# Stored data for newform 152.4.a.b, downloaded from the LMFDB on 12 November 2025. {"Nk2": 2432, "analytic_conductor": 8.968290320872573, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [19, -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": [152, 1, [39, 77, 97], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 3221, "field_disc_factorization": [[3221, 1]], "field_poly": [2, -9, -1, 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": [[3, [28, -52, 5, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503599694479512, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "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": "152.4.a.b", "level": 152, "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": [2, 19], "level_radical": 38, "minimal_twist": "152.4.a.b", "nf_label": "3.3.3221.1", "prim_orbit_index": 1, "qexp_display": "q+(-2-\\beta _{2})q^{3}+(1-\\beta _{1}+2\\beta _{2})q^{5}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "152.4.a", "trace_display": [0, -5, 2, -35], "trace_hash": 113280424510945065, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.717", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "19.688", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "205.995", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 3, 0, -5, 0, 2, 0, -35, 0, 48, 0, -28, 0, -109, 0, -228, 0, -123, 0, 57, 0, 25, 0, -193, 0, 187, 0, -719, 0, -297, 0, -140, 0, 30, 0, -246, 0, 38, 0, 57, 0, 736, 0, -514, 0, 1046, 0, 134, 0, -42, 0, 929, 0, 311, 0, -130, 0, -95, 0, 199, 0, 56, 0, 508, 0, 1156, 0, -509, 0, 621, 0, -874, 0, 203, 0, 129, 0, 616, 0, 242, 0, 3531, 0, -62, 0, -1430, 0, 3237, 0, 1764, 0, -687, 0, -2592, 0, 38, 0, -2178, 0, 86, 0, -1602, 0, 382, 0, 468, 0, -959, 0, -1727, 0, 266, 0, 3278, 0, -2252, 0, -3934, 0, 1235, 0, -3587, 0, 1432, 0, -3366, 0, -62, 0, 1956, 0, 2746, 0, -665, 0, -5100, 0, -1231, 0, 2570, 0, -4552, 0, 38, 0, -5588, 0, 2102, 0, -2006, 0, -3258, 0, -6612, 0, 4740, 0, -5926, 0, 1401, 0, 5301, 0, -4704, 0, 1032, 0, 1444, 0, 4474, 0, 912, 0, -3370, 0, 2537, 0, 11585, 0, -2032, 0, -2486, 0, -4722, 0, 3256, 0, 1048, 0, 3115, 0, -2007, 0, -1554, 0, 14516, 0, 2740, 0, 6497, 0, 7725, 0, 3277, 0, -5456, 0, -310, 0, -532, 0, -7597, 0, -1346, 0, 2878, 0, 3268, 0, 3531, 0, 3721, 0, -1794, 0, 7426, 0, -4613, 0, -2864, 0, 106, 0, 11840, 0, 34, 0, 11586, 0, 1529, 0, 4808, 0, -18128, 0, 5300, 0, -2071, 0, -8850, 0, 3448, 0, 3326, 0, 13668, 0, 10760, 0, -8222, 0, -21486, 0, -14794, 0, 3752, 0, -7296, 0, 16354, 0, -1929, 0, -2493, 0, 614, 0, -9018, 0, 17164, 0, 5172, 0, -6388, 0, -4332, 0, -7328, 0, -5352, 0, 3074, 0, -8043, 0, -23336, 0, 4074, 0, -4259, 0, -4842, 0, 9918, 0, -2022, 0, 5376, 0, 10502, 0, -14227, 0, -11399, 0, 390, 0, 19013, 0, 2678, 0, -713, 0, -2337, 0, -24191, 0, -20737, 0, 15862, 0, 6209, 0, -13036, 0, -21400, 0, -20840, 0, -13126, 0, 2124, 0, -6289, 0, 5492, 0, 8108, 0, 6044, 0, 37323, 0, -8939, 0, 15740, 0, -3397, 0, -5269, 0, 1083, 0, 6603, 0, -9062, 0, 10060, 0, -2288, 0, -18395, 0, -14183, 0, -24, 0, 5965, 0, 20247, 0, -15154, 0, 1954, 0, 3854, 0, -31078, 0, 13384, 0, 9709, 0, -27684, 0, -11484, 0, 6410, 0, 475, 0, -10004, 0, 5016, 0, 63002, 0, -4244, 0, 14032, 0, -22531, 0, -3051, 0, 22608, 0, -304, 0, 5864, 0, 27395, 0, 54254, 0, -5023, 0, 21980, 0, -1446, 0, 2630, 0, -18386, 0, 36940, 0, -3667, 0, 2476, 0, -41040, 0, 20180, 0, 12276, 0, 7128, 0, 16754, 0, -6240, 0, -21466, 0, -2084, 0, -23609, 0, 51251, 0, 5094, 0, 1338, 0, -9208, 0, 4148, 0, 20553, 0, 42, 0, -622, 0, 3553, 0, -28690, 0, 14948, 0, 25186, 0, 543, 0, 9264, 0, -36390, 0, -10224, 0, -6988, 0, 28629, 0, -3466, 0, -11238, 0, 21054, 0, -15044, 0, 2743, 0, -16556, 0, 28876, 0, 21970, 0, 549, 0, -13661, 0, -46964, 0, 7462, 0, -16234, 0, -7424, 0, -4483, 0, 4955, 0, -11212, 0, -6116, 0, -69410, 0, -36464, 0, 16904, 0, -9640, 0, -9000, 0, -6912, 0, -19526, 0, 29720, 0, -12124, 0, 62618, 0, -5643, 0, -27490, 0, 25984, 0, -3458, 0, 54412, 0, -4950, 0, -28428, 0, 1504, 0, -35867, 0, 20304, 0, -25500, 0, -13107, 0, 15685, 0, 9097, 0, 30278, 0, -8762, 0, -10286, 0, -63056, 0, -17998, 0, -2660, 0, -13520, 0, -45690, 0, 10434, 0, -7371, 0, -47876, 0, 26348, 0, -27482, 0, -280, 0, -33566, 0, -10889, 0, -57200, 0, 5060, 0, -47048, 0, 49516, 0, 42098, 0, 31767, 0, -25356, 0, -15841, 0, 570, 0, 418, 0, 6090, 0, 7869, 0, 33064, 0, 63206, 0, -29320, 0, -36070, 0, 17880, 0, 82496, 0, 7809, 0, -2222, 0, 8944, 0, 7830, 0, 59802, 0, -15592, 0, -21507, 0, 33221, 0, -43029, 0, -4674, 0, 29041, 0, -30182, 0, 10794, 0, -752, 0, -67869, 0, 21617, 0, 6202, 0, 7609, 0, -12348, 0, 45234, 0, 14570, 0, 36545, 0, -18296, 0, -14066, 0, 3558, 0, -14224, 0, 6126, 0, 13496, 0, 722, 0, -92816, 0, 20674, 0, 8142, 0, -105064, 0, 6696, 0, -5088, 0, 40597, 0, -17683, 0, 45426, 0, 12632, 0, -3659, 0, 39917, 0, 124095, 0, 27670, 0, -31328, 0, 79096, 0, 12058, 0, -3182, 0, 1083, 0, 34276, 0, -19346, 0, 38500, 0, -14653, 0, 50096, 0, -21882, 0, 49044, 0, 46700, 0, -1902, 0, 9301, 0, 52867, 0, -99962, 0, -28511, 0, 32267, 0, -32336, 0, -58791, 0, -11784, 0, -8450, 0, 13984, 0, -2560, 0, 149367, 0, 25180, 0, -3325, 0, 29352, 0, -6230, 0, -71994, 0, 37644, 0, -8717, 0, -31466, 0, 47196, 0, -436, 0, 33196, 0, -55014, 0, 10095, 0, 22409, 0, 86477, 0, 47296, 0, -9766, 0, 37542, 0, -88946, 0, -45865, 0, 2026, 0, -87017, 0, 8397, 0, 25012, 0, 13914, 0, -30888, 0, -57816, 0, 29664, 0, 19114, 0, -19240, 0, -119190, 0, 35127, 0, 94, 0, -43910, 0, -55850, 0, 19874, 0, 8800, 0, 7608, 0, -584, 0, -914, 0, 2276, 0, -63832, 0, -14592, 0, -46411, 0, -60324, 0, 42250, 0, -30475, 0, 49815, 0, 2416, 0, -43812, 0, 47012, 0, 12538, 0, -4458, 0, -30292, 0, 2546, 0, 81696, 0, -40849, 0, -49488, 0, -1235, 0, -18420, 0, 81420, 0, -6995, 0, -66144, 0, 19936, 0, -4164, 0, -106616, 0, -55550, 0, -13371, 0, -117996, 0, 112382, 0, -61774, 0, 14104, 0, -17427, 0, -798, 0, -77275, 0, 10222, 0, -29141, 0, 43495, 0, 41223, 0, -29792, 0, 37212, 0, 13220, 0, -25325, 0, -50941, 0, -23538, 0, 31002, 0, -16774, 0, 20583, 0, -15405, 0, -40238, 0, -70668, 0, -89408, 0, 17651, 0, 30028, 0, -49590, 0, -52677, 0, -6364, 0, -18852, 0, 163138, 0, -17454, 0, 24476, 0, 31528, 0, -22148, 0, -91776, 0, -73193, 0, 21242, 0, -20658, 0, 58454, 0], "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, 0, 0], [1, 0, 0], [0, 0, 0], [-2, 0, -1], [0, 0, 0], [1, -1, 2], [0, 0, 0], [-11, 2, 0], [0, 0, 0], [19, 3, 6], [0, 0, 0], [-9, 1, 0], [0, 0, 0], [-38, -7, 2], [0, 0, 0], [-80, -7, -5], [0, 0, 0], [-43, 0, -6], [0, 0, 0], [19, 0, 0], [0, 0, 0], [10, 2, 3], [0, 0, 0], [-62, 11, -4], [0, 0, 0], [66, 17, -6], [0, 0, 0], [-254, -15, -28], [0, 0, 0], [-106, 2, -23], [0, 0, 0], [-38, 3, 23], [0, 0, 0], [12, 1, 5], [0, 0, 0], [-79, 11, -2], [0, 0, 0], [4, -27, 1], [0, 0, 0], [34, -13, 58], [0, 0, 0], [240, 7, -23], [0, 0, 0], [-185, -37, -4], [0, 0, 0], [385, 35, 74], [0, 0, 0], [73, 57, 28], [0, 0, 0], [-38, -64, -8], [0, 0, 0], [338, 18, 67], [0, 0, 0], [84, -50, -9], [0, 0, 0], [-43, 9, -8], [0, 0, 0], [-38, 0, -19], [0, 0, 0], [36, 9, -100], [0, 0, 0], [53, 75, 28], [0, 0, 0], [139, -61, -30], [0, 0, 0], [356, 56, -144], [0, 0, 0], [-172, 58, -65], [0, 0, 0], [226, 23, 34], [0, 0, 0], [-306, -78, 34], [0, 0, 0], [61, 14, -34], [0, 0, 0], [18, 35, -110], [0, 0, 0], [191, -39, -4], [0, 0, 0], [26, -75, -89], [0, 0, 0], [1261, -12, 264], [0, 0, 0], [-8, -42, 80], [0, 0, 0], [-511, -11, -92], [0, 0, 0], [1166, 71, 190], [0, 0, 0], [594, -21, 39], [0, 0, 0], [-202, 59, 22], [0, 0, 0], [-908, -66, -66], [0, 0, 0], [19, -19, 38], [0, 0, 0], [-744, -68, 14], [0, 0, 0], [3, -41, -36], [0, 0, 0]]}