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hmf_forms • Show schema
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{'deg': 2, 'dimension': 1, 'disc': 85, 'field_bad_primes': [5, 17], 'field_label': '2.2.85.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.85.1-25.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [5], 'level_ideal': '[25, 5, 5]', 'level_label': '25.1', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.1-a', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[5, 5, w + 2]', 1]], 'hecke_eigenvalues': [-2, 2, -1, 0, -2, 2, 0, 4, 4, -6, 6, -4, 4, 12, 12, 4, -4, 6, 6, -8, 8, 6, 6, -18, 18, 12, -12, 10, -6, -6, 16, 16, -22, 22, 6, -6, -26, -12, 12, 12, 12, 24, 24, 4, -4, 12, -12, -6, 6, 10, 10, 24, -24, 0, 0, -12, -12, 16, 16, -8, 8, -6, -6, 10, -10, -20, 20, 0, 0, 20, 20, -8, 8, -6, 6, 2, 2, 24, 24, -10, 10, 18, 18, 32, -32, -10, -10, -2, -2, -18, -18, 38, -38, 12, 12, 30, -30, -30, -30, -38, 38, 6, 6, 0, 0, 46, -46, -36, 36, -32, -32, 10, -10, 12, -12, 12, 12, -10, -10, 28, -28, -48, 48, -18, 18, -42, -42, 20, 20, 6, -6, -6, -6, 46, 46, -10, 10, 26, -26, 6, -6, -14, -14, 10, 44, -44, -36, 36, -44, -44, 8, -8, 30, -30, -38, 38, 32, 32, -42, 42, -46, -36, -36, 6, -6, -52, 52, 12, -12, -36, -36, 14, 14, 40, 40, 10, 10, -8, 8, -54, -54, -40, 40, -40, 40, 42, -42, 4, 4, 6, 6, 18, -18, 12, -12, -56, 56, -12, 12, -34, -34, -36, -36, -16, -16, -28, -28, 32, -32, -18, -18, -38, 38, -30, -30, 18, -18, 22, 22, -18, -18, -2, 2, 34, 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30, 30, -42, -42, 10, 10, 60, 60, 44, -44, -12, 12, -12, -12, -80, -80, 68, 68, -98, 98, -92, 92, 8, 8, -102, 102, 6, 6, -4, 4, -34, 34, -46, -46, -40, -40, -84, 84, 34, -34, 20, 20, -48, 48, -46, 46, -38, 38, -12, -12, 24, 24, 60, -60, 76, 76, 0, 0, 122, -88, 88, 68, 68, -102, -102, -6, 6, -12, 12, -30, 30, 78, 78, 82, -82, 12, 12, 52, -52, 94, 94, 86, -86, 48, 48, -24, 24, -8, -8, -42, -42, -20, -20, -54, 54, -106, 106, 18, -18, -74, -74, -56, 56, 96, -96, -120, -120, 4, 4, -82, -82, -84, -84, 112, -112, 52, -52, -118, -118, 42, 42, -56, -56, -30, -30, -58, 58, -24, 24, 12, 12, -48, -48, 100, -100, 76, 76, 88, -88, 34, -34, -96, 96, -42, -42, -46, 46, -86, -86, -74, 74, -12, 12, 50, -50, -26, -84, 84, -108, 108, -98, 98, -54, 54, -40, -40, 8, -8, 8, 8, 6, 6, 94, -94, -24, -24, 84, 84, 54, -54, 2, -2, -48, 48, 48, 48, 88, 88, 26, -26, -78, 78, 132, -132, -50, -50, 120, 120, -46, 46, 10, 10, 60, 60, 52, -52, 0, 0, 40, 40, 88, -88, -66, 66, -58, 58, 16, -16, -32, -32, 102, -102, -124, -124, 34, 12, 12, -112, 112, 42, 42, 108, 108, 110, 110, -26, 26, 128, 128, 90, 90, -40, 40, 8, -8, 78, 78, 24, -24, 48, 48, 48, -48, -84, 84, 120, 120, 30, 30, -28, 28, 84, -84, -76, -76, 32, 32, -4, 4, -126, -126, 10, -10, -50, -50, 48, -48, 26, -26, 26, 26, -120, 120, 0, 0, 82, -82, 100, 100, -6, -6, 122, -122, -120, -120, -72, 72, 14, -14, -68, -68, -114, 114, -78, -78, 30, -30, -16, -16, -126, 126, 6, 6, -90, -90, 50, 50, 82, 82, 74, -74, -30, 30, 80, -80, 78, -78, 118, -118, -78, 78, 54, 54, -84, 84, -14, -14, -6, 6, -128, 128, -18, -18, 50, -6, 6, -54, -54, 88, 88, -150, 150, 84, 84, 120, 120, 108, -108, -84, 84, -144, -144, 100, 100, -56, 56, 52, 52, -70, -70, 146, 146, -82, -82, 124, 124, 150, 150, -130, 130, -44, 44, 96, -96, 40, 40, 54, 54, 106, -106, 120, 120, 84, -84, 94, -94, -108, -108, -10, -10, -48, -48, 56, -56, 54, -54, 158, -158, 90, -90, 72, -72, 150, -150, -54, -54, -58, 14, -14, -24, -24, 18, -18, 74, 74, 98, 98, -2, 2, 60, 60, -36, 36, -128, -128, 32, -32, -60, -60, -62, 62, -32, -32, 54, -54, -42, 42, -54, -54, 104, 104, -136, 136, 64, -64, -30, -30, 124, -124, -102, 102, 72, -72, 54, -54, 42, -42, -94, -94, -60, -60, 20, -20, -74, -74, -44, -44, -56, 56, 36, -36, -52, -52, 88, -88, -54, -54, 42, -42, 94, 94, 108, 108, -122, 122, 84, -84, 150, 150, -28, 28, 34, 34, -70, -70, 24, -24, -152, -152, 6, -6, 30, 30, 58, 58, 36, -36, 50, -50, 44, 44, -86, 86, -36, 36, 168, -168, 144, -144, -54, 54, 138, 138, -78, -78, 96, -96, -8, -8, -78, 78, 30, 30, -38, 38, 104, -104, -134, 134, -112, 112, 54, 54, -4, -4, 128, -128, -24, -24, -116, 116, -28, -28, 18, -18, -58, -58, -48, -48, -174, 174, 34, 34, -62, 62, 164, 164, -130, -130, 36, 36, 20, -20, -156, 156, 100, -100, -112, -112, 134, 134, -76, 76, 102, -102, -94, -94, -100, -100, -88, -88, -14, 14, 78, 78, -70, -70, -50, 50, 72, -72, -130, 130, -96, 96, 62, 62, 84, -84, 46, -46, 54, -54, 66, 66, -104, 104, -98, -98, 0, 0, 14, -14, -80, -80, -42, 42, -166, 166, -60, -60, -58, -58, -24, -24, -60, 60, 32, 32, -18, -18, -42, -42, -154, 154, -138, 138, 166, 166, -50, -50, -48, -48, -86, -86, 98, -98, -36, -36, -44, 44, -6, -6, -156, -156, 10, -10, -52, -52, 8, -8, -174, -174, 36, -36, -2, -2, -146, 146, 112, 112, 90, -90, -96, -96, 52, -52, 42, 42, -72, 72, -42, 42, -138, -138, -14, 14, 170, 170, 132, 132, 168, -168, -180, 180, -84, -84, -96, -96, -88, -88, -18, -18, 46, -46, 96, -96, 8, 8, -30, -30, -180, -180, 10, -10, -110, -110, 32, 32, 150, 150, 64, -64, 164, 164, -150, -150, 94, -94, 144, 144, -66, 66, 76, 76, 0, 0, -120, -120, 36, 36, -108, 108, 4, 4, -14, 14, 42, -42, 30, -30, 6, 6, -90, -90, -118, -118, 62, -62, 92, -92], 'hecke_polynomial': 'x', 'label': '2.2.85.1-25.1-a'}
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hmf_fields • Show schema
Hide schema
{'degree': 2, 'discriminant': 85, 'ideals': ['[1, 1, 1]', '[3, 3, w]', '[3, 3, w + 2]', '[4, 2, 2]', '[5, 5, w + 2]', '[7, 7, w]', '[7, 7, w + 6]', '[9, 3, 3]', '[9, 9, w + 3]', '[9, 9, w - 4]', '[12, 6, 2*w]', '[12, 6, 2*w + 4]', '[15, 15, w + 2]', '[15, 15, w - 3]', '[16, 4, 4]', '[17, 17, w + 8]', '[19, 19, w + 1]', '[19, 19, w - 2]', '[20, 10, 2*w + 4]', '[21, 21, w]', '[21, 21, -w - 6]', '[21, 21, -w + 7]', '[21, 21, -w + 1]', '[23, 23, w + 9]', '[23, 23, w + 13]', '[25, 5, 5]', '[27, 9, 3*w]', '[27, 9, 3*w + 6]', '[27, 27, w + 12]', '[27, 27, w + 14]', '[28, 14, 2*w]', '[28, 14, 2*w + 12]', '[35, 35, w + 7]', '[35, 35, w - 8]', '[36, 6, 6]', '[36, 18, 2*w + 6]', '[36, 18, 2*w - 8]', '[37, 37, w + 11]', '[37, 37, w + 25]', '[45, 15, 3*w + 6]', '[45, 45, w + 12]', '[45, 45, w + 32]', '[48, 12, 4*w]', '[48, 12, 4*w + 8]', '[49, 7, 7]', '[49, 49, 2*w - 7]', '[49, 49, 2*w + 5]', '[51, 51, -w - 8]', '[51, 51, w - 9]', '[57, 57, w + 17]', '[57, 57, w + 20]', '[57, 57, w + 36]', '[57, 57, w + 39]', '[59, 59, 3*w + 10]', '[59, 59, 3*w - 13]', '[60, 30, 2*w + 4]', '[60, 30, 2*w - 6]', '[63, 21, 3*w]', '[63, 21, 3*w + 18]', '[63, 63, w + 14]', '[63, 63, w + 21]', '[63, 63, w + 41]', '[63, 63, w + 48]', '[64, 8, 8]', '[68, 34, 2*w + 16]', '[69, 69, -w - 9]', '[69, 69, -2*w + 5]', '[69, 69, -2*w - 3]', '[69, 69, w - 10]', '[73, 73, w + 15]', '[73, 73, w + 57]', '[75, 15, 5*w]', '[75, 15, 5*w + 10]', '[76, 38, 2*w + 2]', '[76, 38, 2*w - 4]', '[80, 20, 4*w + 8]', '[81, 9, 9]', '[81, 27, 3*w + 9]', '[81, 27, 3*w - 12]', '[81, 81, 2*w - 3]', '[81, 81, 2*w + 1]', '[84, 42, 2*w]', '[84, 42, -2*w - 12]', '[84, 42, -2*w + 14]', '[84, 42, -2*w + 2]', '[85, 85, -2*w + 1]', '[89, 89, -w - 10]', '[89, 89, w - 11]', '[92, 46, 2*w + 18]', '[92, 46, 2*w + 26]', '[95, 95, w + 17]', '[95, 95, w + 77]', '[97, 97, w + 22]', '[97, 97, w + 74]', '[100, 10, 10]', '[101, 101, 3*w - 11]', '[101, 101, -3*w - 8]', '[105, 105, w + 27]', '[105, 105, w + 42]', '[105, 105, w + 62]', '[105, 105, w + 77]', '[107, 107, w + 18]', '[107, 107, w + 88]', '[108, 18, 6*w]', '[108, 18, 6*w + 12]', '[108, 54, 2*w + 24]', '[108, 54, 2*w + 28]', '[111, 111, -7*w + 34]', '[111, 111, 2*w - 15]', '[111, 111, -2*w - 13]', '[111, 111, -7*w - 27]', '[112, 28, 4*w]', '[112, 28, 4*w + 24]', '[113, 113, w + 28]', '[113, 113, w + 84]', '[115, 115, 3*w - 19]', '[115, 115, -3*w - 16]', '[119, 119, -3*w - 7]', '[119, 119, 3*w - 10]', '[121, 11, -11]', '[125, 25, 5*w + 10]', '[133, 133, w + 20]', '[133, 133, w + 55]', '[133, 133, w + 77]', '[133, 133, w + 112]', '[135, 45, 3*w + 6]', '[135, 45, 3*w - 9]', '[135, 135, w + 12]', '[135, 135, -w + 13]', '[140, 70, 2*w + 14]', '[140, 70, 2*w - 16]', '[144, 12, 12]', '[144, 36, 4*w + 12]', '[144, 36, 4*w - 16]', '[147, 21, 7*w]', '[147, 21, 7*w + 14]', '[147, 147, w + 21]', '[147, 147, w + 27]', '[147, 147, w + 119]', '[147, 147, w + 125]', '[148, 74, 2*w + 22]', '[148, 74, 2*w + 50]', '[149, 149, 3*w - 8]', '[149, 149, -3*w - 5]', '[151, 151, -3*w - 17]', '[151, 151, 3*w - 20]', '[153, 51, 3*w + 24]', '[153, 153, w + 59]', '[153, 153, w + 93]', '[161, 161, w + 13]', '[161, 161, 3*w + 4]', '[161, 161, -3*w + 7]', '[161, 161, w - 14]', '[163, 163, w + 66]', '[163, 163, w + 96]', '[167, 167, w + 34]', '[167, 167, w + 132]', '[169, 13, -13]', '[171, 57, 3*w + 3]', '[171, 57, 3*w - 6]', '[171, 171, 4*w - 15]', '[171, 171, -2*w + 17]', '[171, 171, 2*w + 15]', '[171, 171, 4*w + 11]', '[173, 173, w + 68]', '[173, 173, w + 104]', '[175, 35, 5*w]', '[175, 35, 5*w + 30]', '[177, 177, w + 23]', '[177, 177, w + 35]', '[177, 177, w + 141]', '[177, 177, w + 153]', '[179, 179, 3*w - 5]', '[179, 179, -3*w - 2]', '[180, 30, 6*w + 12]', '[180, 90, 2*w + 24]', '[180, 90, 2*w + 64]', '[185, 185, -3*w - 1]', '[185, 185, -3*w + 4]', '[189, 63, 3*w]', '[189, 63, -3*w - 18]', '[189, 63, -3*w + 21]', '[189, 63, -3*w + 3]', '[189, 189, w + 14]', '[189, 189, 4*w - 25]', '[189, 189, 4*w + 21]', '[189, 189, w - 15]', '[191, 191, 3*w - 2]', '[191, 191, 3*w - 1]', '[192, 24, 8*w]', '[192, 24, 8*w + 16]', '[193, 193, w + 24]', '[193, 193, w + 168]', '[196, 14, 14]', '[196, 98, 4*w - 14]', '[196, 98, 4*w + 10]', '[197, 197, w + 85]', '[197, 197, w + 111]', '[204, 102, -2*w - 16]', '[204, 102, 2*w - 18]', '[207, 69, 3*w + 27]', '[207, 69, 3*w + 39]', '[207, 207, w + 32]', '[207, 207, w + 59]', '[207, 207, w + 147]', '[207, 207, w + 174]', '[219, 219, -w - 15]', '[219, 219, 4*w + 9]', '[219, 219, -4*w + 13]', '[219, 219, -w + 16]', '[225, 15, 15]', '[225, 45, 5*w + 15]', '[225, 45, 5*w - 20]', '[227, 227, w + 26]', '[227, 227, w + 200]', '[228, 114, 2*w + 34]', '[228, 114, 2*w + 40]', '[228, 114, 2*w + 72]', '[228, 114, 2*w + 78]', '[229, 229, 3*w - 22]', '[229, 229, -3*w - 19]', '[233, 233, w + 102]', '[233, 233, w + 130]', '[236, 118, 6*w + 20]', '[236, 118, 6*w - 26]', '[239, 239, 2*w - 19]', '[239, 239, -2*w - 17]', '[240, 60, 4*w + 8]', '[240, 60, 4*w - 12]', '[243, 27, 9*w]', '[243, 27, 9*w + 18]', '[243, 81, 3*w + 36]', '[243, 81, 3*w + 42]', '[243, 243, w + 41]', '[243, 243, w + 201]', '[245, 35, 7*w + 14]', '[245, 245, w + 27]', '[245, 245, w + 217]', '[251, 251, -w - 16]', '[251, 251, w - 17]', '[252, 42, 6*w]', '[252, 42, 6*w + 36]', '[252, 126, 2*w + 28]', '[252, 126, 2*w + 42]', '[252, 126, 2*w + 82]', '[252, 126, 2*w + 96]', '[255, 255, w + 42]', '[255, 255, w + 212]', '[256, 16, 16]', '[259, 259, 5*w - 19]', '[259, 259, 9*w + 40]', '[259, 259, 9*w - 49]', '[259, 259, -5*w - 14]', '[267, 267, w + 78]', '[267, 267, w + 99]', '[267, 267, w + 167]', '[267, 267, w + 188]', '[271, 271, -3*w - 20]', '[271, 271, 3*w - 23]', '[272, 68, 4*w + 32]', '[276, 138, -2*w - 18]', '[276, 138, -4*w + 10]', '[276, 138, -4*w - 6]', '[276, 138, 2*w - 20]', '[277, 277, w + 37]', '[277, 277, w + 239]', '[281, 281, 5*w - 31]', '[281, 281, -5*w - 26]', '[283, 283, w + 29]', '[283, 283, w + 253]', '[285, 285, w + 17]', '[285, 285, 4*w + 23]', '[285, 285, -4*w + 27]', '[285, 285, -w + 18]', '[289, 17, 17]', '[291, 291, -4*w - 5]', '[291, 291, -5*w - 13]', '[291, 291, -5*w + 18]', '[291, 291, -4*w + 9]', '[292, 146, 2*w + 30]', '[292, 146, 2*w + 114]', '[295, 295, w + 82]', '[295, 295, w + 212]', '[300, 30, 10*w]', '[300, 30, 10*w + 20]', '[303, 303, w + 30]', '[303, 303, w + 131]', '[303, 303, w + 171]', '[303, 303, w + 272]', '[304, 76, 4*w + 4]', '[304, 76, 4*w - 8]', '[313, 313, w + 140]', '[313, 313, w + 172]', '[315, 105, 3*w + 21]', '[315, 105, 3*w - 24]', '[315, 315, 4*w - 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{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-21, -1, 1], 'conductor': 85, 'degree': 2, 'disc_abs': 85, 'disc_rad': 85, 'disc_sign': 1, 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 9.219544457292887, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.85.1', 'local_algs': ['5.1.2.1a1.2', '17.1.2.1a1.2'], 'maxp': 17, 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [5, 17], 'rd': 9.21954445729, 'regulator': {'__RealLiteral__': 0, 'data': '2.20934770862', 'prec': 44}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 2, 'used_grh': False}