# Stored data for newform 153.4.a.c, downloaded from the LMFDB on 05 December 2024. {"Nk2": 2448, "analytic_conductor": 9.027292230878315, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [17, -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": [153, 1, [137, 37], [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, [-1, 1]], [5, [-20, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007199321850009, "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": "153.4.a.c", "level": 153, "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, 17], "level_radical": 51, "minimal_twist": "51.4.a.b", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}-7q^{4}+20q^{5}-2q^{7}-15q^{8}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "153.4.a", "trace_display": [1, 0, 20, -2], "trace_hash": 742572229229663826, "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "1.002", "prec": 17}, {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "2.034", "prec": 17}, {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "5.155", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 1, 1, 0, -7, 20, 0, -2, -15, 0, 20, 48, 0, -14, -2, 0, 41, 17, 0, 92, -140, 0, 48, 122, 0, 275, -14, 0, 14, 36, 0, -182, 161, 0, 17, -40, 0, 76, 92, 0, -300, -294, 0, -428, -336, 0, 122, 12, 0, -339, 275, 0, 98, 234, 0, 960, 30, 0, 36, 540, 0, -820, -182, 0, -167, -280, 0, 700, -119, 0, -40, -794, 0, -1038, 76, 0, -644, -96, 0, 858, 820, 0, -294, -1052, 0, 340, -428, 0, -720, -1102, 0, 28, -854, 0, 12, 1840, 0, 710, -339, 0, -1925, 1210, 0, 644, 210, 0, 234, 256, 0, -1248, 960, 0, -82, 350, 0, 2440, -252, 0, 540, -34, 0, 973, -820, 0, 1274, 3000, 0, -328, -1455, 0, -280, 1952, 0, -184, 700, 0, -255, -2634, 0, 1864, 280, 0, -794, -672, 0, 720, -1038, 0, -532, 286, 0, -1624, -1380, 0, -96, -3640, 0, 2542, 858, 0, 3220, -244, 0, 684, 2058, 0, -1052, -542, 0, -2001, 340, 0, 2996, 836, 0, -550, 1968, 0, -1102, 3444, 0, -3284, 28, 0, -1830, 1520, 0, 816, -84, 0, 1840, 340, 0, -1498, 710, 0, 2373, 1176, 0, -2450, -4125, 0, 1210, -72, 0, -5880, 644, 0, -574, 4416, 0, 1064, -1638, 0, 256, -8560, 0, 364, -1248, 0, -6720, -238, 0, -2244, -322, 0, 350, -516, 0, -2922, 2440, 0, -540, -3114, 0, 240, -3780, 0, -34, -4124, 0, -2034, 973, 0, 5740, -6780, 0, -1288, 2730, 0, 3000, -996, 0, 5856, -328, 0, -119, 3246, 0, -152, 1960, 0, 1952, -932, 0, 4680, -184, 0, -4900, 3884, 0, -1936, 697, 0, -2634, 13200, 0, 872, 1864, 0, 600, -3198, 0, -1936, 5558, 0, -672, 588, 0, 289, 720, 0, 7266, 5718, 0, 10800, -1140, 0, 286, -1708, 0, 856, -1624, 0, 3772, -16400, 0, 684, 672, 0, -3640, 290, 0, -11050, 2542, 0, -6006, -992, 0, 1728, -3340, 0, -244, 1564, 0, -3850, 684, 0, 4410, -24, 0, 2860, 7364, 0, -542, 14000, 0, 6298, -2001, 0, -2380, -8736, 0, 1364, 6420, 0, 836, 3508, 0, -2406, -550, 0, 7728, 1842, 0, -15880, 7714, 0, 3444, -3264, 0, 1605, -3284, 0, -196, -20760, 0, 7354, 5002, 0, 1520, -468, 0, 11322, 816, 0, -180, -504, 0, 12796, -12880, 0, 340, 420, 0, -1920, -1498, 0, -4970, -6426, 0, 2074, 5085, 0, 1176, 17160, 0, -13212, -2450, 0, 11275, 6242, 0, 2548, -8470, 0, -72, 3648, 0, -5194, -5880, 0, -4508, -1080, 0, -21040, -2254, 0, 4416, -15956, 0, -15254, 1064, 0, -3510, 4675, 0, 1640, -1792, 0, -8560, 5538, 0, 11342, 364, 0, 8736, 11224, 0, 982, -14400, 0, -238, 2492, 0, -22040, -2244, 0, 334, 5498, 0, -14112, -2450, 0, -516, 560, 0, 4998, -2922, 0, -17080, 7586, 0, 5900, 1476, 0, -3114, 19404, 0, -1400, 240, 0, -8100, -20544, 0, 25300, 238, 0, -4124, -2586, 0, -1064, -2034, 0, -6811, 14200, 0, 10106, 12300, 0, -6780, 76, 0, 612, -1288, 0, -7462, 1588, 0, 8096, -21000, 0, -996, -15942, 0, 24200, 5856, 0, 2296, 13742, 0, 2076, 11521, 0, 3246, 12880, 0, 576, -152, 0, 4200, -11942, 0, -6012, -13664, 0, -932, -3094, 0, 2717, 4680, 0, 1288, 4116, 0, 5120, -10500, 0, 3884, -16272, 0, 6420, -1936, 0, 2737, -24960, 0, 1576, 18438, 0, 13200, 3312, 0, -1716, 872, 0, -13048, -15318, 0, 5992, -1640, 0, -3198, -13220, 0, 7000, -1936, 0, 11910, -2794, 0, -14756, 4704, 0, 588, 33550, 0, -2846, 289, 0, -5040, 2104, 0, 11232, 15570, 0, 5718, 16820, 0, -16744, 10800, 0, 3116, -13314, 0, -680, -2002, 0, -1708, -2880, 0, -24854, 856, 0, 11368, 19460, 0, 6122, 14812, 0, -16400, -168, 0, 17398, 684, 0, 1440, -2922, 0, 9660, 25480, 0, 290, 2204, 0, 25625, -11050, 0, -17794, 1292, 0, 2788, -12870, 0, -992, -6560, 0, 4746, 1728, 0, -29100, 16290, 0, -16588, 1708, 0, 1564, -22364, 0, 25920, -3850, 0, -4788, 19356, 0, 39040, -12054, 0, -24, 4220, 0, -12070, 2860, 0, 15780, -3680, 0, 4392, 3794, 0, 14000, -39360, 0, -5914, 6298, 0, 14007, 27624, 0, -1420, -5100, 0, -8736, -29132, 0, -52680, 1364, 0, -17548, -3276, 0, -20336, -5852, 0, 3508, 37280, 0, -4998, -2406, 0, 3850, -17142, 0, 6992, -8016, 0, 1842, -2420, 0, 22784, -15880, 0, 16530, -22204, 0, -13440, -24108, 0, -3264, -58, 0, -1288, 1605, 0, 22988, 9900, 0, 712, -420, 0, -20760, -7276, 0, 23050, 7354, 0, 19642, 33600, 0, -38708, -10640, 0, -468, 11034, 0, 5720, 11322, 0, -5712, -512, 0, 7502, 492, 0, -504, -32480, 0, -20954, 12796, 0, -27600, -8186, 0, 2496, -2380, 0, 420, -7560, 0, -5798, -1920, 0, 10486, 39950, 0, -50050, -10650, 0, -6426, -27048, 0, -38112, 2074, 0, -13899, 50840, 0, 20656, -8232, 0, 17160, -700, 0, 11480, -13212, 0, 17150, 3722, 0, 204, 44275, 0, 6242, -49824, 0, -4880, 2548, 0, -18150, -6518, 0, -33068, 504, 0, 3648, 13680, 0, -39376, -5194, 0, 41160, 5328, 0, 25874, -9660, 0, -1080, -29184, 0, -9394, -21040, 0, 2338, -5763, 0, -10840, -30912, 0, -15956, 32062, 0, -23093, -15254, 0, -7448, -40020, 0, -1946, 9594, 0, 4675, 9272, 0, 9152, 1640, 0, -3840, 19706, 0, 28684, 59920, 0, 5538, 6320, 0, 16720, 11342, 0, -2548, 41184, 0, -9800, 18720, 0, 11224, -6000, 0, 49272, 982, 0, 39360, 16462, 0, 21300, 1666, 0, 2492, 16590, 0, 656, -22040, 0, 15708, 1104, 0, 68880, 2910, 0, 5498, -6552, 0, 3978, -14112, 0, -5250, -65680, 0, -36184, 3612, 0, 560, -15626, 0, -50496, 4998, 0, 20454, -3904, 0, 36672, -36600, 0, 7586, 11116, 0, 20900, 5900, 0, 5796, 15810, 0, -31188, 21798, 0, 19404, 16320, 0, 48646, -1400, 0, -1680, -43872, 0, -35868, 22140, 0, -20544, -38552, 0, 14532, 25300, 0, 510, 52954, 0, 6800, 28868, 0, -2586, 5268, 0, 3333, -1064, 0, 14238, -29960, 0, -46428, -14595, 0, 14200, 40980, 0, -3728, 10106, 0, -33620, 10206, 0, -52896, 47460, 0, 76, 44934, 0, 23520, 612, 0, 9016, -52216, 0, 20526, -29302, 0, 1588, -49000, 0, 29260, 8096, 0, -45000], "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, 1, 0, -7, 20, 0, -2, -15, 0, 20, 48, 0, -14, -2, 0, 41, 17, 0, 92, -140, 0, 48, 122, 0, 275, -14, 0, 14, 36, 0, -182, 161, 0, 17, -40, 0, 76, 92, 0, -300, -294, 0, -428, -336, 0, 122, 12, 0, -339, 275, 0, 98, 234, 0, 960, 30, 0, 36, 540, 0, -820, -182, 0, -167, -280, 0, 700, -119, 0, -40, -794, 0, -1038, 76, 0, -644, -96, 0, 858, 820, 0, -294, -1052, 0, 340, -428, 0, -720, -1102, 0, 28, -854, 0, 12, 1840, 0, 710, -339, 0, -1925, 1210, 0, 644, 210, 0, 234, 256, 0, -1248, 960, 0, -82, 350, 0, 2440, -252, 0, 540, -34, 0, 973, -820, 0, 1274, 3000, 0, -328, -1455, 0, -280, 1952, 0, -184, 700, 0, -255, -2634, 0, 1864, 280, 0, -794, -672, 0, 720, -1038, 0, -532, 286, 0, -1624, -1380, 0, -96, -3640, 0, 2542, 858, 0, 3220, -244, 0, 684, 2058, 0, -1052, -542, 0, -2001, 340, 0, 2996, 836, 0, -550, 1968, 0, -1102, 3444, 0, -3284, 28, 0, -1830, 1520, 0, 816, -84, 0, 1840, 340, 0, -1498, 710, 0, 2373, 1176, 0, -2450, -4125, 0, 1210, -72, 0, -5880, 644, 0, -574, 4416, 0, 1064, -1638, 0, 256, -8560, 0, 364, -1248, 0, -6720, -238, 0, -2244, -322, 0, 350, -516, 0, -2922, 2440, 0, -540, -3114, 0, 240, -3780, 0, -34, -4124, 0, -2034, 973, 0, 5740, -6780, 0, -1288, 2730, 0, 3000, -996, 0, 5856, -328, 0, -119, 3246, 0, -152, 1960, 0, 1952, -932, 0, 4680, -184, 0, -4900, 3884, 0, -1936, 697, 0, -2634, 13200, 0, 872, 1864, 0, 600, -3198, 0, -1936, 5558, 0, -672, 588, 0, 289, 720, 0, 7266, 5718, 0, 10800, -1140, 0, 286, -1708, 0, 856, -1624, 0, 3772, -16400, 0, 684, 672, 0, -3640, 290, 0, -11050, 2542, 0, -6006, -992, 0, 1728, -3340, 0, -244, 1564, 0, -3850, 684, 0, 4410, -24, 0, 2860, 7364, 0, -542, 14000, 0, 6298, -2001, 0, -2380, -8736, 0, 1364, 6420, 0, 836, 3508, 0, -2406, -550, 0, 7728, 1842, 0, -15880, 7714, 0, 3444, -3264, 0, 1605, -3284, 0, -196, -20760, 0, 7354, 5002, 0, 1520, -468, 0, 11322, 816, 0, -180, -504, 0, 12796, -12880, 0, 340, 420, 0, -1920, -1498, 0, -4970, -6426, 0, 2074, 5085, 0, 1176, 17160, 0, -13212, -2450, 0, 11275, 6242, 0, 2548, -8470, 0, -72, 3648, 0, -5194, -5880, 0, -4508, -1080, 0, -21040, -2254, 0, 4416, -15956, 0, -15254, 1064, 0, -3510, 4675, 0, 1640, -1792, 0, -8560, 5538, 0, 11342, 364, 0, 8736, 11224, 0, 982, -14400, 0, -238, 2492, 0, -22040, -2244, 0, 334, 5498, 0, -14112, -2450, 0, -516, 560, 0, 4998, -2922, 0, -17080, 7586, 0, 5900, 1476, 0, -3114, 19404, 0, -1400, 240, 0, -8100, -20544, 0, 25300, 238, 0, -4124, -2586, 0, -1064, -2034, 0, -6811, 14200, 0, 10106, 12300, 0, -6780, 76, 0, 612, -1288, 0, -7462, 1588, 0, 8096, -21000, 0, -996, -15942, 0, 24200, 5856, 0, 2296, 13742, 0, 2076, 11521, 0, 3246, 12880, 0, 576, -152, 0, 4200, -11942, 0, -6012, -13664, 0, -932, -3094, 0, 2717, 4680, 0, 1288, 4116, 0, 5120, -10500, 0, 3884, -16272, 0, 6420, -1936, 0, 2737, -24960, 0, 1576, 18438, 0, 13200, 3312, 0, -1716, 872, 0, -13048, -15318, 0, 5992, -1640, 0, -3198, -13220, 0, 7000, -1936, 0, 11910, -2794, 0, -14756, 4704, 0, 588, 33550, 0, -2846, 289, 0, -5040, 2104, 0, 11232, 15570, 0, 5718, 16820, 0, -16744, 10800, 0, 3116, -13314, 0, -680, -2002, 0, -1708, -2880, 0, -24854, 856, 0, 11368, 19460, 0, 6122, 14812, 0, -16400, -168, 0, 17398, 684, 0, 1440, -2922, 0, 9660, 25480, 0, 290, 2204, 0, 25625, -11050, 0, -17794, 1292, 0, 2788, -12870, 0, -992, -6560, 0, 4746, 1728, 0, -29100, 16290, 0, -16588, 1708, 0, 1564, -22364, 0, 25920, -3850, 0, -4788, 19356, 0, 39040, -12054, 0, -24, 4220, 0, -12070, 2860, 0, 15780, -3680, 0, 4392, 3794, 0, 14000, -39360, 0, -5914, 6298, 0, 14007, 27624, 0, -1420, -5100, 0, -8736, -29132, 0, -52680, 1364, 0, -17548, -3276, 0, -20336, -5852, 0, 3508, 37280, 0, -4998, -2406, 0, 3850, -17142, 0, 6992, -8016, 0, 1842, -2420, 0, 22784, -15880, 0, 16530, -22204, 0, -13440, -24108, 0, -3264, -58, 0, -1288, 1605, 0, 22988, 9900, 0, 712, -420, 0, -20760, -7276, 0, 23050, 7354, 0, 19642, 33600, 0, -38708, -10640, 0, -468, 11034, 0, 5720, 11322, 0, -5712, -512, 0, 7502, 492, 0, -504, -32480, 0, -20954, 12796, 0, -27600, -8186, 0, 2496, -2380, 0, 420, -7560, 0, -5798, -1920, 0, 10486, 39950, 0, -50050, -10650, 0, -6426, -27048, 0, -38112, 2074, 0, -13899, 50840, 0, 20656, -8232, 0, 17160, -700, 0, 11480, -13212, 0, 17150, 3722, 0, 204, 44275, 0, 6242, -49824, 0, -4880, 2548, 0, -18150, -6518, 0, -33068, 504, 0, 3648, 13680, 0, -39376, -5194, 0, 41160, 5328, 0, 25874, -9660, 0, -1080, -29184, 0, -9394, -21040, 0, 2338, -5763, 0, -10840, -30912, 0, -15956, 32062, 0, -23093, -15254, 0, -7448, -40020, 0, -1946, 9594, 0, 4675, 9272, 0, 9152, 1640, 0, -3840, 19706, 0, 28684, 59920, 0, 5538, 6320, 0, 16720, 11342, 0, -2548, 41184, 0, -9800, 18720, 0, 11224, -6000, 0, 49272, 982, 0, 39360, 16462, 0, 21300, 1666, 0, 2492, 16590, 0, 656, -22040, 0, 15708, 1104, 0, 68880, 2910, 0, 5498, -6552, 0, 3978, -14112, 0, -5250, -65680, 0, -36184, 3612, 0, 560, -15626, 0, -50496, 4998, 0, 20454, -3904, 0, 36672, -36600, 0, 7586, 11116, 0, 20900, 5900, 0, 5796, 15810, 0, -31188, 21798, 0, 19404, 16320, 0, 48646, -1400, 0, -1680, -43872, 0, -35868, 22140, 0, -20544, -38552, 0, 14532, 25300, 0, 510, 52954, 0, 6800, 28868, 0, -2586, 5268, 0, 3333, -1064, 0, 14238, -29960, 0, -46428, -14595, 0, 14200, 40980, 0, -3728, 10106, 0, -33620, 10206, 0, -52896, 47460, 0, 76, 44934, 0, 23520, 612, 0, 9016, -52216, 0, 20526, -29302, 0, 1588, -49000, 0, 29260, 8096, 0, -45000]}