# Stored data for newform 336.4.q.g, downloaded from the LMFDB on 25 April 2024.
{"label": "336.4.q.g", "space_label": "336.4.q", "level": 336, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27022697342959952, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2295225.4", "trace_hash": 1573015824442454319, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [11236, -954, 187, 9, 1]]], "qexp_display": "q+(-3+3\\beta _{2})q^{3}+(-\\beta _{1}-4\\beta _{2})q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "q", "char_is_real": false, "Nk2": 5376, "analytic_conductor": 19.824641761928845, "hecke_ring_index": 1, "level_radical": 42, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [336, 3, [127, 85, 113, 241], [3, 3, 3, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [193, 289], "field_disc": 2295225, "field_disc_factorization": [[3, 2], [5, 2], [101, 2]], "field_poly": [15876, 126, 127, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.100", "prec": 17}, {"__RealLiteral__": 0, "data": "3.914", "prec": 17}, {"__RealLiteral__": 0, "data": "0.895", "prec": 17}, {"__RealLiteral__": 0, "data": "59.961", "prec": 20}, {"__RealLiteral__": 0, "data": "10.530", "prec": 20}, {"__RealLiteral__": 0, "data": "1546.325", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [0, -6, -9, 0], "traces": [0, 4, 0, -6, 0, -9, 0, 0, 0, -18, 0, 5, 0, -38, 0, 54, 0, 4, 0, 117, 0, -153, 0, 148, 0, -43, 0, 108, 0, -190, 0, -360, 0, 15, 0, 482, 0, 53, 0, 57, 0, -340, 0, -806, 0, -81, 0, 368, 0, -362, 0, 12, 0, -697, 0, -2570, 0, -702, 0, -585, 0, 1160, 0, 459, 0, 338, 0, 233, 0, -888, 0, -1232, 0, 817, 0, -129, 0, -1135, 0, -802, 0, -162, 0, 566, 0, 1984, 0, 285, 0, 1858, 0, 505, 0, -1080, 0, 2294, 0, 3458, 0, -90, 0, 472, 0, -847, 0, -1515, 0, 3573, 0, 873, 0, -318, 0, 1468, 0, -344, 0, 171, 0, 1112, 0, -3663, 0, 510, 0, 2682, 0, -1836, 0, 1209, 0, 2925, 0, -4751, 0, -243, 0, 1778, 0, -5870, 0, -2208, 0, -1310, 0, -835, 0, 543, 0, -4766, 0, 6535, 0, -72, 0, 4250, 0, 378, 0, -2091, 0, -2764, 0, 4348, 0, 3855, 0, -2744, 0, -7922, 0, 1053, 0, 3506, 0, 1176, 0, -1755, 0, 3114, 0, 8874, 0, -6960, 0, -14, 0, 5040, 0, 0, 0, 4006, 0, -2512, 0, -2028, 0, 7524, 0, 260, 0, 699, 0, -2525, 0, -3780, 0, 1332, 0, 18260, 0, 7292, 0, 1848, 0, -5004, 0, -8675, 0, 2451, 0, 972, 0, -10170, 0, 774, 0, -5293, 0, 3015, 0, -4170, 0, 6102, 0, 10746, 0, 4812, 0, -14508, 0, -7613, 0, -486, 0, -12063, 0, -2879, 0, -849, 0, 1898, 0, -9360, 0, -2976, 0, 5404, 0, -1099, 0, 855, 0, 2646, 0, 8798, 0, -11148, 0, -5287, 0, 5291, 0, 696, 0, 11470, 0, -3989, 0, 6480, 0, -5508, 0, -4005, 0, 6882, 0, -9090, 0, 5778, 0, -5187, 0, -8118, 0, -8370, 0, 135, 0, -396, 0, -13635, 0, 1416, 0, 12290, 0, -814, 0, 5082, 0, -9310, 0, 288, 0, 207, 0, -1989, 0, 6075, 0, -21438, 0, -13672, 0, 2681, 0, 2619, 0, -18474, 0, 3643, 0, 477, 0, 34768, 0, -15700, 0, -2202, 0, 3425, 0, 0, 0, -1032, 0, -7056, 0, 24568, 0, -1026, 0, 2066, 0, 21962, 0, 2724, 0, -9630, 0, -5499, 0, 21978, 0, -39168, 0, -11772, 0, 1530, 0, -16511, 0, 8793, 0, -4023, 0, -720, 0, -19798, 0, 2754, 0, -1134, 0, 12625, 0, 3627, 0, 14400, 0, 8672, 0, -17550, 0, 8511, 0, 3517, 0, 10605, 0, 360, 0, 3925, 0, 1458, 0, -2260, 0, -4564, 0, 5334, 0, -21735, 0, -18191, 0, 8805, 0, 32580, 0, 742, 0, 3312, 0, -9004, 0, -36650, 0, -3930, 0, 16870, 0, 34042, 0, 5010, 0, -1588, 0, 16011, 0, 1629, 0, -10589, 0, 2806, 0, 28596, 0, 39276, 0, 22300, 0, 19605, 0, -12154, 0, 34468, 0, 108, 0, -54252, 0, -6494, 0, -6375, 0, -28274, 0, 24374, 0, 1134, 0, 33080, 0, -36846, 0, 12546, 0, -1570, 0, -251, 0, -6060, 0, 6107, 0, 5184, 0, -26088, 0, 31554, 0, -5240, 0, 11565, 0, 38380, 0, -26649, 0, 4116, 0, 15948, 0, -42628, 0, 11883, 0, -26167, 0, 4926, 0, 3159, 0, 5026, 0, 92740, 0, -21036, 0, -25938, 0, 11739, 0, 10107, 0, -1300, 0, 9342, 0, 10530, 0, -5860, 0, 18351, 0, 9342, 0, -64840, 0, 6201, 0, -13311, 0, -31592, 0, -11576, 0, 10440, 0, 3280, 0, 8331, 0, -42, 0, 8531, 0, -5978, 0, -30240, 0, 3277, 0, 2252, 0, -4131, 0, 8158, 0, 20187, 0, -24036, 0, 11816, 0, -766, 0, -7536, 0, -33835, 0, 8055, 0, 3042, 0, 14174, 0, -49190, 0, -11286, 0, 1094, 0, -8080, 0, 780, 0, -12190, 0, -93996, 0, -4194, 0, -22796, 0, 36936, 0, 11055, 0, -12586, 0, 2654, 0, 22680, 0, 48248, 0, 21457, 0, 3996, 0, -41824, 0, 15248, 0, -27390, 0, 2232, 0, 62750, 0, -10938, 0, 9181, 0, 3439, 0, 5544, 0, 34186, 0, -30838, 0, 30024, 0, -33368, 0, -32625, 0, 29055, 0, -34937, 0, -13855, 0, -14706, 0, -4256, 0, 9011, 0, 2916, 0, 35772, 0, -12080, 0, 15255, 0, 76500, 0, -61592, 0, -1161, 0, -711, 0, 27775, 0, -15879, 0, -12195, 0, -8932, 0, -18090, 0, 7884, 0, 22059, 0, 22725, 0, 31640, 0, -18520, 0, -36612, 0, 39538, 0, -1333, 0, 32238, 0, -7154, 0, -7444, 0, -7218, 0, -49240, 0, 37040, 0, 21762, 0, -26644, 0, 12761, 0, -22839, 0, -9320, 0, -16092, 0, 2916, 0, -28076, 0, -1575, 0, -4887, 0, 91580, 0, 23483, 0, 17274, 0, 51768, 0, -45182, 0, -2547, 0, -93384, 0, -18450, 0, -2847, 0, -40130, 0, 54448, 0, 14040, 0, -27792, 0, 10394, 0, -8928, 0, -1260, 0, -45720, 0, -32424, 0, -12484, 0, -12285, 0, -1515, 0, 21870, 0, -97490, 0, -5130, 0, 114768, 0, 1938, 0, 7938, 0, 11110, 0, -18090, 0, -13197, 0, 30366, 0, -71248, 0, 16722, 0, -81580, 0, -22912, 0, -15861, 0, 2830, 0, -42836, 0, -31746, 0, -23864, 0, 24147, 0, -6633, 0, -26375, 0, -5680, 0, -68820, 0, 25838, 0, 42275, 0, -11967, 0, 51148, 0, -1906, 0, -9720, 0, -51624, 0, -75906, 0, 8262, 0, 13027, 0, 99719, 0, -12015, 0, -4932, 0, 99666, 0, -41292, 0, 6498, 0, -8502, 0, 26640, 0, -23608, 0, 12242, 0, -34668, 0, 117190, 0, 16219, 0, -15561, 0, 31815, 0, -29402, 0, 12177, 0, 30412, 0, -45238, 0, 12555, 0, 6638, 0, 10100, 0, 405, 0, -85158, 0, -87616, 0, 2376, 0, 14575, 0, -3656, 0, 51282, 0, 4526, 0, -6173, 0, -8496, 0, 143324, 0, 85295, 0, 36870, 0, -47570, 0, -25209, 0, 1221, 0, 50084, 0, 2266, 0, -7623, 0, -30132, 0, 79554, 0, -27930, 0, 22680, 0, 9956, 0, -1728, 0, 22869, 0, -30760, 0, 13014, 0, 75582, 0, -23669, 0, 11934, 0, 58564, 0, 22572, 0, 18225, 0, 48874, 0, -6228, 0, 32157, 0, 136738, 0, 16652, 0, 20508, 0, -34915, 0, 36865, 0, 8043, 0, 19048, 0, -46260, 0, -15714, 0, -7236, 0, -57834, 0, 54540, 0, -57092, 0, 260, 0, -21858, 0, 165320, 0, 47887, 0, 1431, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 17, "prim_orbit_index": 3, "minimal_twist": "168.4.q.d", "char_is_minimal": false, "conrey_index": 193, "id": 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], [1, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 3, 0], [0, 0, 0, 0], [0, -1, -4, 0], [0, 0, 0, 0], [-9, 0, 17, 1], [0, 0, 0, 0], [0, 0, -9, 0], [0, 0, 0, 0], [5, -5, 0, -5], [0, 0, 0, 0], [-10, 0, 0, 1], [0, 0, 0, 0], [15, 0, 0, -3], [0, 0, 0, 0], [0, 4, -4, 4], [0, 0, 0, 0], [0, 7, 55, 0], [0, 0, 0, 0], [-24, -3, -24, -3], [0, 0, 0, 0], [0, -4, 76, 0], [0, 0, 0, 0], [-26, 9, 17, 9], [0, 0, 0, 0], [27, 0, 0, 0], [0, 0, 0, 0], [-45, 0, 0, -5], [0, 0, 0, 0], [-181, 2, 179, 2], [0, 0, 0, 0], [0, 15, 0, 0], [0, 0, 0, 0], [85, -4, 90, -17], [0, 0, 0, 0], [0, -1, 27, 0], [0, 0, 0, 0], [30, -3, -27, -3], [0, 0, 0, 0], [-76, 0, 0, -18], [0, 0, 0, 0], [-188, 0, 0, -27], [0, 0, 0, 0], [-45, 9, 36, 9], [0, 0, 0, 0], [0, 36, 166, 0], [0, 0, 0, 0], [-82, -34, 17, -17], [0, 0, 0, 0], [0, -12, 12, 0], [0, 0, 0, 0], [-351, 5, 346, 5], [0, 0, 0, 0], [-655, 0, 0, 25], [0, 0, 0, 0], [-186, 0, 0, 21], [0, 0, 0, 0], [-279, -27, 306, -27], [0, 0, 0, 0], [0, 28, 566, 0], [0, 0, 0, 0], [153, 9, -81, 0], [0, 0, 0, 0], [0, 14, 162, 0], [0, 0, 0, 0], [80, 73, -153, 73], [0, 0, 0, 0], [-216, 0, 0, -12], [0, 0, 0, 0], [-346, 0, 0, 76], [0, 0, 0, 0], [440, -63, -377, -63], [0, 0, 0, 0], [0, -27, -51, 0], [0, 0, 0, 0], [-590, 45, 630, -40], [0, 0, 0, 0], [0, 48, -425, 0], [0, 0, 0, 0], [-81, 0, 81, 0], [0, 0, 0, 0], [175, 0, 0, -67], [0, 0, 0, 0], [504, 0, 0, -16], [0, 0, 0, 0], [135, 15, -150, 15], [0, 0, 0, 0], [0, -22, 940, 0], [0, 0, 0, 0], [216, -17, -153, -18], [0, 0, 0, 0], [0, -6, -537, 0], [0, 0, 0, 0], [1192, -90, -1102, -90], [0, 0, 0, 0], [837, 0, 0, 55], [0, 0, 0, 0], [-45, 0, 0, 45], [0, 0, 0, 0]]}