/* 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([1, -2, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([181,181,-5*w^2 + 4*w + 5]) primes_array = [ [7, 7, 2*w^2 - w - 3],\ [8, 2, 2],\ [13, 13, -w^2 - w + 3],\ [13, 13, -w^2 + 2*w + 2],\ [13, 13, -2*w^2 + w + 2],\ [27, 3, 3],\ [29, 29, 3*w^2 - 2*w - 4],\ [29, 29, 2*w^2 + w - 4],\ [29, 29, -w^2 + 3*w + 1],\ [41, 41, w^2 - w - 5],\ [41, 41, 2*w^2 - 3*w - 4],\ [41, 41, -3*w^2 + w + 3],\ [43, 43, w^2 + 2*w - 5],\ [43, 43, 2*w^2 + w - 5],\ [43, 43, 3*w^2 - 2*w - 3],\ [71, 71, 4*w^2 - 3*w - 5],\ [71, 71, 3*w^2 - 4*w - 5],\ [71, 71, -4*w^2 + w + 5],\ [83, 83, w^2 + w - 7],\ [83, 83, w^2 - 2*w - 6],\ [83, 83, -3*w^2 - 2*w + 5],\ [97, 97, 3*w^2 + w - 7],\ [97, 97, 3*w^2 - 4*w - 7],\ [97, 97, 2*w^2 - w - 8],\ [113, 113, 3*w^2 + w - 8],\ [113, 113, 2*w^2 - 4*w - 5],\ [113, 113, 2*w^2 + 2*w - 7],\ [125, 5, -5],\ [127, 127, 2*w^2 - 9],\ [127, 127, -3*w^2 - 2*w + 6],\ [127, 127, -5*w^2 + 3*w + 7],\ [139, 139, 5*w^2 - 4*w - 6],\ [139, 139, 4*w^2 - 5*w - 7],\ [139, 139, -5*w^2 + w + 6],\ [167, 167, w^2 + w - 8],\ [167, 167, 6*w^2 - 4*w - 9],\ [167, 167, -4*w^2 - 2*w + 7],\ [181, 181, 4*w^2 + w - 9],\ [181, 181, 4*w^2 - 5*w - 9],\ [181, 181, 2*w^2 - w - 9],\ [197, 197, 2*w - 7],\ [197, 197, 3*w^2 - 5*w - 6],\ [197, 197, 2*w^2 - 2*w - 9],\ [211, 211, 3*w^2 - 5*w - 7],\ [211, 211, 2*w^2 + 3*w - 8],\ [211, 211, 4*w^2 + w - 10],\ [223, 223, 3*w^2 + 2*w - 9],\ [223, 223, 4*w^2 + w - 11],\ [223, 223, 3*w^2 + 2*w - 10],\ [239, 239, 6*w^2 - 5*w - 7],\ [239, 239, -5*w^2 + 6*w + 9],\ [239, 239, -6*w^2 + w + 7],\ [251, 251, w^2 - 3*w - 8],\ [251, 251, -3*w^2 + 2*w - 3],\ [251, 251, 2*w^2 + w - 11],\ [281, 281, -7*w^2 + 6*w + 9],\ [281, 281, 6*w^2 + w - 11],\ [281, 281, w^2 - 7*w],\ [293, 293, -7*w^2 + 2*w + 10],\ [293, 293, 5*w^2 - 7*w - 7],\ [293, 293, 2*w^2 + 5*w - 6],\ [307, 307, -3*w^2 + w - 3],\ [307, 307, 2*w^2 - 3*w - 10],\ [307, 307, w^2 + 2*w - 10],\ [337, 337, 7*w^2 - 3*w - 10],\ [337, 337, 7*w^2 - 4*w - 10],\ [337, 337, -4*w^2 - 3*w + 8],\ [349, 349, 5*w^2 + w - 15],\ [349, 349, 7*w^2 - 8*w - 11],\ [349, 349, -6*w^2 + 5*w + 2],\ [379, 379, 3*w^2 + 3*w - 11],\ [379, 379, 4*w^2 + 2*w - 11],\ [379, 379, 5*w^2 + w - 14],\ [419, 419, -5*w^2 - 3*w + 9],\ [419, 419, 2*w^2 + w - 12],\ [419, 419, w^2 - 3*w - 9],\ [421, 421, 9*w^2 - 5*w - 15],\ [421, 421, 3*w^2 + 5*w - 7],\ [421, 421, 4*w^2 - w - 15],\ [433, 433, -8*w^2 + 7*w + 10],\ [433, 433, 7*w^2 + w - 13],\ [433, 433, w^2 - 8*w],\ [449, 449, -7*w^2 + 2*w + 8],\ [449, 449, 8*w^2 - 6*w - 11],\ [449, 449, -6*w^2 - 2*w + 11],\ [461, 461, 2*w^2 + 6*w - 7],\ [461, 461, -8*w^2 + 2*w + 11],\ [461, 461, 6*w^2 - 8*w - 9],\ [463, 463, -7*w^2 + 8*w + 12],\ [463, 463, w^2 + 7*w - 7],\ [463, 463, -8*w^2 + w + 10],\ [491, 491, w^2 + 2*w - 11],\ [491, 491, 4*w^2 - 7*w - 7],\ [491, 491, 2*w^2 - 3*w - 11],\ [503, 503, 5*w^2 - 7*w - 10],\ [503, 503, 2*w^2 - 2*w - 11],\ [503, 503, -7*w^2 + 2*w + 7],\ [547, 547, 4*w^2 + 3*w - 15],\ [547, 547, -3*w^2 + 10*w],\ [547, 547, -7*w^2 + 4*w + 3],\ [587, 587, 6*w^2 + w - 17],\ [587, 587, 5*w^2 - 3*w - 17],\ [587, 587, w^2 - 7*w - 6],\ [601, 601, 4*w^2 + 3*w - 14],\ [601, 601, 4*w^2 + 3*w - 12],\ [601, 601, 6*w^2 + w - 16],\ [617, 617, 5*w^2 + 2*w - 14],\ [617, 617, 4*w^2 + 3*w - 13],\ [617, 617, 5*w^2 + 2*w - 15],\ [631, 631, -9*w^2 + 8*w + 11],\ [631, 631, 8*w^2 + w - 15],\ [631, 631, w^2 - 9*w],\ [643, 643, 6*w^2 - 9*w - 8],\ [643, 643, 3*w^2 + 6*w - 8],\ [643, 643, 4*w^2 - w - 16],\ [659, 659, -8*w^2 + 2*w + 9],\ [659, 659, 9*w^2 - 7*w - 12],\ [659, 659, 7*w^2 + 2*w - 13],\ [673, 673, -8*w^2 + 9*w + 14],\ [673, 673, w^2 + 8*w - 8],\ [673, 673, -9*w^2 + w + 11],\ [701, 701, 9*w^2 - 4*w - 13],\ [701, 701, -5*w^2 - 4*w + 10],\ [701, 701, -4*w^2 - 5*w + 9],\ [727, 727, -7*w^2 - 3*w + 12],\ [727, 727, w^2 + 2*w - 12],\ [727, 727, 10*w^2 - 7*w - 15],\ [743, 743, 5*w^2 - 2*w - 18],\ [743, 743, 4*w^2 - 5*w - 16],\ [743, 743, w^2 + 4*w - 14],\ [757, 757, 11*w^2 - 7*w - 18],\ [757, 757, w^2 + 3*w - 13],\ [757, 757, 3*w^2 + 5*w - 15],\ [769, 769, 2*w^2 - 11*w + 1],\ [769, 769, -10*w^2 + w + 13],\ [769, 769, 9*w^2 + 2*w - 15],\ [797, 797, -8*w^2 + 5*w + 3],\ [797, 797, -3*w^2 + 11*w],\ [797, 797, 5*w^2 + 3*w - 18],\ [811, 811, -9*w^2 + 2*w + 11],\ [811, 811, 7*w^2 - 9*w - 12],\ [811, 811, 9*w^2 - 7*w - 11],\ [827, 827, 3*w^2 + 5*w - 14],\ [827, 827, 5*w^2 + 3*w - 13],\ [827, 827, 8*w^2 - 21],\ [839, 839, -6*w^2 - 4*w + 11],\ [839, 839, w^2 - 4*w - 11],\ [839, 839, 3*w^2 + w - 16],\ [853, 853, -8*w^2 + 7*w + 3],\ [853, 853, 7*w^2 + w - 20],\ [853, 853, w^2 - 8*w - 7],\ [881, 881, -10*w^2 + 9*w + 12],\ [881, 881, 9*w^2 + w - 17],\ [881, 881, w^2 - 10*w],\ [883, 883, 7*w^2 + w - 18],\ [883, 883, -8*w^2 + 5*w + 4],\ [883, 883, 5*w^2 + 3*w - 17],\ [911, 911, 10*w^2 - 7*w - 14],\ [911, 911, 2*w^2 + w - 14],\ [911, 911, -7*w^2 - 3*w + 13],\ [937, 937, -9*w^2 + 10*w + 16],\ [937, 937, w^2 + 9*w - 9],\ [937, 937, -10*w^2 + w + 12],\ [953, 953, 9*w^2 - 7*w - 10],\ [953, 953, -10*w^2 + 2*w + 13],\ [953, 953, 8*w^2 - 10*w - 13],\ [967, 967, 2*w^2 + 2*w - 15],\ [967, 967, 11*w^2 - 7*w - 17],\ [967, 967, -7*w^2 - 4*w + 12]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [3, -1, -6, 4, -1, -2, 0, 0, -5, -8, 2, 2, -6, -1, 4, 12, -3, 12, -6, 4, 9, 13, -17, -12, 4, 9, 9, -19, 3, 18, -12, 0, -20, 15, -22, -12, 13, 2, 1, 2, 18, -17, 8, -8, 22, -23, 9, -16, -16, -10, 0, 25, 12, 12, 27, -18, 17, 22, 9, 24, -21, -7, -22, -32, -2, 13, 28, 10, 0, 10, -20, 20, 0, 0, -5, -5, 22, -8, 27, 19, -6, 4, -15, 10, 30, 12, 27, 22, -26, 19, -11, 27, -8, -38, 4, 29, 24, -22, 28, 8, -27, -32, 23, 17, 47, -18, 18, -27, -22, -43, -18, -38, -16, -31, -21, 0, 15, -45, 39, -41, -46, -33, 27, 22, 38, -22, -52, 14, 39, 14, 18, 8, 8, -50, 10, 10, 18, 48, -7, 12, 47, 37, -27, -27, 3, 35, 35, -5, 9, -26, 9, 2, -18, -18, 49, 4, 34, 12, 57, -28, 28, -42, 53, -21, -41, -6, 3, 18, 43] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([181,181,-5*w^2 + 4*w + 5])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]