/* 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([-85, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11, 11, 3*w - 29]) primes_array = [ [4, 2, 2],\ [5, 5, -w + 10],\ [5, 5, w + 9],\ [9, 3, 3],\ [11, 11, 3*w - 29],\ [13, 13, w - 9],\ [13, 13, -w - 8],\ [17, 17, 2*w + 17],\ [17, 17, -2*w + 19],\ [29, 29, -w - 7],\ [29, 29, w - 8],\ [31, 31, 5*w - 49],\ [43, 43, -w - 6],\ [43, 43, w - 7],\ [47, 47, -w - 11],\ [47, 47, w - 12],\ [49, 7, -7],\ [59, 59, 2*w - 21],\ [59, 59, 2*w + 19],\ [61, 61, 5*w - 48],\ [61, 61, -5*w - 43],\ [67, 67, -6*w - 53],\ [67, 67, 6*w - 59],\ [71, 71, -w - 12],\ [71, 71, w - 13],\ [73, 73, -w - 3],\ [73, 73, w - 4],\ [79, 79, -w - 2],\ [79, 79, w - 3],\ [83, 83, -w - 1],\ [83, 83, w - 2],\ [97, 97, -w - 13],\ [97, 97, w - 14],\ [103, 103, 3*w - 31],\ [103, 103, -3*w - 28],\ [113, 113, 7*w + 62],\ [113, 113, 7*w - 69],\ [127, 127, 8*w - 77],\ [127, 127, -8*w - 69],\ [139, 139, 4*w + 33],\ [139, 139, -4*w + 37],\ [151, 151, -5*w + 47],\ [151, 151, 5*w + 42],\ [157, 157, 4*w - 41],\ [157, 157, -4*w - 37],\ [163, 163, 3*w + 29],\ [163, 163, -3*w + 32],\ [167, 167, 3*w - 26],\ [167, 167, 3*w + 23],\ [191, 191, -14*w - 123],\ [191, 191, 14*w - 137],\ [197, 197, 2*w - 13],\ [197, 197, -2*w - 11],\ [239, 239, 5*w + 41],\ [239, 239, -5*w + 46],\ [241, 241, 2*w - 11],\ [241, 241, -2*w - 9],\ [257, 257, -w - 18],\ [257, 257, w - 19],\ [263, 263, -9*w - 77],\ [263, 263, 9*w - 86],\ [271, 271, -7*w + 66],\ [271, 271, 7*w + 59],\ [277, 277, 2*w - 9],\ [277, 277, -2*w - 7],\ [311, 311, -10*w - 89],\ [311, 311, -10*w + 99],\ [317, 317, -4*w - 39],\ [317, 317, 4*w - 43],\ [337, 337, 2*w - 3],\ [337, 337, -2*w - 1],\ [347, 347, -3*w - 19],\ [347, 347, 3*w - 22],\ [361, 19, -19],\ [379, 379, 7*w - 71],\ [379, 379, -7*w - 64],\ [397, 397, -11*w - 98],\ [397, 397, 11*w - 109],\ [409, 409, 5*w - 44],\ [409, 409, -5*w - 39],\ [419, 419, 5*w - 53],\ [419, 419, 5*w + 48],\ [421, 421, -w - 22],\ [421, 421, w - 23],\ [443, 443, 2*w - 29],\ [443, 443, -2*w - 27],\ [457, 457, 17*w - 164],\ [457, 457, -22*w + 213],\ [461, 461, -3*w - 16],\ [461, 461, 3*w - 19],\ [467, 467, -w - 23],\ [467, 467, w - 24],\ [491, 491, -5*w - 38],\ [491, 491, 5*w - 43],\ [521, 521, -5*w - 49],\ [521, 521, 5*w - 54],\ [523, 523, 4*w - 31],\ [523, 523, -4*w - 27],\ [529, 23, -23],\ [557, 557, -3*w - 13],\ [557, 557, 3*w - 16],\ [569, 569, 6*w - 53],\ [569, 569, -6*w - 47],\ [571, 571, 5*w - 42],\ [571, 571, -5*w - 37],\ [577, 577, 9*w - 91],\ [577, 577, -9*w - 82],\ [599, 599, -13*w - 116],\ [599, 599, 13*w - 129],\ [601, 601, -13*w - 111],\ [601, 601, 13*w - 124],\ [613, 613, 11*w - 104],\ [613, 613, 11*w + 93],\ [617, 617, -w - 26],\ [617, 617, w - 27],\ [653, 653, -7*w - 66],\ [653, 653, 7*w - 73],\ [661, 661, -4*w - 43],\ [661, 661, 4*w - 47],\ [673, 673, -19*w - 164],\ [673, 673, 19*w - 183],\ [677, 677, 3*w - 11],\ [677, 677, -3*w - 8],\ [683, 683, 2*w - 33],\ [683, 683, -2*w - 31],\ [691, 691, 10*w - 101],\ [691, 691, 10*w + 91],\ [727, 727, -w - 28],\ [727, 727, w - 29],\ [739, 739, 4*w - 27],\ [739, 739, -4*w - 23],\ [743, 743, -9*w + 83],\ [743, 743, 9*w + 74],\ [751, 751, -9*w - 83],\ [751, 751, 9*w - 92],\ [761, 761, -3*w - 1],\ [761, 761, 3*w - 4],\ [787, 787, 23*w - 222],\ [787, 787, -28*w + 271],\ [809, 809, 11*w + 92],\ [809, 809, -11*w + 103],\ [821, 821, -15*w - 128],\ [821, 821, 15*w - 143],\ [827, 827, 12*w + 101],\ [827, 827, -12*w + 113],\ [839, 839, -5*w - 52],\ [839, 839, -5*w + 57],\ [907, 907, -w - 31],\ [907, 907, w - 32],\ [941, 941, 5*w - 37],\ [941, 941, -5*w - 32],\ [953, 953, -6*w - 43],\ [953, 953, 6*w - 49],\ [967, 967, -8*w + 71],\ [967, 967, -8*w - 63],\ [971, 971, -w - 32],\ [971, 971, w - 33],\ [977, 977, -16*w - 143],\ [977, 977, 16*w - 159]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 1, 1, -5, -1, -4, -4, 2, 2, 0, 0, 7, 6, 6, 8, 8, -10, 5, 5, -12, -12, -7, -7, -3, -3, -4, -4, 10, 10, 6, 6, -7, -7, -16, -16, 9, 9, -8, -8, -10, -10, -2, -2, -7, -7, 4, 4, 12, 12, 17, 17, 2, 2, 30, 30, 8, 8, -2, -2, -14, -14, 28, 28, 2, 2, 12, 12, 13, 13, 22, 22, -28, -28, -38, -5, -5, -2, -2, 30, 30, 20, 20, 22, 22, -11, -11, 12, 12, -12, -12, -27, -27, 8, 8, -3, -3, 16, 16, -45, 2, 2, 0, 0, 28, 28, 33, 33, 40, 40, -2, -2, 16, 16, 18, 18, -41, -41, 37, 37, -14, -14, 42, 42, -16, -16, 17, 17, 3, 3, -50, -50, -4, -4, -23, -23, -12, -12, 32, 32, 0, 0, -22, -22, 52, 52, -5, -5, -12, -12, -42, -42, -34, -34, 32, 32, 47, 47, -27, -27] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([11, 11, 3*w - 29])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]