/* 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([-3, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([2, 2, w + 1]) primes_array = [ [2, 2, w + 1],\ [3, 3, w],\ [4, 2, -w^2 + w + 5],\ [7, 7, -w + 2],\ [19, 19, -2*w^2 + w + 10],\ [23, 23, -w^2 + 8],\ [23, 23, -w^2 + 2],\ [29, 29, -w^2 + 2*w + 4],\ [37, 37, w^2 - 2*w - 8],\ [41, 41, 4*w^2 - 3*w - 20],\ [43, 43, -w - 4],\ [47, 47, 2*w - 1],\ [49, 7, -2*w^2 + 3*w + 4],\ [59, 59, 2*w^2 - 13],\ [61, 61, -3*w^2 + 4*w + 10],\ [67, 67, 2*w^2 - 2*w - 7],\ [71, 71, -3*w - 4],\ [79, 79, 2*w^2 - 3*w - 8],\ [83, 83, 2*w^2 - w - 14],\ [83, 83, -4*w^2 + 3*w + 22],\ [83, 83, 2*w^2 - w - 8],\ [97, 97, 4*w^2 - 2*w - 25],\ [101, 101, 3*w^2 - 2*w - 14],\ [103, 103, 2*w^2 - 7],\ [109, 109, 2*w^2 + 2*w - 1],\ [113, 113, w^2 - 4*w - 4],\ [113, 113, 4*w^2 - 4*w - 17],\ [113, 113, 2*w^2 - 2*w - 5],\ [125, 5, -5],\ [131, 131, -5*w^2 + 2*w + 26],\ [137, 137, 3*w^2 - 2*w - 20],\ [137, 137, -w^2 + 2*w - 2],\ [137, 137, -w^2 - 2],\ [149, 149, w^2 + 2*w - 4],\ [149, 149, 2*w^2 + w - 2],\ [149, 149, 4*w^2 - 4*w - 19],\ [151, 151, w^2 - 10],\ [151, 151, -6*w^2 + 4*w + 31],\ [151, 151, 2*w^2 - 3*w - 14],\ [157, 157, 2*w^2 + w - 4],\ [163, 163, 4*w + 5],\ [163, 163, 2*w^2 - w - 4],\ [163, 163, 3*w^2 - 20],\ [167, 167, 2*w^2 - 3*w - 10],\ [173, 173, 2*w^2 - 5],\ [179, 179, -3*w^2 + 16],\ [181, 181, 3*w - 2],\ [197, 197, 3*w^2 - 4*w - 8],\ [199, 199, -2*w - 7],\ [229, 229, -w^2 - 2*w - 4],\ [233, 233, 3*w - 4],\ [239, 239, 5*w^2 - 2*w - 32],\ [241, 241, 2*w^2 + 1],\ [257, 257, w^2 + 2*w - 10],\ [269, 269, -5*w^2 + 4*w + 28],\ [283, 283, 2*w^2 + w - 14],\ [307, 307, -6*w - 5],\ [307, 307, -3*w^2 + 4*w + 14],\ [307, 307, 2*w^2 - w - 16],\ [311, 311, -w^2 - 2*w + 14],\ [313, 313, -2*w^2 + 4*w - 1],\ [317, 317, 3*w^2 + 4*w - 2],\ [337, 337, w^2 - 4*w - 8],\ [347, 347, -8*w^2 + 3*w + 46],\ [353, 353, 2*w^2 - 17],\ [361, 19, -3*w^2 + 2*w + 4],\ [367, 367, 2*w^2 + 5*w - 2],\ [373, 373, -2*w^2 + 2*w - 1],\ [379, 379, 3*w^2 - 4*w - 20],\ [397, 397, -w^2 + 2*w - 4],\ [397, 397, 3*w^2 - 10],\ [397, 397, 3*w^2 - 2*w - 10],\ [409, 409, -w^2 - 4],\ [409, 409, -4*w^2 + 4*w + 23],\ [409, 409, 2*w^2 - 5*w - 8],\ [421, 421, 2*w^2 - 4*w - 11],\ [433, 433, 8*w^2 - 4*w - 49],\ [443, 443, -3*w^2 + 4*w + 16],\ [449, 449, 6*w^2 - 3*w - 38],\ [457, 457, -6*w^2 + 5*w + 32],\ [461, 461, w - 8],\ [467, 467, -w - 8],\ [467, 467, 2*w^2 - 4*w - 13],\ [467, 467, -4*w - 11],\ [491, 491, 2*w^2 + 6*w - 1],\ [509, 509, 8*w^2 - 6*w - 43],\ [521, 521, 4*w^2 - 2*w - 17],\ [521, 521, 6*w + 7],\ [521, 521, 4*w - 7],\ [523, 523, 5*w^2 - 4*w - 22],\ [541, 541, 6*w^2 - w - 32],\ [541, 541, 4*w^2 - 8*w - 11],\ [541, 541, 3*w^2 - 4],\ [547, 547, 2*w^2 + 2*w - 17],\ [547, 547, 4*w - 5],\ [547, 547, -3*w^2 + 8*w + 8],\ [557, 557, 3*w^2 - 8],\ [557, 557, 6*w^2 - 4*w - 29],\ [557, 557, -2*w^2 + w - 2],\ [571, 571, -2*w^2 - 4*w + 5],\ [587, 587, 3*w^2 + 2*w + 2],\ [593, 593, -6*w^2 + 5*w + 34],\ [599, 599, -w^2 - 8*w - 10],\ [601, 601, -4*w^2 - 6*w + 1],\ [601, 601, 4*w^2 - 3*w - 28],\ [601, 601, 2*w^2 + 2*w - 11],\ [613, 613, 6*w^2 - w - 38],\ [617, 617, 2*w^2 - 5*w - 10],\ [617, 617, -10*w^2 + 6*w + 53],\ [617, 617, 7*w^2 - 4*w - 44],\ [619, 619, -3*w^2 - 4*w + 8],\ [631, 631, 6*w^2 - 6*w - 29],\ [641, 641, w^2 + 4*w - 4],\ [641, 641, -6*w^2 + 2*w + 29],\ [641, 641, -w^2 - 4*w - 8],\ [643, 643, 4*w^2 - w - 16],\ [647, 647, 3*w^2 + 6*w - 4],\ [653, 653, 7*w^2 - 6*w - 32],\ [661, 661, 4*w^2 - 4*w - 13],\ [673, 673, 2*w^2 + 8*w + 1],\ [673, 673, -8*w^2 + 6*w + 47],\ [673, 673, 2*w^2 + 3*w - 8],\ [683, 683, 8*w^2 - 7*w - 40],\ [709, 709, 5*w^2 - 26],\ [719, 719, 2*w^2 + 2*w - 13],\ [727, 727, -w^2 + 6*w - 2],\ [733, 733, w^2 - 6*w - 8],\ [751, 751, 4*w^2 - 7*w - 14],\ [757, 757, 4*w^2 - 5*w - 26],\ [761, 761, 2*w^2 - 5*w - 16],\ [769, 769, -2*w^2 + 8*w + 1],\ [787, 787, 5*w^2 - 2*w - 34],\ [797, 797, 2*w^2 + w - 20],\ [797, 797, 4*w^2 - 3*w - 14],\ [797, 797, -8*w^2 + 2*w + 53],\ [809, 809, -5*w^2 - 2*w + 40],\ [811, 811, -7*w - 8],\ [811, 811, 3*w^2 + 2*w - 14],\ [811, 811, -6*w^2 + 8*w + 19],\ [821, 821, -6*w^2 + w + 34],\ [823, 823, 4*w^2 + 2*w - 17],\ [823, 823, 4*w^2 - 4*w - 7],\ [823, 823, 4*w^2 - 6*w - 17],\ [841, 29, 2*w^2 - 5*w - 14],\ [857, 857, -8*w^2 + 4*w + 41],\ [859, 859, -10*w^2 + 7*w + 56],\ [859, 859, 2*w^2 - 19],\ [859, 859, 5*w^2 - 2*w - 22],\ [863, 863, 6*w - 1],\ [887, 887, w^2 - 14],\ [907, 907, 10*w^2 - 9*w - 46],\ [911, 911, -7*w - 10],\ [911, 911, 6*w^2 - 5*w - 26],\ [911, 911, 5*w - 4],\ [919, 919, -2*w^2 - 11*w - 8],\ [929, 929, w^2 - 6*w - 10],\ [937, 937, w - 10],\ [947, 947, 5*w^2 - 4*w - 20],\ [967, 967, -7*w^2 + 6*w + 38],\ [967, 967, 2*w^2 - 2*w - 19],\ [967, 967, 8*w^2 - 5*w - 40],\ [977, 977, 2*w^2 + 3*w - 10],\ [977, 977, 2*w^2 + 4*w - 7],\ [977, 977, 2*w^2 - 6*w - 19],\ [997, 997, -12*w^2 + 7*w + 64],\ [997, 997, 4*w^2 - 13],\ [997, 997, 5*w^2 - 32]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 0, -1, -4, -4, 0, 0, -6, -10, 6, -4, 12, -10, -12, 2, -4, 12, 8, 0, -12, 12, -10, 6, -4, -10, -18, -18, -6, 6, 12, 6, -6, 18, 18, 6, -18, 8, -4, 8, 2, 20, -16, -4, 0, 6, 12, 2, -6, -16, -22, -6, -12, 14, 6, 6, -4, -28, -16, -4, -24, -10, -6, -22, -24, 30, 26, 32, -10, -28, 2, 38, 2, -22, 14, 2, 26, -22, -36, 6, 14, 18, -12, 12, -12, 0, -6, 18, 6, -42, 20, 2, 2, 2, -28, 20, 44, -6, 30, 18, -28, -36, -30, 0, -46, 26, 38, 26, 30, -42, -6, 44, -16, -30, -18, 18, -4, 24, -18, 2, 26, 14, -10, 0, -10, -36, -16, -22, -4, -10, 42, -10, 20, 30, -18, 18, 30, -16, -16, -40, -42, 32, -16, -40, -22, -42, -4, 20, -4, -48, -48, 32, -36, 0, -12, -16, 42, 2, -24, 8, -40, -40, -30, 30, 18, -46, 26, -46] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]