# Stored data for newform 30.4.a.a, downloaded from the LMFDB on 04 December 2024. {"Nk2": 480, "analytic_conductor": 1.7700573001722184, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [3, -1], [5, -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": [30, 1, [11, 7], [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": [[7, [-32, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 67108894, "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": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "30.4.a.a", "level": 30, "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": true, "level_primes": [2, 3, 5], "level_radical": 30, "minimal_twist": "30.4.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "30.4.a", "trace_display": [-2, 3, 5, 32], "trace_hash": 2184677728804782922, "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "0.994", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.988", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.984", "prec": 17}], "trace_zratio": 0, "traces": [0, 1, -2, 3, 4, 5, -6, 32, -8, 9, -10, -60, 12, -34, -64, 15, 16, 42, -18, -76, 20, 96, 120, 0, -24, 25, 68, 27, 128, 6, -30, -232, -32, -180, -84, 160, 36, 134, 152, -102, -40, 234, -192, -412, -240, 45, 0, -360, 48, 681, -50, 126, -136, 222, -54, -300, -256, -228, -12, 660, 60, -490, 464, 288, 64, -170, 360, 812, 168, 0, -320, 120, -72, 746, -268, 75, -304, -1920, 204, 152, 80, 81, -468, -804, 384, 210, 824, 18, 480, -678, -90, -1088, 0, -696, 720, -380, -96, 194, -1362, -540, 100, 798, -252, 1088, 272, 480, -444, 1716, 108, -970, 600, 402, 512, 426, 456, 0, 24, -306, -1320, 1344, -120, 2269, 980, 702, -928, 125, -576, 200, -128, -1236, 340, 60, -720, -2432, -1624, 135, -336, 642, 0, -2836, 640, -1080, -240, 2040, 144, 30, -1492, 2043, 536, -1554, -150, -2272, 608, 378, 3840, -1160, -408, 1694, -304, 666, -160, 0, -162, -52, 936, -900, 1608, -1200, -768, -1041, -420, -684, -1648, 54, -36, 800, -960, 1980, 1356, 876, 180, 3854, 2176, -1470, 0, 670, 1392, -2520, -1440, 864, 760, -2784, 192, 914, -388, -510, 2724, -5202, 1080, 3152, -200, 2436, -1596, 192, 504, 1170, -2176, 0, -544, 4560, -960, 740, 888, 360, -3432, -2060, -216, -7424, 1940, 2238, -1200, -1428, -804, -520, -1024, 225, -852, 396, -912, -1330, 0, -5760, -48, 4866, 612, -1800, 2640, 456, -2688, -1824, 240, 6482, -4538, 243, -1960, 3405, -1404, 2584, 1856, -2412, -250, 1476, 1152, 0, -400, 630, 256, 4314, 2472, 4288, -680, 54, -120, -5280, 1440, 1110, 4864, -2034, 3248, 5526, -270, 2024, 672, -3264, -1284, -1500, 0, 2054, 5672, -2088, -1280, -7302, 2160, -3724, 480, -1140, -4080, 7488, -288, -3149, -60, 582, 2984, -7218, -4086, 3300, -1072, -1620, 3108, 0, 300, -13184, 4544, 2394, -1216, -2450, -756, 2540, -7680, 3264, 2320, 1560, 816, -934, -3388, 1440, 608, -1674, -1332, -360, 320, 5148, 0, -3192, 324, -850, 104, -2910, -1872, -11520, 1800, -3988, -3216, 1206, 2400, 4060, 1536, 2, 2082, 1278, 840, 13920, 1368, 10816, 3296, 0, -108, 1764, 72, 4310, -1600, -918, 1920, 138, -3960, 600, -2712, 4032, -1752, -11976, -360, -1083, -7708, 6807, -4352, 3730, 2940, 9704, 0, 2106, -1340, 7104, -2784, -8122, 5040, 375, 2880, -204, -1728, 3404, -1520, 600, 5568, -2520, -384, -9600, -1828, -3708, 776, 1566, 1020, 0, -5448, 180, 10404, 760, -2160, -4354, -6304, -7296, 400, -8046, -4872, 7888, 3192, 405, -384, -8040, -1008, -2806, -2340, 1926, 4352, 21120, 0, -4020, 1088, -8508, -9120, 11580, 1920, -370, -1480, -3240, -1776, 1050, -720, -15680, 6864, 6120, 4120, 5040, 432, -3742, 14848, 90, -3880, 0, -4476, -6208, 2400, 6129, 2856, -15564, 1608, -3390, 1040, -4662, 2048, -15774, -450, -14040, 1704, -6816, -792, -5440, 1824, 9722, 2660, 1134, 0, -10890, 11520, 15128, 96, -3480, -9732, 10668, -1224, 25984, 3600, 5082, -5280, 24720, -912, -1900, 5376, 1998, 3648, 15264, -480, -4556, -12964, 0, 9076, 970, -486, -5776, 3920, -156, -6810, 14244, 2808, 252, -5168, -2700, -3712, 3840, 4824, -17116, 500, -3600, -2952, -16848, -2304, 3990, 0, -3123, 800, -3834, -1260, 23872, -512, -2052, -8628, 5440, -4944, 21600, -8576, 162, 1360, -18822, -108, -15340, 240, 2400, 10560, -9744, -2880, -12167, -2220, 5940, -9728, -7956, 4068, 8580, -6496, 2628, -11052, -40860, 540, 18950, -4048, 11562, -1344, -4850, 6528, -10036, 2568, -4410, 3000, -456, 0, 4864, -4108, 2010, -11344, 10326, 4176, 14008, 2560, -7560, 14604, 4524, -4320, 2130, 7448, 2592, -960, 16362, 2280, 6620, 8160, -8352, -14976, 0, 576, 8834, 6298, 2742, 120, -25728, -1164, -13320, -5968, -1530, 14436, 3636, 8172, 17632, -6600, -15606, 2144, 6570, 3240, 6720, -6216, 9456, 0, 16584, -600, -502, 26368, 7308, -9088, 11345, -4788, -18568, 2432, 576, 4900, 12240, 1512, -13114, -5080, 3510, 15360, 5250, -6528, -10804, -4640, 0, -3120, -21696, -1632, 625, 1868, 13680, 6776, 5628, -2880, -27088, -1216, 2220, 3348, 1000, 2664, -23154, 720, 1080, -640, 18930, -10296, 20108, 0, -6180, 6384, -7152, -648, -39600, 1700, -22272, -208, -31626, 5820, 300, 3744, 6714, 23040, 28092, -3600, -13186, 7976, -4284, 6432, -12160, -2412, 0, -4800, -1560, -8120, 29400, -3072, 5138, -4, 675, -4164, 6078, -2556, 6208, -1680, 1188, -27840, 32244, -2736, 3210, -21632, -3990, -6592, -7548, 0, 4484, 216, -17280, -3528, -14180, -144, 9828, -8620, 14598, 3200, -30426, 1836, -10184, -3840, -5400, -276, 25536, 7920, 13262, -1200, 1368, 5424, 0, -8064, 10200, 3504, -5472, 23952, 13920, 720, 34816, 2166, 19446, 15416, 150, -13614, -9376, 8704, 729, -7460, -17304, -5880, 6014, -19408, 10215, 0, -48720, -4212, -7468, 2680, 7752, -14208, 31248, 5568, -7770, 16244, -7236, -10080, 54912, -750, 32840, -5760, 4428, 408, -11360, 3456, -19066, -6808, 0, 3040, 6858, -1200, -31040, -11136, 1890, 5040, -22440, 768, 22178, 19200, 12942, 3656, 14286, 7416, -5800, -1552, 12864, -3132, -17784, -2040, -7200, 0, 162, 10896, 8470, -360, -18868, -20808, -15840, -1520, 13632, 4320, 16660, 8708, 3330, 12608, -21690, 14592, -15120, -800, -6102, 16092, -44760, 9744, 0, -15776, 16578, -6384, -24726, -810, -2644, 768, 6072, 16080, -260, 2016, 31312, 5612, -9792, 4680, -37842, -3852, -880, -8704, -4500, -42240, -12876, 0, -25498, 8040, 6162, -2176, 28602, 17016, -6000, 18240, -6264, -23160, -40584, -3840, -24353, 740, -21906, 2960, -5205, 6480, 72608, 3552, -11172, -2100, 0, 1440, -25738, 31360, -3420, -13728, 13314, -12240, 24524, -8240, 22464, -10080, 5592, -864, 270, 7484, -9447, -29696, -9120, -180, -27608, 7760, 1746, 0, 4000, 8952, -14386, 12416, -21654, -4800, 47106, -12258, 51548, -5712, 9900, 31128, 34080, -3216, 6400, 6780, -4860, -2080, 27360, 9324, 4380, -4096, 0, 31548, -1392, 900, 9324, 28080, -39552, -3408, 19270, 13632, 25748, 1584, 7182, 10880, -24768, -3648, 48240, -19444, -7350, -5320, 1920, -2268, -31264, 0, 7620, 21780, -4080, -23040, 3350, -30256, 9792, -192, -6174, 6960, -51756, 19464, 4680, -21336, -12600, 2448, 28922, -51968, -2802, -7200, 29238, -10164, 0, 10560, 4320, -49440, -2868, 1824, -25364, 3800, -5022, -10752, 24018, -3996, -13920, -7296, -1080, -30528, 20544, 960, 24033, 9112, 15444, 25928, 4570, 0, 25712, -18152, -9576, -1940, -12396, 972, -90752, 11552, -2550, -7840, -46614, 312, 40680, 13620, -8730, -28488, -672, -5616, -26010, -504, -34560, 10336, 0, 5400, -38776, 7424, -11964, -7680, 15760, -9648, 30422, 34232, 3618, -1000], "weight": 4, "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, -2, 3, 4, 5, -6, 32, -8, 9, -10, -60, 12, -34, -64, 15, 16, 42, -18, -76, 20, 96, 120, 0, -24, 25, 68, 27, 128, 6, -30, -232, -32, -180, -84, 160, 36, 134, 152, -102, -40, 234, -192, -412, -240, 45, 0, -360, 48, 681, -50, 126, -136, 222, -54, -300, -256, -228, -12, 660, 60, -490, 464, 288, 64, -170, 360, 812, 168, 0, -320, 120, -72, 746, -268, 75, -304, -1920, 204, 152, 80, 81, -468, -804, 384, 210, 824, 18, 480, -678, -90, -1088, 0, -696, 720, -380, -96, 194, -1362, -540, 100, 798, -252, 1088, 272, 480, -444, 1716, 108, -970, 600, 402, 512, 426, 456, 0, 24, -306, -1320, 1344, -120, 2269, 980, 702, -928, 125, -576, 200, -128, -1236, 340, 60, -720, -2432, -1624, 135, -336, 642, 0, -2836, 640, -1080, -240, 2040, 144, 30, -1492, 2043, 536, -1554, -150, -2272, 608, 378, 3840, -1160, -408, 1694, -304, 666, -160, 0, -162, -52, 936, -900, 1608, -1200, -768, -1041, -420, -684, -1648, 54, -36, 800, -960, 1980, 1356, 876, 180, 3854, 2176, -1470, 0, 670, 1392, -2520, -1440, 864, 760, -2784, 192, 914, -388, -510, 2724, -5202, 1080, 3152, -200, 2436, -1596, 192, 504, 1170, -2176, 0, -544, 4560, -960, 740, 888, 360, -3432, -2060, -216, -7424, 1940, 2238, -1200, -1428, -804, -520, -1024, 225, -852, 396, -912, -1330, 0, -5760, -48, 4866, 612, -1800, 2640, 456, -2688, -1824, 240, 6482, -4538, 243, -1960, 3405, -1404, 2584, 1856, -2412, -250, 1476, 1152, 0, -400, 630, 256, 4314, 2472, 4288, -680, 54, -120, -5280, 1440, 1110, 4864, -2034, 3248, 5526, -270, 2024, 672, -3264, -1284, -1500, 0, 2054, 5672, -2088, -1280, -7302, 2160, -3724, 480, -1140, -4080, 7488, -288, -3149, -60, 582, 2984, -7218, -4086, 3300, -1072, -1620, 3108, 0, 300, -13184, 4544, 2394, -1216, -2450, -756, 2540, -7680, 3264, 2320, 1560, 816, -934, -3388, 1440, 608, -1674, -1332, -360, 320, 5148, 0, -3192, 324, -850, 104, -2910, -1872, -11520, 1800, -3988, -3216, 1206, 2400, 4060, 1536, 2, 2082, 1278, 840, 13920, 1368, 10816, 3296, 0, -108, 1764, 72, 4310, -1600, -918, 1920, 138, -3960, 600, -2712, 4032, -1752, -11976, -360, -1083, -7708, 6807, -4352, 3730, 2940, 9704, 0, 2106, -1340, 7104, -2784, -8122, 5040, 375, 2880, -204, -1728, 3404, -1520, 600, 5568, -2520, -384, -9600, -1828, -3708, 776, 1566, 1020, 0, -5448, 180, 10404, 760, -2160, -4354, -6304, -7296, 400, -8046, -4872, 7888, 3192, 405, -384, -8040, -1008, -2806, -2340, 1926, 4352, 21120, 0, -4020, 1088, -8508, -9120, 11580, 1920, -370, -1480, -3240, -1776, 1050, -720, -15680, 6864, 6120, 4120, 5040, 432, -3742, 14848, 90, -3880, 0, -4476, -6208, 2400, 6129, 2856, -15564, 1608, -3390, 1040, -4662, 2048, -15774, -450, -14040, 1704, -6816, -792, -5440, 1824, 9722, 2660, 1134, 0, -10890, 11520, 15128, 96, -3480, -9732, 10668, -1224, 25984, 3600, 5082, -5280, 24720, -912, -1900, 5376, 1998, 3648, 15264, -480, -4556, -12964, 0, 9076, 970, -486, -5776, 3920, -156, -6810, 14244, 2808, 252, -5168, -2700, -3712, 3840, 4824, -17116, 500, -3600, -2952, -16848, -2304, 3990, 0, -3123, 800, -3834, -1260, 23872, -512, -2052, -8628, 5440, -4944, 21600, -8576, 162, 1360, -18822, -108, -15340, 240, 2400, 10560, -9744, -2880, -12167, -2220, 5940, -9728, -7956, 4068, 8580, -6496, 2628, -11052, -40860, 540, 18950, -4048, 11562, -1344, -4850, 6528, -10036, 2568, -4410, 3000, -456, 0, 4864, -4108, 2010, -11344, 10326, 4176, 14008, 2560, -7560, 14604, 4524, -4320, 2130, 7448, 2592, -960, 16362, 2280, 6620, 8160, -8352, -14976, 0, 576, 8834, 6298, 2742, 120, -25728, -1164, -13320, -5968, -1530, 14436, 3636, 8172, 17632, -6600, -15606, 2144, 6570, 3240, 6720, -6216, 9456, 0, 16584, -600, -502, 26368, 7308, -9088, 11345, -4788, -18568, 2432, 576, 4900, 12240, 1512, -13114, -5080, 3510, 15360, 5250, -6528, -10804, -4640, 0, -3120, -21696, -1632, 625, 1868, 13680, 6776, 5628, -2880, -27088, -1216, 2220, 3348, 1000, 2664, -23154, 720, 1080, -640, 18930, -10296, 20108, 0, -6180, 6384, -7152, -648, -39600, 1700, -22272, -208, -31626, 5820, 300, 3744, 6714, 23040, 28092, -3600, -13186, 7976, -4284, 6432, -12160, -2412, 0, -4800, -1560, -8120, 29400, -3072, 5138, -4, 675, -4164, 6078, -2556, 6208, -1680, 1188, -27840, 32244, -2736, 3210, -21632, -3990, -6592, -7548, 0, 4484, 216, -17280, -3528, -14180, -144, 9828, -8620, 14598, 3200, -30426, 1836, -10184, -3840, -5400, -276, 25536, 7920, 13262, -1200, 1368, 5424, 0, -8064, 10200, 3504, -5472, 23952, 13920, 720, 34816, 2166, 19446, 15416, 150, -13614, -9376, 8704, 729, -7460, -17304, -5880, 6014, -19408, 10215, 0, -48720, -4212, -7468, 2680, 7752, -14208, 31248, 5568, -7770, 16244, -7236, -10080, 54912, -750, 32840, -5760, 4428, 408, -11360, 3456, -19066, -6808, 0, 3040, 6858, -1200, -31040, -11136, 1890, 5040, -22440, 768, 22178, 19200, 12942, 3656, 14286, 7416, -5800, -1552, 12864, -3132, -17784, -2040, -7200, 0, 162, 10896, 8470, -360, -18868, -20808, -15840, -1520, 13632, 4320, 16660, 8708, 3330, 12608, -21690, 14592, -15120, -800, -6102, 16092, -44760, 9744, 0, -15776, 16578, -6384, -24726, -810, -2644, 768, 6072, 16080, -260, 2016, 31312, 5612, -9792, 4680, -37842, -3852, -880, -8704, -4500, -42240, -12876, 0, -25498, 8040, 6162, -2176, 28602, 17016, -6000, 18240, -6264, -23160, -40584, -3840, -24353, 740, -21906, 2960, -5205, 6480, 72608, 3552, -11172, -2100, 0, 1440, -25738, 31360, -3420, -13728, 13314, -12240, 24524, -8240, 22464, -10080, 5592, -864, 270, 7484, -9447, -29696, -9120, -180, -27608, 7760, 1746, 0, 4000, 8952, -14386, 12416, -21654, -4800, 47106, -12258, 51548, -5712, 9900, 31128, 34080, -3216, 6400, 6780, -4860, -2080, 27360, 9324, 4380, -4096, 0, 31548, -1392, 900, 9324, 28080, -39552, -3408, 19270, 13632, 25748, 1584, 7182, 10880, -24768, -3648, 48240, -19444, -7350, -5320, 1920, -2268, -31264, 0, 7620, 21780, -4080, -23040, 3350, -30256, 9792, -192, -6174, 6960, -51756, 19464, 4680, -21336, -12600, 2448, 28922, -51968, -2802, -7200, 29238, -10164, 0, 10560, 4320, -49440, -2868, 1824, -25364, 3800, -5022, -10752, 24018, -3996, -13920, -7296, -1080, -30528, 20544, 960, 24033, 9112, 15444, 25928, 4570, 0, 25712, -18152, -9576, -1940, -12396, 972, -90752, 11552, -2550, -7840, -46614, 312, 40680, 13620, -8730, -28488, -672, -5616, -26010, -504, -34560, 10336, 0, 5400, -38776, 7424, -11964, -7680, 15760, -9648, 30422, 34232, 3618, -1000]}