# Stored data for newform 30.4.e.a, downloaded from the LMFDB on 27 April 2024.
{"label": "30.4.e.a", "space_label": "30.4.e", "level": 30, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 274945015838, "dim": 12, "is_polredabs": true, "trace_hash": 2076346968623104101, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\beta _{1}q^{2}+(1-\\beta _{3}-\\beta _{9})q^{3}-4\\beta _{3}q^{4}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 15, "char_orbit_label": "e", "char_is_real": false, "Nk2": 480, "analytic_conductor": 1.7700573001722184, "hecke_ring_index": 1152, "level_radical": 30, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.627", "prec": 17}, "analytic_rank_proved": true, "char_values": [30, 4, [11, 7], [2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3, 5], "conrey_indexes": [17, 23], "field_disc": 4581019027620495360000, "field_disc_factorization": [[2, 24], [3, 4], [5, 4], [271, 4]], "field_poly": [810000, 0, 0, 0, 284056, 0, 0, 0, 1577, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 7], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "10.526", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "913.962", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "156289.674", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "3.2.3.c4", "trace_display": [0, 8, 0, 12], "traces": [0, 12, 0, 8, 0, 0, 8, 12, 0, 0, 24, 0, -32, -120, 0, -172, -192, 0, -16, 0, 0, 464, 312, 0, 0, 504, 0, -688, 48, 0, 168, -504, 0, 788, 0, 0, 368, 768, 0, 0, -192, 0, -872, -1968, 0, -1328, -1152, 0, -128, 0, 0, 256, 480, 0, 0, 1572, 0, 968, 2280, 0, 896, 1848, 0, 1268, 0, 0, 944, -1752, 0, 0, -2616, 0, 64, 180, 0, -1112, -1152, 0, -4080, 0, 0, -4316, 2208, 0, 0, -1872, 0, 3620, 1248, 0, 5168, 4080, 0, 584, 0, 0, -128, -7596, 0, 0, -2352, 0, -1984, -108, 0, -1692, -288, 0, -2752, 0, 0, -4584, -192, 0, 0, 10008, 0, 7680, 6744, 0, 2336, 4668, 0, 6032, 0, 0, 5312, -636, 0, 0, -9600, 0, -3152, -11232, 0, -5240, 576, 0, -7168, 0, 0, -6840, 1200, 0, 0, 900, 0, -2680, 3072, 0, 7696, -6048, 0, 3928, 0, 0, 4320, 2760, 0, 0, -384, 0, -7072, -2568, 0, -4216, -6144, 0, -3488, 0, 0, 6928, 7872, 0, 0, 5604, 0, 2804, 1584, 0, -96, 8376, 0, 12192, 0, 0, 7664, 24, 0, 0, -3552, 0, 512, 3180, 0, -15000, -2160, 0, -3112, 0, 0, 4136, 8136, 0, 0, 16848, 0, -14056, 1920, 0, 1328, -25824, 0, -80, 0, 0, -5920, -4824, 0, 0, -1296, 0, -1248, -28548, 0, -1932, -14832, 0, 3872, 0, 0, 4904, -9120, 0, 0, -3000, 0, 8112, 7056, 0, 2752, 31008, 0, 9808, 0, 0, -2944, 25680, 0, 0, 9168, 0, -5072, 20448, 0, 5736, 3072, 0, 4848, 0, 0, -4640, 5976, 0, 0, -34488, 0, -11456, -7008, 0, -4136, -8160, 0, -21240, 0, 0, 5792, -27888, 0, 0, -3552, 0, 10080, 14520, 0, 22696, 22080, 0, 256, 0, 0, 5088, -720, 0, 0, 31212, 0, 26540, -13512, 0, -8704, -2784, 0, -17276, 0, 0, -23024, -4176, 0, 0, 3312, 0, 16320, -6612, 0, 2552, -9888, 0, 11728, 0, 0, -30632, -33312, 0, 0, -55800, 0, -14840, 8832, 0, -18792, 27744, 0, -35688, 0, 0, -7424, -8892, 0, 0, 18336, 0, 16544, 27696, 0, 34696, 27216, 0, 14480, 0, 0, 46680, -4992, 0, 0, -7560, 0, 21056, -26376, 0, 6176, -2844, 0, 6912, 0, 0, -27888, 32148, 0, 0, 38256, 0, -2336, 69048, 0, 15256, 24960, 0, 25400, 0, 0, -52672, -17136, 0, 0, 72, 0, -38088, -30384, 0, -32400, -57264, 0, -28156, 0, 0, 10112, -24864, 0, 0, -8064, 0, 12832, -44160, 0, 25008, -14640, 0, -7936, 0, 0, 74592, 432, 0, 0, -37704, 0, -5864, -24672, 0, -28144, -5112, 0, -3960, 0, 0, 18400, 74808, 0, 0, 22992, 0, 11008, 44868, 0, -30320, -5280, 0, 31160, 0, 0, -5300, 24960, 0, 0, -26328, 0, -71652, -768, 0, -21776, -74016, 0, 3488, 0, 0, -28288, 13740, 0, 0, 29856, 0, 4624, -9660, 0, 36464, 53904, 0, 30720, 0, 0, 57960, -26976, 0, 0, 59568, 0, 13576, -47472, 0, -2688, 58320, 0, 38312, 0, 0, 11032, 63972, 0, 0, 2640, 0, -24128, 8040, 0, -37076, 8064, 0, 20064, 0, 0, 9896, -44088, 0, 0, -16884, 0, -34624, -2544, 0, -20288, -158040, 0, -42872, 0, 0, -2976, -23280, 0, 0, -19200, 0, -3880, -36600, 0, 43528, -6624, 0, -12608, 0, 0, -35984, 44928, 0, 0, -15816, 0, 43204, 19608, 0, -1840, 82056, 0, -15296, 0, 0, -7680, 55968, 0, 0, 29064, 0, 28672, 8712, 0, -47448, -7104, 0, 32, 0, 0, 19648, -25392, 0, 0, 27768, 0, -38716, 4800, 0, 16096, 26400, 0, -35264, 0, 0, -5888, -159396, 0, 0, 24720, 0, 4536, 31392, 0, 47400, -91200, 0, -10720, 0, 0, 44952, -12288, 0, 0, -3192, 0, 52872, 42720, 0, 22752, 37800, 0, 59792, 0, 0, -10928, 11484, 0, 0, -69264, 0, -15712, 64176, 0, 5216, 37824, 0, -42712, 0, 0, -127400, 93168, 0, 0, -10332, 0, 8288, 11040, 0, 48648, 214392, 0, -28976, 0, 0, 41248, -40200, 0, 0, 3072, 0, 8288, -144312, 0, 2064, 36096, 0, -28288, 0, 0, 13712, 10272, 0, 0, -77484, 0, 90740, -6720, 0, -1792, -84840, 0, 47640, 0, 0, -43392, -60480, 0, 0, -49344, 0, 13952, -32964, 0, -69176, -100944, 0, -38048, 0, 0, -188944, -41424, 0, 0, 1296, 0, -13512, 31488, 0, 61952, -48816, 0, 32, 0, 0, -18880, -48864, 0, 0, -70992, 0, -34800, 60432, 0, -39600, 28656, 0, 11216, 0, 0, 161832, -6336, 0, 0, 229200, 0, 77208, 151296, 0, 21248, 209736, 0, 67832, 0, 0, 92712, 124116, 0, 0, 13560, 0, -48768, -74592, 0, -24560, 18432, 0, -71968, 0, 0, -78480, 5952, 0, 0, -70836, 0, 67128, 96, 0, 39816, -107400, 0, -5892, 0, 0, 20864, -105360, 0, 0, -48384, 0, -58904, -52920, 0, -3344, -79968, 0, 2048, 0, 0, -44992, -12720, 0, 0, 56352, 0, -3624, 58536, 0, 43200, -33360, 0, 23620, 0, 0, 60272, -14616, 0, 0, -133248, 0, 12448, 17520, 0, -75256, 7872, 0, -69568, 0, 0, 60656, 205872, 0, 0, 71088, 0, -117172, 32544, 0, 25768, -45168, 0, 77760, 0, 0, -4096, 31632, 0, 0, 48576, 0, -71808, -126180, 0, -87692, -56208, 0, -56224, 0, 0, -115656, -7680, 0, 0, 93288, 0, -4024, -109800, 0, 17536, 36012, 0, 128712, 0, 0, 34560, -69732, 0, 0, -30864, 0, 320, 33696, 0, -28416, -26112, 0, -51840, 0, 0, 120416, -30816, 0, 0, -6504, 0, 7376, -19296, 0, 64600, -169680, 0, 143916, 0, 0, 95360, 106872, 0, 0, -25152, 0, -31600, -123432, 0, -56456, 1008, 0, -4992, 0, 0, -7136, 114192, 0, 0, 128892, 0, 26520, 151920, 0, -21824, 140784, 0, -40776, 0, 0, 50048, 134016, 0, 0, 93600, 0, -15488, -51264, 0, -175848, 75168, 0, 1696, 0, 0, 92088, -99240, 0, 0, -12144, 0, -114028, -36480, 0, 3984, 143520, 0, 14992, 0, 0, -3840, -116460, 0, 0, -45600, 0, -22320, 3072, 0, 33700, -138144, 0, 32448, 0, 0, 57936, -28224, 0, 0, -9336, 0, 72680, -39696, 0, -14336, -237924, 0, 4264, 0, 0, -88864, -92388, 0, 0, -136872, 0, -39232, -14544, 0, 165600, -29568, 0, 21088, 0, 0, -239560, 131352, 0, 0, 98856, 0, 65880, 102720, 0, -3808, -3840, 0, -79504, 0, 0, -71136, 273096, 0, 0, 67296], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 5, 3, -1, 4, 0], [1, 1, 15, 5, 1, 4, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "30.4.e.a", "char_is_minimal": true, "conrey_index": 17, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, -1, 0, -1, -1, 1, 0, -1, -1, -1], [1, 0, 0, -1, -1, -1, -1, 0, 0, -1, 0, 1], [2, 1, 2, 2, 1, 0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0], [-1, -2, 0, 7, 0, 1, 0, -3, 1, -1, 0, 2], [2, 1, 0, -3, -1, 0, 0, 1, -1, 2, 1, -1], [-2, -7, -3, 0, 0, 7, 1, 0, 0, 3, -1, 0], [-4, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0], [-15, 5, 0, 20, 5, 5, 5, 0, -5, 10, 5, -5], [-2, 1, 4, 4, 0, 5, 2, -4, 0, 4, 2, 2], [-14, -15, -3, 14, -4, 1, -3, -2, -1, -2, -3, -1], [-16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -3, 2, 3, 0, 5, 2, -3, 0, 0, 5, 5], [-2, -3, 0, -1, 1, 6, -4, 1, -1, -2, -3, 3], [7, 2, 6, -26, 0, -4, -1, 6, 8, -2, -1, 1], [0, 4, -4, 0, 0, -4, 4, 0, 0, 0, 0, -4], [40, 18, -3, -3, -3, -21, 2, 0, 0, 0, -5, -4], [28, 2, 4, 28, 4, 0, 2, 2, 4, 0, 0, 0], [7, -4, 0, -11, 0, -35, -15, 11, 0, -14, -4, 4], [4, -4, 0, -8, 0, -8, -4, 4, 4, -4, -4, 0], [39, -7, -8, -57, -9, -1, -5, -6, -7, -6, -3, 3], [10, -5, 10, 0, 0, 5, 0, 0, 0, -10, 0, -10], [-55, 32, 17, -50, 4, 5, 0, -5, 4, 0, 5, 5], [0, 0, 0, 0, 4, 4, 4, -4, -4, 0, 0, 0], [1, 51, -9, -2, 0, 49, 6, 2, 0, -9, 6, -1], [15, -12, -8, 46, 0, 15, 1, 9, -3, -3, -1, -2], [-37, -5, 0, -10, -10, -5, -5, 0, 0, -10, -5, 5], [0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [58, 12, 0, -46, 8, 30, 13, -1, -8, 18, 12, -12], [-2, -7, -6, 4, 0, -1, -4, -6, 2, -8, -4, 4], [-6, 13, 1, 1, 0, -58, -5, -1, 0, 21, -14, -3], [28, 0, 0, 4, 4, 4, -4, 0, 0, 4, 8, 0], [56, -8, -16, 56, 3, 0, -8, -8, 3, 0, 0, 0], [-14, -2, 0, 12, 0, -12, 10, -12, 0, 28, -2, 2], [5, -65, 10, 110, 0, -75, 20, 10, 0, 10, 20, -5], [-8, 0, 8, -12, -4, -4, 0, 4, 4, -8, -4, 4], [-16, -54, -16, 0, 0, 54, 0, 0, 0, 16, 0, 16], [-70, 45, 8, -65, 1, 5, 10, 5, 1, 0, 5, 5], [-156, -11, 0, 145, -8, -8, -8, -3, 8, -22, -11, 11], [-4, 24, 12, 8, 0, 32, 0, -8, 0, 12, 0, 4], [-115, -24, 25, 23, 11, 119, 9, -6, 0, 25, 5, -4], [-104, -3, -22, -6, -6, -3, -14, 0, 0, 16, 8, -8], [10, -130, 10, -5, 0, -15, -10, 5, 0, 0, -15, -15], [-16, 0, 0, 16, 0, 0, 0, 0, 0, 16, 0, 0], [-14, -4, -12, -41, 0, 8, 2, -12, -16, 4, 2, -2], [6, 43, -22, -16, 0, -58, -4, 16, 0, -26, 4, 2], [14, 45, 10, 16, 16, -29, 9, 0, 0, 6, 7, 10], [40, 0, 0, 40, -20, 0, 0, 0, -20, 0, 0, 0], [8, 19, 0, 11, 0, 5, 30, -11, 0, -16, 19, -19], [-17, -64, -2, -114, 0, -47, -1, -17, -17, 15, -1, 0], [129, 1, -2, -25, 25, 1, 0, 0, 23, 4, 2, -2], [8, 4, 16, 0, 0, -4, -8, 0, 0, -16, 8, 8], [81, 142, -48, 51, -9, -30, -11, 19, -9, 0, -30, -30], [206, -14, 0, -220, -16, -16, -16, 2, 16, -28, -14, 14], [12, 136, -15, -24, 0, 112, -21, 24, 0, -15, -21, -12], [84, 16, 4, 52, -4, 48, 0, 0, 16, -8, 8, 4], [160, 16, 44, 32, 32, 16, 38, 0, 0, -12, -6, 6], [-10, -42, -20, 0, 0, 10, 10, 0, 0, 0, 10, 10], [149, -19, 0, -168, -29, 72, -34, 15, 29, -76, -19, 19], [0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0], [15, 110, 80, 35, 0, -160, 5, -35, 0, -40, 60, 40], [100, 72, 18, -6, -6, -78, 2, 0, 0, -24, -8, -16], [-141, 5, 10, -141, -18, 0, 5, 5, -18, 0, 0, 0], [4, -8, 0, -12, 0, 0, -20, 12, 0, -8, -8, 8], [2, -191, -30, 62, 0, -202, -65, 11, -7, -23, -65, -9], [-230, 29, 18, -24, 32, 21, 30, 8, -10, 40, 20, -20], [1, -18, -12, 0, 0, 18, 13, 0, 0, 12, -13, -27], [8, 24, -16, -12, -4, -20, -16, 4, -4, 0, -20, -20], [49, 14, 0, -35, -34, -34, -34, 48, 34, 28, 14, -14], [16, 53, -10, -32, 0, 21, -38, 32, 0, -10, -38, -16], [-110, -143, -25, -201, 12, 177, -8, -20, 6, -44, 12, 45], [-100, 16, 24, 32, 32, 16, 28, 0, 0, 8, 4, -4], [-7, -197, -18, -2, 0, 5, 7, 2, 0, 0, 5, 5], [-340, -5, 0, 335, -15, 105, 30, -35, 15, -10, -5, 5], [-22, 43, 14, -134, 0, 29, 36, 14, -58, 72, 36, -36], [-16, -16, 0, 16, 0, 16, 16, -16, 0, 16, 16, 16], [-382, 117, -52, -34, -34, -151, -19, 0, 0, 18, -15, 31], [184, 0, 0, 184, 32, 0, 0, 0, 32, 0, 0, 0], [-43, 6, 0, 49, 0, -79, 55, -49, 0, 86, 6, -6], [-8, -76, 12, -144, 0, -48, 16, -28, 12, 0, 16, 20], [-156, 22, 20, 414, 23, 10, 20, 12, 3, 24, 12, -12], [-16, -175, -10, 0, 0, 175, -6, 0, 0, 10, 6, 28], [259, 78, 10, 329, -31, 70, 2, -68, -31, 0, 70, 70], [88, 8, 0, -80, 16, 16, 16, -8, -16, 16, 8, -8], [-23, 31, 50, 46, 0, 77, 19, -46, 0, 50, 19, 23], [414, -95, 30, 176, 16, 26, 26, -24, -26, 30, 14, -16], [295, 10, -70, 20, 20, 10, -25, 0, 0, 90, 45, -45], [16, -96, -56, -44, 0, -60, -16, 44, 0, 0, -60, -60], [23, -25, 0, -48, 0, 165, -15, -10, 0, 42, -25, 25], [-10, 25, 10, 560, 0, 15, 20, 10, -30, 40, 20, -20], [-45, 234, -94, -20, 0, -94, 9, 20, 0, 90, -65, -29], [-16, 0, 0, 16, 16, 16, 16, 0, 0, 16, 0, -16], [-613, 20, 40, -613, -14, 0, 20, 20, -14, 0, 0, 0], [28, 4, 0, -24, 0, -69, -20, 24, 0, -56, 4, -4], [-3, -30, -61, 218, 0, -32, 64, 2, -8, -53, 64, -5], [-172, -24, -16, -224, -28, -32, -40, 8, 36, -32, -16, 16]]}