/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([7, -6, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([512, 8, 8]) primes_array = [ [7, 7, w],\ [7, 7, w^2 - 4],\ [7, 7, w^2 + w - 5],\ [8, 2, 2],\ [11, 11, w + 1],\ [11, 11, -w^2 - w + 6],\ [11, 11, -w^2 + 3],\ [19, 19, -w^2 + w + 4],\ [27, 3, -3],\ [31, 31, w^2 - 8],\ [31, 31, 2*w^2 - 9],\ [31, 31, 2*w^2 + 2*w - 9],\ [37, 37, 2*w^2 + w - 8],\ [37, 37, w^2 + 2*w - 6],\ [37, 37, w^2 - w - 5],\ [83, 83, -2*w - 3],\ [83, 83, 2*w^2 - 5],\ [83, 83, 2*w^2 + 2*w - 13],\ [103, 103, 3*w^2 + 2*w - 17],\ [103, 103, 2*w^2 - w - 5],\ [103, 103, 3*w^2 + 2*w - 18],\ [107, 107, w^2 - 3*w - 1],\ [107, 107, -3*w^2 - 4*w + 12],\ [107, 107, 4*w^2 + w - 20],\ [113, 113, -w^2 - 4*w + 5],\ [113, 113, 2*w^2 - w - 13],\ [113, 113, -3*w^2 - 2*w + 9],\ [125, 5, -5],\ [151, 151, w^2 - 10],\ [151, 151, -w^2 - w - 1],\ [151, 151, w - 6],\ [163, 163, w^2 - 2*w - 5],\ [163, 163, 2*w^2 + 3*w - 11],\ [163, 163, 3*w^2 + w - 12],\ [179, 179, -4*w^2 - 3*w + 15],\ [179, 179, 3*w^2 - w - 16],\ [179, 179, 4*w^2 + w - 19],\ [191, 191, 4*w^2 + 3*w - 20],\ [191, 191, 2*w^2 + 3*w - 15],\ [191, 191, 3*w^2 - w - 11],\ [197, 197, 2*w^2 + 3*w - 12],\ [197, 197, 3*w^2 + w - 11],\ [197, 197, w^2 - 2*w - 6],\ [227, 227, 2*w^2 - 2*w - 9],\ [227, 227, 2*w^2 + 4*w - 11],\ [227, 227, 4*w^2 + 2*w - 17],\ [229, 229, 2*w^2 + w - 16],\ [229, 229, -w^2 + w - 3],\ [229, 229, -w^2 - 2*w - 2],\ [239, 239, 3*w^2 + 3*w - 16],\ [239, 239, -3*w - 1],\ [239, 239, 3*w^2 - 11],\ [277, 277, -3*w - 2],\ [277, 277, 3*w^2 + 3*w - 17],\ [277, 277, 3*w^2 - 10],\ [293, 293, 3*w^2 - 8],\ [293, 293, -3*w - 4],\ [293, 293, 3*w^2 + 3*w - 19],\ [311, 311, w^2 + 4*w - 2],\ [311, 311, -4*w^2 - 3*w + 22],\ [311, 311, 3*w^2 - w - 9],\ [331, 331, 4*w^2 - w - 22],\ [331, 331, 4*w^2 + w - 27],\ [331, 331, 5*w^2 + w - 24],\ [349, 349, 4*w - 1],\ [349, 349, -4*w^2 - 4*w + 19],\ [349, 349, 4*w^2 - 17],\ [353, 353, 2*w^2 + 4*w - 13],\ [353, 353, 4*w^2 + 2*w - 15],\ [353, 353, 2*w^2 - 2*w - 11],\ [373, 373, -6*w^2 - w + 30],\ [373, 373, -5*w^2 - 4*w + 17],\ [373, 373, -5*w^2 - 6*w + 20],\ [379, 379, -w^2 + w - 4],\ [379, 379, -w^2 - 2*w - 3],\ [379, 379, 2*w^2 + w - 17],\ [419, 419, 3*w^2 + 4*w - 16],\ [419, 419, 4*w^2 + w - 16],\ [419, 419, w^2 - 3*w - 5],\ [449, 449, 2*w^2 + 5*w - 13],\ [449, 449, 5*w^2 + 3*w - 20],\ [449, 449, 3*w^2 - 2*w - 15],\ [457, 457, 5*w^2 + w - 23],\ [457, 457, w^2 - 4*w - 2],\ [457, 457, -4*w^2 - 5*w + 18],\ [463, 463, 5*w^2 + 2*w - 22],\ [463, 463, 2*w^2 - 3*w - 8],\ [463, 463, 3*w^2 + 5*w - 15],\ [467, 467, 4*w^2 - w - 15],\ [467, 467, w^2 + 5*w - 4],\ [467, 467, 5*w^2 + 4*w - 25],\ [487, 487, 3*w^2 + 4*w - 17],\ [487, 487, 4*w^2 + w - 15],\ [487, 487, w^2 - 3*w - 6],\ [521, 521, -w - 8],\ [521, 521, -w^2 - 4],\ [521, 521, w^2 + w - 13],\ [563, 563, 5*w^2 + 5*w - 23],\ [563, 563, 5*w - 2],\ [563, 563, 5*w^2 - 22],\ [569, 569, w^2 - 3*w - 8],\ [569, 569, 3*w^2 + 4*w - 19],\ [569, 569, 4*w^2 + w - 13],\ [571, 571, w^2 - 3*w - 9],\ [571, 571, 3*w^2 + 4*w - 20],\ [571, 571, 4*w^2 + w - 12],\ [577, 577, 2*w^2 + w - 18],\ [577, 577, -w^2 + w - 5],\ [577, 577, -w^2 - 2*w - 4],\ [601, 601, w^2 - 13],\ [601, 601, -w^2 - w - 4],\ [601, 601, w - 9],\ [607, 607, 5*w^2 + 3*w - 18],\ [607, 607, 2*w^2 + 5*w - 15],\ [607, 607, 3*w^2 - 2*w - 17],\ [619, 619, -2*w - 9],\ [619, 619, 2*w^2 + 2*w - 19],\ [619, 619, -2*w^2 - 1],\ [647, 647, 3*w^2 - 2*w - 18],\ [647, 647, 5*w^2 + 3*w - 17],\ [647, 647, 2*w^2 + 5*w - 16],\ [653, 653, 2*w^2 + 5*w - 17],\ [653, 653, 3*w^2 - 2*w - 19],\ [653, 653, -5*w^2 - 3*w + 16],\ [673, 673, 4*w^2 - 13],\ [673, 673, -4*w - 3],\ [673, 673, 4*w^2 + 4*w - 23],\ [677, 677, 5*w^2 + 4*w - 27],\ [677, 677, w^2 + 5*w - 2],\ [677, 677, 4*w^2 - w - 13],\ [683, 683, 3*w^2 + 6*w - 16],\ [683, 683, 3*w^2 - 3*w - 13],\ [683, 683, 6*w^2 + 3*w - 26],\ [691, 691, -5*w^2 - 2*w + 20],\ [691, 691, 3*w^2 + 5*w - 17],\ [691, 691, 2*w^2 - 3*w - 10],\ [733, 733, -6*w^2 - 5*w + 29],\ [733, 733, 5*w^2 - w - 20],\ [733, 733, 2*w^2 - w - 19],\ [761, 761, 6*w^2 + 4*w - 33],\ [761, 761, 4*w^2 - 2*w - 11],\ [761, 761, 5*w^2 + 4*w - 31],\ [787, 787, 2*w^2 - 3*w - 11],\ [787, 787, 3*w^2 + 5*w - 18],\ [787, 787, 5*w^2 + 2*w - 19],\ [797, 797, 5*w^2 + 4*w - 30],\ [797, 797, -w^2 - 5*w - 1],\ [797, 797, 4*w^2 - w - 10],\ [809, 809, -7*w^2 - 6*w + 24],\ [809, 809, 7*w^2 + w - 34],\ [809, 809, 6*w^2 - w - 34],\ [829, 829, -w^2 + w - 6],\ [829, 829, -w^2 - 2*w - 5],\ [829, 829, 2*w^2 + w - 19],\ [863, 863, 3*w^2 + 5*w - 19],\ [863, 863, 2*w^2 - 3*w - 12],\ [863, 863, 5*w^2 + 2*w - 18],\ [881, 881, -2*w^2 - 2*w - 1],\ [881, 881, 2*w^2 - 19],\ [881, 881, 2*w - 11],\ [911, 911, 2*w^2 - 3*w - 15],\ [911, 911, 5*w^2 + 2*w - 15],\ [911, 911, 3*w^2 + 5*w - 22],\ [919, 919, 6*w^2 + 5*w - 30],\ [919, 919, 5*w^2 - w - 19],\ [919, 919, w^2 + 6*w - 4],\ [977, 977, 7*w^2 + 5*w - 27],\ [977, 977, 5*w^2 - 2*w - 26],\ [977, 977, 7*w^2 + 2*w - 33]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 0, 0, 0, -4, -4, -4, 8, -8, 4, 4, 4, 2, 2, 2, 16, 16, 16, 0, 0, 0, -12, -12, -12, 6, 6, 6, -18, 16, 16, 16, -4, -4, -4, -12, -12, -12, -16, -16, -16, 10, 10, 10, 12, 12, 12, -22, -22, -22, 12, 12, 12, -30, -30, -30, 10, 10, 10, 12, 12, 12, 20, 20, 20, -14, -14, -14, -10, -10, -10, -10, -10, -10, -12, -12, -12, 12, 12, 12, -2, -2, -2, 10, 10, 10, -20, -20, -20, 12, 12, 12, -40, -40, -40, -6, -6, -6, 4, 4, 4, -18, -18, -18, -4, -4, -4, -2, -2, -2, -34, -34, -34, 0, 0, 0, -20, -20, -20, 0, 0, 0, -6, -6, -6, 30, 30, 30, -30, -30, -30, 0, 0, 0, 36, 36, 36, -6, -6, -6, 38, 38, 38, 20, 20, 20, 42, 42, 42, -42, -42, -42, 30, 30, 30, -36, -36, -36, 14, 14, 14, -56, -56, -56, -40, -40, -40, 30, 30, 30] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]