


• Representatives of Left O-Ideal Classes :
  A₁ = < 1+0I+1J+0K, 1I+0J+1K, 2J+0K, 2K > ( norm = 4 )
  A₂ = < 1+0I+1J+0K, 1I+0J+1K, 4J+0K, 4K > ( norm = 8 )
  A₃ = < 1+0I+5J+0K, 1I+0J+5K, 8J+0K, 8K > ( norm = 16 )
  A₄ = < 1+0I+5J+4K, 1I+4J+5K, 8J+0K, 8K > ( norm = 16 )
  A₅ = < 1+0I+5J+0K, 1I+0J+5K, 16J+0K, 16K > ( norm = 32 )
  A₆ = < 1+0I+5J+8K, 1I+8J+5K, 16J+0K, 16K > ( norm = 32 )
  A₇ = < 1+0I+13J+12K, 1I+4J+13K, 16J+0K, 16K > ( norm = 32 )
  A₈ = < 1+0I+13J+4K, 1I+12J+13K, 16J+0K, 16K > ( norm = 32 )
  A₉ = < 1+0I+5J+16K, 1I+16J+5K, 32J+0K, 32K > ( norm = 64 )
  A₁₀ = < 1+0I+5J+24K, 1I+8J+5K, 32J+0K, 32K > ( norm = 64 )
  A₁₁ = < 1+0I+5J+8K, 1I+24J+5K, 32J+0K, 32K > ( norm = 64 )
  A₁₂ = < 1+0I+29J+28K, 1I+4J+29K, 32J+0K, 32K > ( norm = 64 )
  A₁₃ = < 1+0I+29J+4K, 1I+28J+29K, 32J+0K, 32K > ( norm = 64 )
  


• Maximal Orders O_j = (A_j)^-1(A_j) :
  O₁ = (1/2) < 1+0I+1J+0K, 1I+0J+1K, 2J+0K, 2K >
  O₂ = (1/4) < 2+0I+2J+0K, 1I+0J+5K, 4J+0K, 8K >
  O₃ = (1/8) < 4+0I+4J+0K, 1I+0J+5K, 8J+0K, 32K >
  O₄ = (1/8) < 4+0I+4J+16K, 1I+4J+29K, 8J+0K, 32K >
  O₅ = (1/16) < 8+0I+8J+0K, 1I+0J+101K, 16J+0K, 128K >
  O₆ = (1/16) < 8+0I+8J+64K, 1I+8J+69K, 16J+0K, 128K >
  O₇ = (1/16) < 8+0I+8J+96K, 1I+4J+93K, 16J+64K, 128K >
  O₈ = (1/16) < 8+0I+8J+32K, 1I+12J+29K, 16J+64K, 128K >
  O₉ = (1/32) < 16+0I+16J+256K, 1I+16J+101K, 32J+0K, 512K >
  O₁₀ = (1/32) < 16+0I+16J+384K, 1I+8J+325K, 32J+256K, 512K >
  O₁₁ = (1/32) < 16+0I+16J+128K, 1I+24J+69K, 32J+256K, 512K >
  O₁₂ = (1/32) < 16+0I+16J+192K, 1I+4J+477K, 32J+384K, 512K >
  O₁₃ = (1/32) < 16+0I+16J+320K, 1I+28J+93K, 32J+128K, 512K >
  


• Isomorphic Relations Among O_j's :
  O₇ is isomorphic to O₈
  O₁₀ is isomorphic to O₁₁
  O₁₂ is isomorphic to O₁₃
  


• Group Order e_j of the Unit Group of O_j :
  e₁ = 4, e_j = 2 ( 2 <= j <= H )

Further Data ( Text Files )

• Factorization of the Characteristic Polynomials of the Hecke Operators on S₂⁺(Γ₀(q))


• Factorization of the Characteristic Polynomials of the Hecke Operators on M₂^-(Γ₀(q)) ( Including the Eisenstein Series )


• The eigenvalues of B(2) and the common eigenvectors v_j ( j = 1, ..., H ) of B(n)'s
  • 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_ij } _{i = 1,...,H} of Left O_j-Ideal Classes


• Theta Series θ_ij Associated to A_ij
  • The range of the Fourier expansion = 1024
  • The Fourier coefficients of e_j θ_ij(z) = Σ_n=0,1,2,... a_ij(n) exp(2πinz) are stored in the order
         for j = 1 to H
             for i = j to H
                 a_ij(0), a_ij(1), ..., a_ij(1024)