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hmf_forms • Show schema
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{'deg': 2, 'dimension': 1, 'disc': 109, 'field_bad_primes': [109], 'field_label': '2.2.109.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.109.1-15.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [3, 5], 'level_ideal': '[15, 15, -w - 3]', 'level_label': '15.1', 'level_norm': 15, 'parallel_weight': 2, 'short_label': '15.1-a', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[3, 3, -w + 6]', 1], ['[5, 5, -3*w - 14]', -1]], 'hecke_eigenvalues': [-1, -3, 2, -2, 1, 3, -2, -1, 4, 2, -4, 8, -11, -12, -10, 14, -15, 8, 3, -6, -2, -7, -14, 13, 18, 4, 14, -6, 4, -15, 0, -10, -15, 11, 12, -8, -14, 3, -8, -6, -11, -14, 14, 1, -22, 22, 1, 4, 7, -25, 0, -12, 4, -12, -21, -21, 6, 1, 10, 26, 30, 23, 12, -10, -13, -28, 24, -18, 4, -2, 12, -2, -11, 11, -10, 0, -22, -9, 13, -17, -17, 34, -2, -33, -38, 6, 11, 16, 30, -32, -28, -9, 37, -12, -19, -4, -28, 9, 33, 6, 5, -4, -7, -30, 0, 37, -25, -9, -46, 25, 2, -12, -20, 9, -34, -37, 17, -2, 6, -39, 3, -36, 15, -20, 22, -23, -51, 33, 14, -2, -50, 23, 35, 22, 14, 41, -6, -20, -26, -24, 0, -18, 12, -47, -14, 19, -27, -2, -18, 46, -38, -8, 15, -38, -26, 2, 44, -8, 20, -30, 6, 19, 2, 3, -6], 'hecke_polynomial': 'x', 'label': '2.2.109.1-15.1-a'}
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hmf_fields • Show schema
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{'degree': 2, 'discriminant': 109, 'ideals': ['[1, 1, 1]', '[3, 3, -w + 6]', '[3, 3, w + 5]', '[4, 2, 2]', '[5, 5, -3*w + 17]', '[5, 5, -3*w - 14]', '[7, 7, w - 5]', '[7, 7, w + 4]', '[9, 3, 3]', '[9, 9, -2*w - 9]', '[9, 9, -2*w + 11]', '[12, 6, -2*w + 12]', '[12, 6, 2*w + 10]', '[15, 15, -w - 3]', '[15, 15, w + 6]', '[15, 15, -w + 7]', '[15, 15, -w + 4]', '[16, 4, 4]', '[20, 10, -6*w + 34]', '[20, 10, -6*w - 28]', '[21, 21, w + 2]', '[21, 21, -5*w - 24]', '[21, 21, 5*w - 29]', '[21, 21, w - 3]', '[25, 5, 5]', '[25, 25, -w - 1]', '[25, 25, -w + 2]', '[27, 9, -3*w + 18]', '[27, 9, 3*w + 15]', '[27, 27, -w]', '[27, 27, -w + 1]', '[28, 14, 2*w - 10]', '[28, 14, 2*w + 8]', '[29, 29, -w - 7]', '[29, 29, -w + 8]', '[31, 31, -5*w + 28]', '[31, 31, -5*w - 23]', '[35, 35, 2*w - 13]', '[35, 35, 3*w + 13]', '[35, 35, 3*w - 16]', '[35, 35, -2*w - 11]', '[36, 6, 6]', '[36, 18, -4*w - 18]', '[36, 18, -4*w + 22]', '[43, 43, 6*w + 29]', '[43, 43, -6*w + 35]', '[45, 15, -9*w + 51]', '[45, 15, -9*w - 42]', '[45, 45, w + 8]', '[45, 45, -2*w + 9]', '[45, 45, -2*w - 7]', '[45, 45, -w + 9]', '[48, 12, -4*w + 24]', '[48, 12, 4*w + 20]', '[49, 7, 7]', '[49, 49, -9*w + 52]', '[49, 49, 9*w + 43]', '[60, 30, -2*w - 6]', '[60, 30, 2*w + 12]', '[60, 30, -2*w + 14]', '[60, 30, -2*w + 8]', '[61, 61, 3*w - 19]', '[61, 61, -3*w - 16]', '[63, 21, 3*w - 15]', '[63, 21, 3*w + 12]', '[63, 63, -w - 9]', '[63, 63, 8*w - 45]', '[63, 63, 8*w + 37]', '[63, 63, w - 10]', '[64, 8, 8]', '[71, 71, -7*w - 34]', '[71, 71, 7*w - 41]', '[73, 73, 2*w - 7]', '[73, 73, -2*w - 5]', '[75, 15, -5*w + 30]', '[75, 15, 5*w + 25]', '[75, 75, -4*w - 17]', '[75, 75, -7*w - 32]', '[75, 75, -7*w + 39]', '[75, 75, -4*w + 21]', '[80, 20, -12*w + 68]', '[80, 20, -12*w - 56]', '[81, 9, 9]', '[81, 27, -6*w - 27]', '[81, 27, -6*w + 33]', '[81, 81, -5*w + 27]', '[81, 81, -5*w - 22]', '[83, 83, -w - 10]', '[83, 83, w - 11]', '[84, 42, 2*w + 4]', '[84, 42, -10*w - 48]', '[84, 42, 10*w - 58]', '[84, 42, 2*w - 6]', '[87, 87, -13*w + 75]', '[87, 87, 2*w - 15]', '[87, 87, 2*w + 13]', '[87, 87, -13*w - 62]', '[89, 89, 3*w - 14]', '[89, 89, 3*w + 11]', '[93, 93, -4*w + 25]', '[93, 93, -2*w + 5]', '[93, 93, -2*w - 3]', '[93, 93, 4*w + 21]', '[97, 97, 3*w + 17]', '[97, 97, 3*w - 20]', '[100, 10, 10]', '[100, 50, -2*w - 2]', '[100, 50, -2*w + 4]', '[105, 105, -w - 11]', '[105, 105, -8*w - 39]', '[105, 105, 11*w - 62]', '[105, 105, 2*w - 3]', '[105, 105, 2*w + 1]', '[105, 105, 11*w + 51]', '[105, 105, 8*w - 47]', '[105, 105, w - 12]', '[108, 18, -6*w + 36]', '[108, 18, 6*w + 30]', '[108, 54, -2*w]', '[108, 54, -2*w + 2]', '[109, 109, 2*w - 1]', '[112, 28, 4*w - 20]', '[112, 28, 4*w + 16]', '[113, 113, -3*w - 10]', '[113, 113, 3*w - 13]', '[116, 58, -2*w - 14]', '[116, 58, -2*w + 16]', '[121, 11, -11]', '[124, 62, -10*w + 56]', '[124, 62, -10*w - 46]', '[125, 25, -15*w + 85]', '[125, 25, -15*w - 70]', '[125, 125, -11*w + 64]', '[125, 125, 11*w + 53]', '[129, 129, w + 12]', '[129, 129, -5*w - 21]', '[129, 129, -5*w + 26]', '[129, 129, -w + 13]', '[131, 131, 5*w - 31]', '[131, 131, -5*w - 26]', '[135, 45, -3*w - 9]', '[135, 45, 3*w + 18]', '[135, 45, -3*w + 21]', '[135, 45, -3*w + 12]', '[135, 135, -17*w + 98]', '[135, 135, 14*w + 67]', '[135, 135, -14*w + 81]', '[135, 135, 17*w + 81]', '[137, 137, -9*w - 41]', '[137, 137, 9*w - 50]', '[140, 70, 4*w - 26]', '[140, 70, 6*w + 26]', '[140, 70, 6*w - 32]', '[140, 70, -4*w - 22]', '[144, 12, 12]', '[144, 36, -8*w - 36]', '[144, 36, -8*w + 44]', '[145, 145, 9*w + 44]', '[145, 145, 7*w - 38]', '[145, 145, -7*w - 31]', '[145, 145, 9*w - 53]', '[147, 21, -7*w + 42]', '[147, 21, 7*w + 35]', '[147, 147, -4*w + 19]', '[147, 147, -2*w + 17]', '[147, 147, 2*w + 15]', '[147, 147, -4*w - 15]', '[155, 155, w + 13]', '[155, 155, -3*w + 11]', '[155, 155, -3*w - 8]', '[155, 155, -w + 14]', '[157, 157, -14*w + 79]', '[157, 157, 14*w + 65]', '[169, 13, -13]', '[172, 86, 12*w + 58]', '[172, 86, -12*w + 70]', '[173, 173, -3*w - 7]', '[173, 173, 3*w - 10]', '[175, 35, 5*w - 25]', '[175, 35, 5*w + 20]', '[175, 175, 6*w - 37]', '[175, 175, 3*w - 22]', '[175, 175, -3*w - 19]', '[175, 175, -6*w - 31]', '[180, 30, -18*w + 102]', '[180, 30, -18*w - 84]', '[180, 90, 2*w + 16]', '[180, 90, -4*w + 18]', '[180, 90, -4*w - 14]', '[180, 90, -2*w + 18]', '[183, 183, -w - 14]', '[183, 183, 13*w + 60]', '[183, 183, 13*w - 73]', '[183, 183, w - 15]', '[189, 63, 3*w + 6]', '[189, 63, -15*w - 72]', '[189, 63, 15*w - 87]', '[189, 63, 3*w - 9]', '[189, 189, -4*w - 23]', '[189, 189, -5*w - 27]', '[189, 189, 5*w - 32]', '[189, 189, 4*w - 27]', '[191, 191, -10*w - 49]', '[191, 191, 10*w - 59]', '[192, 24, -8*w + 48]', '[192, 24, 8*w + 40]', '[193, 193, 22*w + 103]', '[193, 193, 22*w - 125]', '[196, 14, 14]', '[196, 98, -18*w + 104]', '[196, 98, 18*w + 86]', '[197, 197, 6*w + 25]', '[197, 197, -6*w + 31]', '[203, 203, -3*w + 8]', '[203, 203, 12*w - 67]', '[203, 203, -12*w - 55]', '[203, 203, 3*w + 5]', '[211, 211, -4*w - 13]', '[211, 211, 4*w - 17]', '[213, 213, -w - 15]', '[213, 213, 7*w - 37]', '[213, 213, 7*w + 30]', '[213, 213, w - 16]', '[215, 215, -3*w - 4]', '[215, 215, -2*w + 19]', '[215, 215, 2*w + 17]', '[215, 215, -3*w + 7]', '[217, 217, 11*w + 50]', '[217, 217, -3*w - 20]', '[217, 217, 3*w - 23]', '[217, 217, 11*w - 61]', '[219, 219, 17*w - 96]', '[219, 219, -5*w + 24]', '[219, 219, 5*w + 19]', '[219, 219, -17*w - 79]', '[223, 223, 8*w + 35]', '[223, 223, -8*w + 43]', '[225, 15, 15]', '[225, 45, -10*w - 45]', '[225, 45, -10*w + 55]', '[225, 75, -3*w - 3]', '[225, 75, -3*w + 6]', '[225, 225, -7*w + 43]', '[225, 225, -13*w + 76]', '[225, 225, 13*w + 63]', '[225, 225, 7*w + 36]', '[227, 227, 9*w - 49]', '[227, 227, 9*w + 40]', '[233, 233, 3*w - 5]', '[233, 233, -3*w - 2]', '[239, 239, -3*w - 1]', '[239, 239, 3*w - 4]', '[240, 60, -4*w - 12]', '[240, 60, 4*w + 24]', '[240, 60, -4*w + 28]', '[240, 60, -4*w + 16]', '[243, 27, -9*w + 54]', '[243, 27, 9*w + 45]', '[243, 81, -3*w]', '[243, 81, -3*w + 3]', '[243, 243, 11*w + 54]', '[243, 243, -11*w + 65]', '[244, 122, 6*w - 38]', '[244, 122, -6*w - 32]', '[245, 35, -21*w + 119]', '[245, 35, -21*w - 98]', '[245, 245, w + 16]', '[245, 245, -3*w + 2]', '[245, 245, -3*w + 1]', '[245, 245, -w + 17]', '[249, 249, 16*w - 93]', '[249, 249, 5*w - 33]', '[249, 249, -5*w - 28]', '[249, 249, -16*w - 77]', '[252, 42, 6*w - 30]', '[252, 42, 6*w + 24]', '[252, 126, -2*w - 18]', '[252, 126, 16*w - 90]', '[252, 126, 16*w + 74]', '[252, 126, 2*w - 20]', '[256, 16, 16]', '[261, 87, -3*w - 21]', '[261, 87, -3*w + 24]', '[261, 261, 25*w + 117]', '[261, 261, -5*w - 18]', '[261, 261, 5*w - 23]', '[261, 261, -25*w + 142]', '[263, 263, 33*w - 188]', '[263, 263, 33*w + 155]', '[267, 267, 4*w - 15]', '[267, 267, -22*w - 105]', '[267, 267, 22*w - 127]', '[267, 267, 4*w + 11]', '[279, 93, -15*w + 84]', '[279, 93, -15*w - 69]', '[279, 279, w + 17]', '[279, 279, -7*w - 29]', '[279, 279, -7*w + 36]', '[279, 279, -w + 18]', '[281, 281, 8*w - 49]', '[281, 281, -8*w - 41]', '[284, 142, -14*w - 68]', '[284, 142, 14*w - 82]', '[289, 17, -17]', '[291, 291, 35*w + 166]', '[291, 291, -2*w + 21]', '[291, 291, -2*w - 19]', '[291, 291, 35*w - 201]', '[292, 146, 4*w - 14]', '[292, 146, -4*w - 10]', '[293, 293, 4*w - 29]', '[293, 293, 4*w + 25]', '[300, 30, -10*w + 60]', '[300, 30, 10*w + 50]', '[300, 150, -8*w - 34]', '[300, 150, -14*w - 64]', '[300, 150, -14*w + 78]', '[300, 150, -8*w + 42]', '[301, 301, -12*w - 59]', '[301, 301, 5*w - 22]', '[301, 301, 5*w + 17]', '[301, 301, 12*w - 71]', '[305, 305, 6*w - 29]', '[305, 305, -7*w - 37]', '[305, 305, 7*w - 44]', '[305, 305, 6*w + 23]', '[307, 307, 3*w - 25]', '[307, 307, -3*w - 22]', '[311, 311, -5*w - 29]', '[311, 311, 5*w - 34]', '[315, 105, 6*w - 39]', '[315, 105, 9*w + 39]', '[315, 105, 9*w - 48]', '[315, 105, -6*w - 33]', '[315, 315, -w - 18]', '[315, 315, 13*w + 59]', '[315, 315, 4*w + 9]', '[315, 315, -17*w - 82]', '[315, 315, 17*w - 99]', '[315, 315, 4*w - 13]', '[315, 315, 13*w - 72]', '[315, 315, w - 19]', '[320, 40, -24*w + 136]', '[320, 40, -24*w - 112]', '[324, 18, 18]', '[324, 54, -12*w - 54]', '[324, 54, -12*w + 66]', '[324, 162, -10*w + 54]', '[324, 162, -10*w - 44]', '[327, 327, 11*w - 60]', '[327, 327, 11*w + 49]', '[331, 331, 19*w + 88]', '[331, 331, -19*w + 107]', '[332, 166, -2*w - 20]', '[332, 166, 2*w - 22]', '[336, 84, 4*w + 8]', '[336, 84, -20*w - 96]', '[336, 84, 20*w - 116]', '[336, 84, 4*w - 12]', '[339, 339, -28*w - 131]', '[339, 339, 5*w + 16]', '[339, 339, -5*w + 21]', '[339, 339, 28*w - 159]', '[343, 49, 7*w - 35]', '[343, 49, 7*w + 28]', '[343, 343, 9*w - 55]', '[343, 343, -9*w - 46]', '[347, 347, 23*w - 133]', '[347, 347, 36*w - 205]', '[348, 174, -26*w + 150]', '[348, 174, 4*w - 30]', '[348, 174, 4*w + 26]', '[348, 174, -26*w - 124]', '[349, 349, 15*w - 88]', '[349, 349, -15*w - 73]', '[353, 353, -w - 19]', '[353, 353, w - 20]', '[355, 355, 4*w - 11]', '[355, 355, -3*w - 23]', '[355, 355, 3*w - 26]', '[355, 355, 4*w + 7]', '[356, 178, 6*w - 28]', '[356, 178, 6*w + 22]', '[361, 19, -19]', '[363, 33, 11*w - 66]', '[363, 33, -11*w - 55]', '[365, 365, -13*w - 64]', '[365, 365, 49*w - 281]', '[365, 365, 49*w + 232]', '[365, 365, -13*w + 77]', '[372, 186, -8*w + 50]', '[372, 186, -4*w + 10]', '[372, 186, -4*w - 6]', '[372, 186, 8*w + 42]', '[373, 373, 23*w - 130]', '[373, 373, 23*w + 107]', '[375, 75, -5*w - 15]', '[375, 75, 5*w + 30]', '[375, 75, -5*w + 35]', '[375, 75, -5*w + 20]', '[375, 375, -8*w - 33]', '[375, 375, -2*w + 23]', '[375, 375, 2*w + 21]', '[375, 375, -8*w + 41]', '[387, 129, 18*w + 87]', '[387, 129, -18*w + 105]', '[387, 387, -4*w - 5]', '[387, 387, 7*w + 38]', '[387, 387, -7*w + 45]', '[387, 387, -4*w + 9]', '[388, 194, 6*w + 34]', '[388, 194, 6*w - 40]', '[393, 393, -w - 20]', '[393, 393, 17*w - 95]', '[393, 393, 17*w + 78]', '[393, 393, w - 21]', '[400, 20, 20]', '[400, 100, -4*w - 4]', '[400, 100, -4*w + 8]', '[401, 401, -9*w + 47]', '[401, 401, 9*w + 38]', '[405, 45, -27*w + 153]', '[405, 45, -27*w - 126]', '[405, 135, 3*w + 24]', '[405, 135, -6*w + 27]', '[405, 135, -6*w - 21]', '[405, 135, -3*w + 27]', '[405, 405, -7*w + 34]', '[405, 405, 4*w + 27]', '[405, 405, -4*w + 31]', '[405, 405, -7*w - 27]', '[409, 409, 5*w - 19]', '[409, 409, -5*w - 14]', '[411, 411, -10*w + 61]', '[411, 411, 4*w - 7]', '[411, 411, -4*w - 3]', '[411, 411, -10*w - 51]', '[415, 415, 47*w + 221]', '[415, 415, 16*w - 89]', '[415, 415, 16*w + 73]', '[415, 415, 47*w - 268]', '[420, 210, -2*w - 22]', '[420, 210, -16*w - 78]', '[420, 210, 22*w - 124]', '[420, 210, 4*w - 6]', '[420, 210, 4*w + 2]', '[420, 210, 22*w + 102]', '[420, 210, 16*w - 94]', '[420, 210, 2*w - 24]', '[421, 421, -10*w + 53]', '[421, 421, 10*w + 43]', '[427, 427, -33*w + 190]', '[427, 427, -4*w - 1]', '[427, 427, -4*w + 5]', '[427, 427, 33*w + 157]', '[431, 431, -15*w - 68]', '[431, 431, 15*w - 83]', '[432, 36, -12*w + 72]', '[432, 36, 12*w + 60]', '[432, 108, -4*w]', '[432, 108, -4*w + 4]', '[433, 433, 43*w - 245]', '[433, 433, 43*w + 202]', '[435, 435, w + 21]', '[435, 435, -14*w - 69]', '[435, 435, -4*w + 3]', '[435, 435, 11*w + 48]', '[435, 435, -11*w + 59]', '[435, 435, 4*w - 1]', '[435, 435, -14*w + 83]', '[435, 435, w - 22]', '[436, 218, 4*w - 2]', '[439, 439, 35*w - 199]', '[439, 439, 35*w + 164]', '[441, 21, 21]', '[441, 63, -14*w - 63]', '[441, 63, -14*w + 77]', '[441, 147, -27*w + 156]', '[441, 147, 27*w + 129]', '[441, 441, -5*w + 36]', '[441, 441, -5*w - 13]', '[441, 441, -5*w + 18]', '[441, 441, 5*w + 31]', '[443, 443, 12*w + 53]', '[443, 443, 12*w - 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34]', '[811, 811, -3*w - 31]', '[823, 823, -13*w + 68]', '[823, 823, 13*w + 55]', '[827, 827, 7*w - 50]', '[827, 827, 7*w + 43]', '[829, 829, -7*w - 19]', '[829, 829, 7*w - 26]', '[857, 857, -8*w - 47]', '[857, 857, 8*w - 55]', '[863, 863, -11*w + 70]', '[863, 863, -11*w - 59]', '[877, 877, -3*w - 32]', '[877, 877, 3*w - 35]', '[881, 881, -6*w - 7]', '[881, 881, 6*w - 13]', '[887, 887, -21*w - 95]', '[887, 887, 21*w - 116]', '[907, 907, 19*w - 104]', '[907, 907, 19*w + 85]', '[947, 947, 9*w - 40]', '[947, 947, -9*w - 31]', '[953, 953, 29*w + 140]', '[953, 953, -29*w + 169]', '[977, 977, 6*w - 5]', '[977, 977, 6*w - 1]', '[997, 997, -26*w - 119]', '[997, 997, 26*w - 145]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-27, -1, 1], 'conductor': 109, 'degree': 2, 'dirichlet_group': [1, 108], 'disc_abs': 109, 'disc_rad': 109, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[1, 2]]], [5, [[1, 2]]], [7, [[1, 2]]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[2, 1]]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[1, 2]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[1, 2]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1], 'galois_label': '2T1', 'galt': 1, 'grd': 10.44030650891055, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.109.1', 'local_algs': ['109.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [109], 'rd': 10.4403065089, 'regulator': {'__RealLiteral__': 0, 'data': '5.56453508676', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 25 a + 118 \\)'], 'used_grh': False, 'zk': ['1', 'a']}