-
hmf_forms • Show schema
{'deg': 2, 'dimension': 13, 'disc': 197, 'field_bad_primes': [197], 'field_label': '2.2.197.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.197.1-49.2-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [7], 'level_ideal': '[49, 49, w]', 'level_label': '49.2', 'level_norm': 49, 'parallel_weight': 2, 'short_label': '49.2-g', 'weight': '[2, 2]'} -
hmf_hecke • Show schema
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32*x^9 + 709*x^8 + 624*x^7 - 1981*x^6 - 2292*x^5 + 2289*x^4 + 3181*x^3 - 662*x^2 - 1476*x - 259', 'label': '2.2.197.1-49.2-g'} -
hmf_fields • Show schema
{'degree': 2, 'discriminant': 197, 'ideals': ['[1, 1, 1]', '[4, 2, 2]', '[7, 7, w - 7]', '[7, 7, w + 6]', '[9, 3, 3]', '[16, 4, 4]', '[19, 19, w + 5]', '[19, 19, w - 6]', '[23, 23, w + 8]', '[23, 23, -w + 9]', '[25, 5, 5]', '[28, 14, 2*w - 14]', '[28, 14, 2*w + 12]', '[29, 29, -w - 4]', '[29, 29, w - 5]', '[36, 6, 6]', '[37, 37, -w - 3]', '[37, 37, w - 4]', '[41, 41, -w - 9]', '[41, 41, w - 10]', '[43, 43, -w - 2]', '[43, 43, w - 3]', '[47, 47, -w - 1]', '[47, 47, w - 2]', '[49, 7, 7]', '[49, 49, w]', '[49, 49, w - 1]', '[53, 53, 2*w - 13]', '[53, 53, -2*w - 11]', '[59, 59, -4*w - 25]', '[59, 59, -4*w + 29]', '[61, 61, -w - 10]', '[61, 61, w - 11]', '[63, 21, 3*w - 21]', '[63, 21, 3*w + 18]', '[64, 8, 8]', '[76, 38, 2*w + 10]', '[76, 38, 2*w - 12]', '[81, 9, 9]', '[83, 83, -w - 11]', '[83, 83, w - 12]', '[92, 46, 2*w + 16]', '[92, 46, -2*w + 18]', '[97, 97, 2*w - 11]', '[97, 97, -2*w - 9]', '[100, 10, 10]', '[101, 101, 3*w - 20]', '[101, 101, -3*w - 17]', '[107, 107, -w - 12]', '[107, 107, w - 13]', '[109, 109, -5*w - 31]', '[109, 109, -5*w + 36]', '[112, 28, 4*w - 28]', '[112, 28, 4*w + 24]', '[116, 58, -2*w - 8]', '[116, 58, 2*w - 10]', '[121, 11, -11]', '[127, 127, 2*w - 19]', '[127, 127, -2*w - 17]', '[133, 133, w + 13]', '[133, 133, 2*w - 9]', '[133, 133, 2*w + 7]', '[133, 133, -w + 14]', '[137, 137, -3*w - 16]', '[137, 137, 3*w - 19]', '[144, 12, 12]', '[148, 74, -2*w - 6]', '[148, 74, 2*w - 8]', '[157, 157, -3*w - 23]', '[157, 157, 3*w - 26]', '[161, 161, w + 14]', '[161, 161, 2*w - 7]', '[161, 161, 2*w + 5]', '[161, 161, -w + 15]', '[163, 163, -4*w + 27]', '[163, 163, 4*w + 23]', '[164, 82, -2*w - 18]', '[164, 82, 2*w - 20]', '[169, 13, -13]', '[171, 57, 3*w + 15]', '[171, 57, 3*w - 18]', '[172, 86, -2*w - 4]', '[172, 86, 2*w - 6]', '[173, 173, -6*w - 37]', '[173, 173, -6*w + 43]', '[175, 35, 5*w - 35]', '[175, 35, 5*w + 30]', '[181, 181, 2*w - 5]', '[181, 181, -2*w - 3]', '[188, 94, -2*w - 2]', '[188, 94, 2*w - 4]', '[191, 191, -w - 15]', '[191, 191, w - 16]', '[193, 193, 2*w - 3]', '[193, 193, -2*w - 1]', '[196, 14, 14]', '[196, 98, 2*w]', '[196, 98, 2*w - 2]', '[197, 197, 2*w - 1]', '[203, 203, -11*w - 73]', '[203, 203, 2*w - 21]', '[203, 203, 2*w + 19]', '[203, 203, -11*w + 84]', '[207, 69, 3*w + 24]', '[207, 69, -3*w + 27]', '[212, 106, 4*w - 26]', '[212, 106, -4*w - 22]', '[223, 223, -w - 16]', '[223, 223, w - 17]', '[225, 15, 15]', '[233, 233, -3*w - 13]', '[233, 233, 3*w - 16]', '[236, 118, -8*w - 50]', '[236, 118, -8*w + 58]', '[239, 239, -5*w + 34]', '[239, 239, -5*w - 29]', '[244, 122, -2*w - 20]', '[244, 122, 2*w - 22]', '[251, 251, 5*w - 41]', '[251, 251, 5*w + 36]', '[252, 42, 6*w - 42]', '[252, 42, 6*w + 36]', '[256, 16, 16]', '[257, 257, -w - 17]', '[257, 257, w - 18]', '[259, 259, -10*w + 77]', '[259, 259, 3*w - 28]', '[259, 259, 3*w + 25]', '[259, 259, -10*w - 67]', '[261, 87, -3*w - 12]', '[261, 87, 3*w - 15]', '[287, 287, -3*w + 14]', '[287, 287, -16*w - 103]', '[287, 287, -16*w + 119]', '[287, 287, -3*w - 11]', '[289, 17, -17]', '[293, 293, -w - 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366]', '[9652, 4826, -58*w + 424]', '[9652, 4826, -14*w + 8]', '[9653, 1379, 14*w - 7]', '[9653, 9653, w + 98]', '[9653, 9653, -w + 99]', '[9657, 3219, -3*w - 99]', '[9657, 3219, -24*w - 183]', '[9657, 3219, 24*w - 207]', '[9657, 3219, 3*w - 102]', '[9668, 4834, -14*w - 132]', '[9668, 4834, 14*w - 146]', '[9675, 645, -15*w - 30]', '[9675, 645, 15*w - 45]', '[9676, 4838, 22*w - 130]', '[9676, 4838, 6*w - 110]', '[9676, 4838, -6*w - 104]', '[9676, 4838, -22*w - 108]', '[9677, 9677, 17*w - 76]', '[9677, 9677, -17*w - 59]', '[9679, 9679, 27*w - 227]', '[9679, 9679, 27*w + 200]', '[9689, 9689, -5*w - 102]', '[9689, 9689, 5*w - 107]', '[9692, 4846, 16*w - 62]', '[9692, 4846, -16*w - 46]', '[9700, 970, 20*w - 110]', '[9700, 970, -20*w - 90]', '[9712, 2428, -28*w - 156]', '[9712, 2428, 28*w - 184]', '[9716, 4858, -94*w - 620]', '[9716, 4858, 10*w - 126]', '[9716, 4858, 10*w + 116]', '[9716, 4858, -94*w + 714]', '[9729, 3243, -30*w - 171]', '[9729, 3243, 21*w + 99]', '[9729, 3243, -21*w + 120]', '[9729, 3243, 30*w - 201]', '[9743, 9743, -33*w - 193]', '[9743, 9743, -33*w + 226]', '[9749, 9749, 15*w - 44]', '[9749, 9749, -15*w - 29]', '[9767, 9767, 13*w - 141]', '[9767, 9767, -13*w - 128]', '[9769, 9769, -19*w - 80]', '[9769, 9769, 19*w - 99]', '[9787, 9787, -21*w - 167]', '[9787, 9787, -21*w + 188]', '[9788, 4894, 28*w - 234]', '[9788, 4894, 28*w + 206]', '[9791, 9791, -11*w - 120]', '[9791, 9791, 11*w - 131]', '[9797, 9797, -23*w - 116]', '[9797, 9797, -7*w - 107]', '[9797, 9797, 7*w - 114]', '[9797, 9797, 23*w - 139]', '[9799, 9799, -16*w - 45]', '[9799, 9799, -15*w - 137]', '[9799, 9799, 15*w - 152]', '[9799, 9799, 16*w - 61]', '[9801, 99, -99]', '[9803, 9803, 2*w - 101]', '[9803, 9803, -2*w - 99]', '[9808, 2452, 12*w - 136]', '[9808, 2452, -12*w - 124]', '[9811, 9811, -17*w - 58]', '[9811, 9811, 17*w - 75]', '[9817, 9817, 9*w - 122]', '[9817, 9817, -9*w - 113]', '[9821, 9821, -27*w + 175]', '[9821, 9821, 4*w - 105]', '[9821, 9821, 25*w - 214]', '[9821, 9821, -15*w - 28]', '[9821, 9821, -15*w + 43]', '[9821, 9821, -25*w - 189]', '[9821, 9821, -4*w - 101]', '[9821, 9821, -27*w - 148]', '[9844, 4922, -8*w - 110]', '[9844, 4922, 42*w - 332]', '[9844, 4922, -42*w - 290]', '[9844, 4922, 8*w - 118]', '[9851, 9851, -w - 99]', '[9851, 9851, w - 100]', '[9857, 9857, -23*w - 178]', '[9857, 9857, 23*w - 201]', '[9859, 9859, 3*w - 103]', '[9859, 9859, -3*w - 100]', '[9872, 2468, -24*w - 124]', '[9872, 2468, 24*w - 148]', '[9873, 3291, 18*w - 87]', '[9873, 3291, -18*w - 69]', '[9883, 9883, -47*w - 291]', '[9883, 9883, -47*w + 338]', '[9884, 4942, 20*w - 182]', '[9884, 4942, -58*w - 390]', '[9884, 4942, -58*w + 448]', '[9884, 4942, 20*w + 162]', '[9887, 9887, -31*w + 209]', '[9887, 9887, -31*w - 178]', '[9891, 3297, -15*w + 42]', '[9891, 3297, -132*w - 855]', '[9891, 3297, -132*w + 987]', '[9891, 3297, -15*w - 27]', '[9892, 4946, -16*w - 142]', '[9892, 4946, 16*w - 158]', '[9899, 9899, 5*w - 108]', '[9899, 9899, -20*w - 89]', '[9899, 9899, -20*w + 109]', '[9899, 9899, -5*w - 103]', '[9901, 9901, 25*w - 157]', '[9901, 9901, -25*w - 132]', '[9904, 2476, 16*w - 60]', '[9904, 2476, -16*w - 44]', '[9913, 9913, 29*w - 192]', '[9913, 9913, 22*w + 107]', '[9913, 9913, -22*w + 129]', '[9913, 9913, -29*w - 163]', '[9931, 9931, -35*w + 242]', '[9931, 9931, -35*w - 207]', '[9943, 9943, -17*w - 57]', '[9943, 9943, 19*w - 176]', '[9943, 9943, -19*w - 157]', '[9943, 9943, 17*w - 74]', '[9947, 1421, -77*w - 511]', '[9947, 1421, 14*w - 147]', '[9947, 1421, 14*w + 133]', '[9947, 1421, -77*w + 588]', '[9947, 9947, 73*w - 539]', '[9947, 9947, -19*w + 98]', '[9947, 9947, 19*w + 79]', '[9947, 9947, -73*w - 466]', '[9959, 9959, -15*w + 41]', '[9959, 9959, 10*w - 127]', '[9959, 9959, -10*w - 117]', '[9959, 9959, -15*w - 26]', '[9964, 4982, -18*w - 152]', '[9964, 4982, -46*w - 284]', '[9964, 4982, -46*w + 330]', '[9964, 4982, 18*w - 170]', '[9971, 767, 26*w - 221]', '[9971, 767, -26*w - 195]', '[10000, 100, 100]'], 'label': '2.2.197.1', 'narrow_class_no': 1, 'primes': ['[4, 2, 2]', '[7, 7, w - 7]', '[7, 7, w + 6]', '[9, 3, 3]', '[19, 19, w + 5]', '[19, 19, w - 6]', '[23, 23, w + 8]', '[23, 23, -w + 9]', '[25, 5, 5]', '[29, 29, -w - 4]', '[29, 29, w - 5]', '[37, 37, -w - 3]', '[37, 37, w - 4]', '[41, 41, -w - 9]', '[41, 41, w - 10]', '[43, 43, -w - 2]', '[43, 43, w - 3]', '[47, 47, -w - 1]', '[47, 47, w - 2]', '[53, 53, 2*w - 13]', '[53, 53, -2*w - 11]', '[59, 59, -4*w - 25]', '[59, 59, -4*w + 29]', '[61, 61, -w - 10]', '[61, 61, w - 11]', '[83, 83, -w - 11]', '[83, 83, w - 12]', '[97, 97, 2*w - 11]', '[97, 97, -2*w - 9]', '[101, 101, 3*w - 20]', '[101, 101, -3*w - 17]', '[107, 107, -w - 12]', '[107, 107, w - 13]', '[109, 109, -5*w - 31]', '[109, 109, -5*w + 36]', '[121, 11, -11]', '[127, 127, 2*w - 19]', '[127, 127, -2*w - 17]', '[137, 137, -3*w - 16]', '[137, 137, 3*w - 19]', '[157, 157, -3*w - 23]', '[157, 157, 3*w - 26]', '[163, 163, -4*w + 27]', '[163, 163, 4*w + 23]', '[169, 13, -13]', '[173, 173, -6*w - 37]', '[173, 173, -6*w + 43]', '[181, 181, 2*w - 5]', '[181, 181, -2*w - 3]', '[191, 191, -w - 15]', '[191, 191, w - 16]', '[193, 193, 2*w - 3]', '[193, 193, -2*w - 1]', '[197, 197, 2*w - 1]', '[223, 223, -w - 16]', '[223, 223, w - 17]', '[233, 233, -3*w - 13]', '[233, 233, 3*w - 16]', '[239, 239, -5*w + 34]', '[239, 239, -5*w - 29]', '[251, 251, 5*w - 41]', '[251, 251, 5*w + 36]', '[257, 257, -w - 17]', '[257, 257, w - 18]', '[289, 17, -17]', '[293, 293, -w - 18]', '[293, 293, w - 19]', '[311, 311, -3*w - 10]', '[311, 311, 3*w - 13]', '[313, 313, -3*w - 26]', '[313, 313, 3*w - 29]', '[331, 331, -w - 19]', '[331, 331, w - 20]', '[347, 347, 4*w - 23]', '[347, 347, -4*w - 19]', '[353, 353, 3*w - 11]', '[353, 353, -3*w - 8]', '[379, 379, 2*w - 25]', '[379, 379, -2*w - 23]', '[401, 401, 3*w - 8]', '[401, 401, -3*w - 5]', '[409, 409, 5*w - 43]', '[409, 409, 5*w + 38]', '[419, 419, -5*w - 26]', '[419, 419, 5*w - 31]', '[431, 431, 3*w - 5]', '[431, 431, -3*w - 2]', '[433, 433, -7*w + 48]', '[433, 433, -7*w - 41]', '[443, 443, 3*w - 2]', '[443, 443, 3*w - 1]', '[449, 449, -9*w - 55]', '[449, 449, -9*w + 64]', '[457, 457, -w - 22]', '[457, 457, w - 23]', '[479, 479, 2*w - 27]', '[479, 479, -2*w - 25]', '[487, 487, -3*w - 29]', '[487, 487, 3*w - 32]', '[491, 491, -5*w - 39]', '[491, 491, 5*w - 44]', '[499, 499, 4*w - 19]', '[499, 499, -4*w - 15]', '[503, 503, -w - 23]', '[503, 503, w - 24]', '[521, 521, 11*w - 86]', '[521, 521, -7*w + 47]', '[557, 557, 7*w + 51]', '[557, 557, 7*w - 58]', '[563, 563, -4*w - 13]', '[563, 563, 4*w - 17]', '[569, 569, -10*w - 61]', '[569, 569, -10*w + 71]', '[587, 587, 2*w - 29]', '[587, 587, -2*w - 27]', '[601, 601, -w - 25]', '[601, 601, w - 26]', '[607, 607, -7*w - 39]', '[607, 607, 7*w - 46]', '[613, 613, 3*w - 34]', '[613, 613, -3*w - 31]', '[617, 617, -6*w - 31]', '[617, 617, 6*w - 37]', '[619, 619, 4*w - 15]', '[619, 619, -4*w - 11]', '[631, 631, 5*w - 27]', '[631, 631, -5*w - 22]', '[653, 653, -w - 26]', '[653, 653, w - 27]', '[661, 661, 5*w - 46]', '[661, 661, -5*w - 41]', '[683, 683, -9*w + 62]', '[683, 683, -9*w - 53]', '[691, 691, 7*w - 45]', '[691, 691, -7*w - 38]', '[727, 727, -6*w - 47]', '[727, 727, 6*w - 53]', '[733, 733, 4*w - 41]', '[733, 733, -4*w - 37]', '[739, 739, -4*w - 5]', '[739, 739, 4*w - 9]', '[751, 751, 8*w - 53]', '[751, 751, -8*w - 45]', '[769, 769, 5*w - 24]', '[769, 769, -5*w - 19]', '[773, 773, 7*w - 44]', '[773, 773, -7*w - 37]', '[787, 787, 4*w - 3]', '[787, 787, 4*w - 1]', '[797, 797, -9*w - 52]', '[797, 797, -9*w + 61]', '[811, 811, -5*w - 18]', '[811, 811, 5*w - 23]', '[821, 821, -w - 29]', '[821, 821, w - 30]', '[827, 827, 2*w - 33]', '[827, 827, -2*w - 31]', '[829, 829, -10*w + 69]', '[829, 829, -10*w - 59]', '[839, 839, 5*w - 48]', '[839, 839, -5*w - 43]', '[853, 853, -7*w - 36]', '[853, 853, 7*w - 43]', '[881, 881, -w - 30]', '[881, 881, w - 31]', '[961, 31, -31]', '[991, 991, -5*w - 13]', '[991, 991, 5*w - 18]']} -
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-49, -1, 1], 'conductor': 197, 'degree': 2, 'dirichlet_group': [1, 196], 'disc_abs': 197, 'disc_rad': 197, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[2, 1]]], [5, [[2, 1]]], [7, [[1, 2]]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[2, 1]]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[1, 2]]], [43, [[1, 2]]], [47, [[1, 2]]], [53, [[1, 2]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1], 'galois_label': '2T1', 'galt': 1, 'grd': 14.035668847618199, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.197.1', 'local_algs': ['197.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [197], 'rd': 14.0356688476, 'regulator': {'__RealLiteral__': 0, 'data': '3.33347758688', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 2 a + 13 \\)'], 'used_grh': False, 'zk': ['1', 'a']}
Hilbert modular form data - 2.2.197.1-49.2-g