# Stored data for newform 99.6.a.c, downloaded from the LMFDB on 08 November 2025. {"Nk2": 3564, "analytic_conductor": 15.877998161485083, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [11, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [99, 1, [56, 46], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-4, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007199355404387, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "99.6.a.c", "level": 99, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 11], "level_radical": 33, "minimal_twist": "11.6.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+4q^{2}-2^{4}q^{4}+19q^{5}+10q^{7}-192q^{8}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "99.6.a", "trace_display": [4, 0, 19, 10], "trace_hash": 192654334845427669, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.042", "prec": 17}, {"__RealLiteral__": 0, "data": "1.966", "prec": 17}, {"__RealLiteral__": 0, "data": "0.209", "prec": 17}, {"__RealLiteral__": 0, "data": "4.884", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 1, 4, 0, -16, 19, 0, 10, -192, 0, 76, 121, 0, -1148, 40, 0, -256, -686, 0, -384, -304, 0, 484, -3709, 0, -2764, -4592, 0, -160, 5424, 0, -6443, 5120, 0, -2744, 190, 0, 12063, -1536, 0, -3648, 1528, 0, -4026, -1936, 0, -14836, -7168, 0, -16707, -11056, 0, 18368, 29862, 0, 2299, -1920, 0, 21696, 6461, 0, -16980, -25772, 0, 28672, -21812, 0, 29999, 10976, 0, 760, -31023, 0, 1924, 48252, 0, 6144, 1210, 0, 65138, -4864, 0, 6112, 102714, 0, -13034, -16104, 0, -23232, -17415, 0, -11480, 59344, 0, -28672, -7296, 0, 66905, -66828, 0, 44224, -96730, 0, -95704, 220416, 0, 119448, 32658, 0, -185438, 9196, 0, -2560, -72849, 0, -70471, -86784, 0, 25844, -6860, 0, 14641, -67920, 0, 103088, -111891, 0, -78184, -49152, 0, -87248, 462, 0, -3840, 119996, 0, 131712, -296233, 0, -399818, -3040, 0, -124092, -138908, 0, 103056, 7696, 0, -193008, -72670, 0, -303082, 73728, 0, 4840, -122417, 0, -532987, 260552, 0, 97280, -37090, 0, 282076, -24448, 0, 410856, 573588, 0, 946611, -52136, 0, 64416, 386286, 0, -27640, -30976, 0, -69660, -545079, 0, -279485, -45920, 0, 712128, 229197, 0, -83006, 114688, 0, -29184, 444437, 0, -18476, 267620, 0, 267312, -270182, 0, 43320, 530688, 0, -386920, 54240, 0, 29032, -382816, 0, 293888, -46464, 0, 1029684, -477792, 0, 130632, -76494, 0, -64430, -741752, 0, -36784, 787528, 0, 461281, 51200, 0, -291396, 855570, 0, -665805, -281884, 0, -1041408, -1209336, 0, -136192, -103376, 0, -27440, 571482, 0, -267080, 58564, 0, 271680, -317433, 0, 440832, 1237056, 0, -447564, -1387367, 0, -448789, -312736, 0, -1114112, 885922, 0, 120630, 348992, 0, 1848, -1446874, 0, 567378, -15360, 0, -479984, 353878, 0, 525260, 175616, 0, -1184932, -334444, 0, -595610, -1599272, 0, -36480, -732318, 0, 2233804, 496368, 0, -555632, 15280, 0, -949261, 412224, 0, -30784, 1531080, 0, 122759, -2316096, 0, -290680, 4257932, 0, -40260, -1212328, 0, 98304, -322620, 0, -1142680, -19360, 0, -489668, -586956, 0, -233857, -2131948, 0, -1042208, 935503, 0, 656304, 544768, 0, -148360, 263424, 0, 3173072, 1128304, 0, -293376, -71680, 0, -1058231, -1643424, 0, 2294352, 569981, 0, 506186, 3786444, 0, 208544, -779603, 0, -335140, 772992, 0, 1545144, -467636, 0, 304470, -110560, 0, 619520, -2518683, 0, -589437, 278640, 0, -2180316, 3018412, 0, -2328643, -1117940, 0, 183680, 36556, 0, 994429, 949504, 0, 916788, 298620, 0, 1728958, -332024, 0, 1376256, -6226752, 0, 454765, 116736, 0, 1777748, -2275573, 0, 22990, -73904, 0, -1070480, -389781, 0, 2544374, 3207744, 0, -1080728, 1237622, 0, -1619330, 173280, 0, 707584, 5543678, 0, 7396564, 1547680, 0, 216960, 1459623, 0, -2704926, 116128, 0, 1531264, 64610, 0, 1951566, -5877760, 0, -185856, -3373372, 0, -4525514, 4118736, 0, -5733504, 1896104, 0, -169800, -522528, 0, -305976, 684534, 0, -4225907, -257720, 0, 2967008, 1424256, 0, -2091848, -441408, 0, 3150112, -1562843, 0, -330885, 1845124, 0, 286720, 3004493, 0, 184888, 1165584, 0, 3422280, -218120, 0, -2445516, -2663220, 0, 1127536, -7791036, 0, -1051961, -1388544, 0, -4837344, -3970035, 0, 299990, -544768, 0, -1240512, -487146, 0, 1061376, 109760, 0, 2285928, 8539076, 0, -13848324, -1068320, 0, -234256, 1271195, 0, -1864867, 3260160, 0, -1269732, -5157272, 0, -3720864, 1763328, 0, 1649408, -310230, 0, 4533404, 1790256, 0, -5549468, -1711634, 0, -1837870, -1795156, 0, 1250944, -9738219, 0, 19240, -2883584, 0, 3543688, -1818376, 0, -867328, 482520, 0, 4187904, -4302789, 0, 2622800, -7392, 0, -5787496, 4419898, 0, 7320338, 2269512, 0, 61440, -1754144, 0, 620502, -5759808, 0, 1415512, -2021547, 0, -2496344, 2101040, 0, -3512320, -3523322, 0, 11432312, 4739728, 0, -1337776, -2082816, 0, 651380, -2382440, 0, 6397088, 9815290, 0, 4621848, -48640, 0, -2929272, 8191924, 0, -1384131, 8935216, 0, 5956416, 7542864, 0, -8694004, 2222528, 0, 61120, 10251676, 0, 2033793, -3797044, 0, -1648896, 1027140, 0, 3613302, -369408, 0, 6124320, -3517796, 0, 2474112, 491036, 0, -3088128, 8345348, 0, -130340, 1162720, 0, 17031728, -6150224, 0, -6862318, -161040, 0, 4849312, 278179, 0, -9455362, -1966080, 0, -1290480, 8228864, 0, -4636576, -4570720, 0, -232320, -6057042, 0, -5639935, 1958672, 0, -2347824, -174150, 0, 6511571, -935428, 0, 8527792, -8275218, 0, 1126165, -12506496, 0, 3742012, -1485496, 0, 19179636, 2625216, 0, -933888, 14201961, 0, 1607939, 593440, 0, 1053696, -3102355, 0, 781781, 12692288, 0, -4513216, -6888515, 0, 8778, -391168, 0, -286720, 12413434, 0, -8109935, -4232924, 0, -19721088, -72960, 0, -20117616, -9177408, 0, 2279924, -2054580, 0, 17806334, 2024744, 0, -15145776, -15517902, 0, 669050, 2502528, 0, -3118412, 2181056, 0, -5628427, -1340560, 0, 1030656, -34281576, 0, 22989167, -6180576, 0, -1870544, -7596542, 0, -1048208, 1217880, 0, 442240, -2340922, 0, -4632192, 3469312, 0, -10074732, -967300, 0, -19269445, -2357748, 0, 3343680, 23897087, 0, -2639252, 8721264, 0, 12073648, 21466515, 0, -957040, -9314572, 0, 4471760, -14991936, 0, -16770543, 2204160, 0, 146224, 2761836, 0, -17537268, 3977716, 0, -18990080, 3629879, 0, 14738654, -3667152, 0, 1194480, 4809460, 0, -1380730, 6915832, 0, 1328096, 326580, 0, 8293171, 1835008, 0, -24907008, -5758558, 0, -352294, 1819060, 0, 1400832, -16898460, 0, -1854380, -7110992, 0, -9102292, -7417228, 0, -36652, 91960, 0, 295616, 31746246, 0, 17808452, -12845760, 0, -1559124, -586752, 0, -3753783, 10177496, 0, 4276992, -10126753, 0, 20198512, 4322912, 0, 4950488, -728490, 0, 19493040, -6477320, 0, -693120, -15565993, 0, 4917248, -14151680, 0, 22174712, 232804, 0, -704710, 29586256, 0, 18572160, 29166672, 0, -16521482, -867840, 0, 5838492, 5359444, 0, 1545984, -10819704, 0, -464512, -5566142, 0, 11880069, 18375168, 0, 258440, 13285628, 0, -653987, 7806264, 0, -32915456, 11461002, 0, 10898172, 743424, 0, -13493488, -24774713, 0, 8908627, -18102056, 0, -16474944, 17985609, 0, 146410, -7644672, 0, 7584416, -44741667, 0, 27129062, -679200, 0, -6270336, 28423208, 0, 26592183, 1223904, 0, 2738136, 22250016, 0, 7339434, -16903628, 0, 1030880, 7881698, 0, -34438852, 35604096, 0, 5697024, -1118910, 0, 28342788, -8367392, 0, -588544, -36644533, 0, 16877164, -12600448, 0, -6251372, -2739406, 0, -781840, -1323540, 0, -7380496, 2752512, 0, -10356501, -491520, 0, 12017972, -34946832, 0, -20485332, 739552, 0, 13987008, -5310215, 0, -31328580, -13689120, 0, -872480, 24976212, 0, 12428394, -9782064, 0, 10652880, 4620, 0, -11061266, 13530432, 0, -31164144, 35614404, 0, -33342132, -4207844, 0, 27770880, 20173854, 0, 6415488, 19349376, 0, -15880140, -1577114, 0, 9107336, 1199960, 0, 2179072, 36770862, 0, -5667352, -1654016, 0, -1948584, 49574325, 0, -2208752, 4245504, 0, 1317120, -35378738, 0, 8444303, -9143712, 0, 34156304, -2962330, 0, 12883098, -55393296, 0, 4273280, -351044, 0, 27805888, -2811072, 0, 5084780, -15683521, 0, -3998180, -7459468, 0, 4346880, -20113965, 0, -2107215, 5078928, 0, -20629088, 20926899, 0, -5133458, -14883456, 0, -7053312, 14932434, 0, -31866272, -32988160, 0, -1240920, 823080, 0, 1389134, 18133616, 0, 21483072], "weight": 6, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 4, 0, -16, 19, 0, 10, -192, 0, 76, 121, 0, -1148, 40, 0, -256, -686, 0, -384, -304, 0, 484, -3709, 0, -2764, -4592, 0, -160, 5424, 0, -6443, 5120, 0, -2744, 190, 0, 12063, -1536, 0, -3648, 1528, 0, -4026, -1936, 0, -14836, -7168, 0, -16707, -11056, 0, 18368, 29862, 0, 2299, -1920, 0, 21696, 6461, 0, -16980, -25772, 0, 28672, -21812, 0, 29999, 10976, 0, 760, -31023, 0, 1924, 48252, 0, 6144, 1210, 0, 65138, -4864, 0, 6112, 102714, 0, -13034, -16104, 0, -23232, -17415, 0, -11480, 59344, 0, -28672, -7296, 0, 66905, -66828, 0, 44224, -96730, 0, -95704, 220416, 0, 119448, 32658, 0, -185438, 9196, 0, -2560, -72849, 0, -70471, -86784, 0, 25844, -6860, 0, 14641, -67920, 0, 103088, -111891, 0, -78184, -49152, 0, -87248, 462, 0, -3840, 119996, 0, 131712, -296233, 0, -399818, -3040, 0, -124092, -138908, 0, 103056, 7696, 0, -193008, -72670, 0, -303082, 73728, 0, 4840, -122417, 0, -532987, 260552, 0, 97280, -37090, 0, 282076, -24448, 0, 410856, 573588, 0, 946611, -52136, 0, 64416, 386286, 0, -27640, -30976, 0, -69660, -545079, 0, -279485, -45920, 0, 712128, 229197, 0, -83006, 114688, 0, -29184, 444437, 0, -18476, 267620, 0, 267312, -270182, 0, 43320, 530688, 0, -386920, 54240, 0, 29032, -382816, 0, 293888, -46464, 0, 1029684, -477792, 0, 130632, -76494, 0, -64430, -741752, 0, -36784, 787528, 0, 461281, 51200, 0, -291396, 855570, 0, -665805, -281884, 0, -1041408, -1209336, 0, -136192, -103376, 0, -27440, 571482, 0, -267080, 58564, 0, 271680, -317433, 0, 440832, 1237056, 0, -447564, -1387367, 0, -448789, -312736, 0, -1114112, 885922, 0, 120630, 348992, 0, 1848, -1446874, 0, 567378, -15360, 0, -479984, 353878, 0, 525260, 175616, 0, -1184932, -334444, 0, -595610, -1599272, 0, -36480, -732318, 0, 2233804, 496368, 0, -555632, 15280, 0, -949261, 412224, 0, -30784, 1531080, 0, 122759, -2316096, 0, -290680, 4257932, 0, -40260, -1212328, 0, 98304, -322620, 0, -1142680, -19360, 0, -489668, -586956, 0, -233857, -2131948, 0, -1042208, 935503, 0, 656304, 544768, 0, -148360, 263424, 0, 3173072, 1128304, 0, -293376, -71680, 0, -1058231, -1643424, 0, 2294352, 569981, 0, 506186, 3786444, 0, 208544, -779603, 0, -335140, 772992, 0, 1545144, -467636, 0, 304470, -110560, 0, 619520, -2518683, 0, -589437, 278640, 0, -2180316, 3018412, 0, -2328643, -1117940, 0, 183680, 36556, 0, 994429, 949504, 0, 916788, 298620, 0, 1728958, -332024, 0, 1376256, -6226752, 0, 454765, 116736, 0, 1777748, -2275573, 0, 22990, -73904, 0, -1070480, -389781, 0, 2544374, 3207744, 0, -1080728, 1237622, 0, -1619330, 173280, 0, 707584, 5543678, 0, 7396564, 1547680, 0, 216960, 1459623, 0, -2704926, 116128, 0, 1531264, 64610, 0, 1951566, -5877760, 0, -185856, -3373372, 0, -4525514, 4118736, 0, -5733504, 1896104, 0, -169800, -522528, 0, -305976, 684534, 0, -4225907, -257720, 0, 2967008, 1424256, 0, -2091848, -441408, 0, 3150112, -1562843, 0, -330885, 1845124, 0, 286720, 3004493, 0, 184888, 1165584, 0, 3422280, -218120, 0, -2445516, -2663220, 0, 1127536, -7791036, 0, -1051961, -1388544, 0, -4837344, -3970035, 0, 299990, -544768, 0, -1240512, -487146, 0, 1061376, 109760, 0, 2285928, 8539076, 0, -13848324, -1068320, 0, -234256, 1271195, 0, -1864867, 3260160, 0, -1269732, -5157272, 0, -3720864, 1763328, 0, 1649408, -310230, 0, 4533404, 1790256, 0, -5549468, -1711634, 0, -1837870, -1795156, 0, 1250944, -9738219, 0, 19240, -2883584, 0, 3543688, -1818376, 0, -867328, 482520, 0, 4187904, -4302789, 0, 2622800, -7392, 0, -5787496, 4419898, 0, 7320338, 2269512, 0, 61440, -1754144, 0, 620502, -5759808, 0, 1415512, -2021547, 0, -2496344, 2101040, 0, -3512320, -3523322, 0, 11432312, 4739728, 0, -1337776, -2082816, 0, 651380, -2382440, 0, 6397088, 9815290, 0, 4621848, -48640, 0, -2929272, 8191924, 0, -1384131, 8935216, 0, 5956416, 7542864, 0, -8694004, 2222528, 0, 61120, 10251676, 0, 2033793, -3797044, 0, -1648896, 1027140, 0, 3613302, -369408, 0, 6124320, -3517796, 0, 2474112, 491036, 0, -3088128, 8345348, 0, -130340, 1162720, 0, 17031728, -6150224, 0, -6862318, -161040, 0, 4849312, 278179, 0, -9455362, -1966080, 0, -1290480, 8228864, 0, -4636576, -4570720, 0, -232320, -6057042, 0, -5639935, 1958672, 0, -2347824, -174150, 0, 6511571, -935428, 0, 8527792, -8275218, 0, 1126165, -12506496, 0, 3742012, -1485496, 0, 19179636, 2625216, 0, -933888, 14201961, 0, 1607939, 593440, 0, 1053696, -3102355, 0, 781781, 12692288, 0, -4513216, -6888515, 0, 8778, -391168, 0, -286720, 12413434, 0, -8109935, -4232924, 0, -19721088, -72960, 0, -20117616, -9177408, 0, 2279924, -2054580, 0, 17806334, 2024744, 0, -15145776, -15517902, 0, 669050, 2502528, 0, -3118412, 2181056, 0, -5628427, -1340560, 0, 1030656, -34281576, 0, 22989167, -6180576, 0, -1870544, -7596542, 0, -1048208, 1217880, 0, 442240, -2340922, 0, -4632192, 3469312, 0, -10074732, -967300, 0, -19269445, -2357748, 0, 3343680, 23897087, 0, -2639252, 8721264, 0, 12073648, 21466515, 0, -957040, -9314572, 0, 4471760, -14991936, 0, -16770543, 2204160, 0, 146224, 2761836, 0, -17537268, 3977716, 0, -18990080, 3629879, 0, 14738654, -3667152, 0, 1194480, 4809460, 0, -1380730, 6915832, 0, 1328096, 326580, 0, 8293171, 1835008, 0, -24907008, -5758558, 0, -352294, 1819060, 0, 1400832, -16898460, 0, -1854380, -7110992, 0, -9102292, -7417228, 0, -36652, 91960, 0, 295616, 31746246, 0, 17808452, -12845760, 0, -1559124, -586752, 0, -3753783, 10177496, 0, 4276992, -10126753, 0, 20198512, 4322912, 0, 4950488, -728490, 0, 19493040, -6477320, 0, -693120, -15565993, 0, 4917248, -14151680, 0, 22174712, 232804, 0, -704710, 29586256, 0, 18572160, 29166672, 0, -16521482, -867840, 0, 5838492, 5359444, 0, 1545984, -10819704, 0, -464512, -5566142, 0, 11880069, 18375168, 0, 258440, 13285628, 0, -653987, 7806264, 0, -32915456, 11461002, 0, 10898172, 743424, 0, -13493488, -24774713, 0, 8908627, -18102056, 0, -16474944, 17985609, 0, 146410, -7644672, 0, 7584416, -44741667, 0, 27129062, -679200, 0, -6270336, 28423208, 0, 26592183, 1223904, 0, 2738136, 22250016, 0, 7339434, -16903628, 0, 1030880, 7881698, 0, -34438852, 35604096, 0, 5697024, -1118910, 0, 28342788, -8367392, 0, -588544, -36644533, 0, 16877164, -12600448, 0, -6251372, -2739406, 0, -781840, -1323540, 0, -7380496, 2752512, 0, -10356501, -491520, 0, 12017972, -34946832, 0, -20485332, 739552, 0, 13987008, -5310215, 0, -31328580, -13689120, 0, -872480, 24976212, 0, 12428394, -9782064, 0, 10652880, 4620, 0, -11061266, 13530432, 0, -31164144, 35614404, 0, -33342132, -4207844, 0, 27770880, 20173854, 0, 6415488, 19349376, 0, -15880140, -1577114, 0, 9107336, 1199960, 0, 2179072, 36770862, 0, -5667352, -1654016, 0, -1948584, 49574325, 0, -2208752, 4245504, 0, 1317120, -35378738, 0, 8444303, -9143712, 0, 34156304, -2962330, 0, 12883098, -55393296, 0, 4273280, -351044, 0, 27805888, -2811072, 0, 5084780, -15683521, 0, -3998180, -7459468, 0, 4346880, -20113965, 0, -2107215, 5078928, 0, -20629088, 20926899, 0, -5133458, -14883456, 0, -7053312, 14932434, 0, -31866272, -32988160, 0, -1240920, 823080, 0, 1389134, 18133616, 0, 21483072]}