# Stored data for newform 128.4.a.g, downloaded from the LMFDB on 25 April 2024. {"label": "128.4.a.g", "space_label": "128.4.a", "level": 128, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27021597831331968, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 1258530576696644147, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-44, -4, 1]], [5, [-188, 4, 1]]], "qexp_display": "q+(2+\\beta )q^{3}+(-2+2\\beta )q^{5}+(4-2\\beta )q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2048, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 7.552244480734799, "hecke_ring_index": 4, "level_radical": 2, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [128, 1, [127, 5], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2], "conrey_indexes": [1], "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.020", "prec": 17}, {"__RealLiteral__": 0, "data": "1.952", "prec": 17}, {"__RealLiteral__": 0, "data": "0.046", "prec": 17}, {"__RealLiteral__": 0, "data": "9.260", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.097", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1]], "trace_display": [0, 4, -4, 8], "traces": [0, 2, 0, 4, 0, -4, 0, 8, 0, 50, 0, 92, 0, -100, 0, 184, 0, 92, 0, 4, 0, -176, 0, -8, 0, 142, 0, 376, 0, -84, 0, 384, 0, 88, 0, -400, 0, 172, 0, -776, 0, -300, 0, 300, 0, 668, 0, 16, 0, -270, 0, -968, 0, 12, 0, -376, 0, -664, 0, -644, 0, -292, 0, -568, 0, -952, 0, -172, 0, 1712, 0, -408, 0, 412, 0, -484, 0, 560, 0, 400, 0, -22, 0, 948, 0, -2488, 0, 792, 0, 572, 0, 752, 0, -768, 0, -1352, 0, 2204, 0, 1916, 0, 2124, 0, 3464, 0, 352, 0, -1444, 0, -1428, 0, -1000, 0, 196, 0, 3472, 0, -4804, 0, 2672, 0, 1666, 0, -1368, 0, -1320, 0, 2656, 0, 120, 0, 948, 0, 1360, 0, 400, 0, -1420, 0, 2188, 0, 4256, 0, -4024, 0, 2088, 0, -2076, 0, -1764, 0, -1544, 0, -2308, 0, -3840, 0, -4164, 0, -1320, 0, -3488, 0, 772, 0, 8272, 0, -728, 0, 4062, 0, -2588, 0, 5244, 0, 2104, 0, -4456, 0, -1356, 0, -2500, 0, -7304, 0, -3032, 0, 5384, 0, 352, 0, -4960, 0, -484, 0, -10352, 0, 5788, 0, -760, 0, -8312, 0, -2256, 0, -936, 0, 6712, 0, 856, 0, -5612, 0, -4848, 0, -1560, 0, 4608, 0, 5816, 0, 2312, 0, 8832, 0, 478, 0, 4260, 0, -2276, 0, -8096, 0, 4572, 0, 8416, 0, -2656, 0, -1872, 0, 1244, 0, -1364, 0, -2532, 0, 3832, 0, 3144, 0, -6084, 0, -2096, 0, 6160, 0, 4644, 0, 3376, 0, 1740, 0, 4968, 0, -2712, 0, 12280, 0, -3764, 0, 3824, 0, 8800, 0, 7300, 0, -7284, 0, 3456, 0, -2916, 0, 9132, 0, -976, 0, 336, 0, 8230, 0, -4424, 0, -6884, 0, -5048, 0, 16720, 0, -9968, 0, 2160, 0, 2904, 0, -12856, 0, -1884, 0, 8272, 0, 11192, 0, -4300, 0, -5392, 0, -8148, 0, -4824, 0, -16808, 0, 8248, 0, -2492, 0, 1176, 0, -8384, 0, -14084, 0, -1076, 0, -15592, 0, 6308, 0, 9608, 0, 19200, 0, -752, 0, 2720, 0, -6084, 0, 8716, 0, -22256, 0, 10020, 0, -7248, 0, -8096, 0, 17288, 0, -9006, 0, -5500, 0, 9160, 0, 3856, 0, -10572, 0, 2736, 0, 14188, 0, -11472, 0, -1560, 0, -14116, 0, 16832, 0, -12288, 0, -19552, 0, 5580, 0, -15572, 0, -21104, 0, -14520, 0, -7712, 0, -6420, 0, -352, 0, 10140, 0, -9984, 0, 17708, 0, 9256, 0, 4532, 0, -6680, 0, 3760, 0, 600, 0, 21560, 0, 17908, 0, 3388, 0, 17296, 0, 15748, 0, 12272, 0, -29744, 0, -19664, 0, -20196, 0, -5808, 0, -12112, 0, 6456, 0, -12894, 0, 2988, 0, 21128, 0, 33528, 0, -6692, 0, -13032, 0, -32080, 0, 13088, 0, -9132, 0, 10384, 0, 2380, 0, -5744, 0, 32256, 0, 14948, 0, 15248, 0, -8904, 0, 14280, 0, 5660, 0, -5076, 0, 22656, 0, -536, 0, 704, 0, -22072, 0, -21464, 0, 40040, 0, 652, 0, -15384, 0, 26696, 0, 6432, 0, 5908, 0, 22160, 0, -3880, 0, -6936, 0, 65724, 0, -32132, 0, -8336, 0, -3280, 0, -4240, 0, -3488, 0, 12984, 0, -14540, 0, 1276, 0, -12496, 0, 36096, 0, 6802, 0, -28772, 0, 19608, 0, -24952, 0, 21576, 0, -10884, 0, 24604, 0, 4408, 0, 10920, 0, -26764, 0, -34180, 0, -6888, 0, 8512, 0, 13136, 0, 16412, 0, -12120, 0, -46640, 0, 19620, 0, 18040, 0, -17752, 0, 4180, 0, -25364, 0, 12352, 0, -14392, 0, 4228, 0, 11704, 0, 1296, 0, 1896, 0, -57592, 0, 25372, 0, 11520, 0, 14840, 0, 15972, 0, -32224, 0, -17072, 0, 11160, 0, -36228, 0, -36172, 0, -20996, 0, 13856, 0, 7392, 0, -26144, 0, 21052, 0, -29136, 0, 34172, 0, -4036, 0, 8864, 0, -19984, 0, -32774, 0, -29392, 0, 24040, 0, -23720, 0, 3080, 0, 17728, 0, 22716, 0, -26328, 0, -35748, 0, 2196, 0, 26640, 0, -22680, 0, -26456, 0, -33792, 0, 6156, 0, -34728, 0, 30268, 0, 20916, 0, -16004, 0, 35728, 0, -8864, 0, 17616, 0, 31488, 0, -6712, 0, 2204, 0, 22088, 0, -5140, 0, 26480, 0, 30888, 0, -26292, 0, -4840, 0, 1784, 0, 7464, 0, 23220, 0, -22864, 0, 29992, 0, -4584, 0, -31944, 0, -5668, 0, 9752, 0, 9920, 0, 11184, 0, 6764, 0, -3824, 0, -29184, 0, -35344, 0, -44832, 0, -18864, 0, 11168, 0, 75064, 0, -13644, 0, 6552, 0, -1078, 0, 19560, 0, -27732, 0, -27912, 0, 56, 0, 22692, 0, 40112, 0, 18344, 0, 77640, 0, 28692, 0, 22064, 0, 4976, 0, -16872, 0, -54896, 0, -32740, 0, 75680, 0, 27188, 0, -13776, 0, -17656, 0, 51208, 0, -16676, 0, 27720, 0, -16212, 0, 39552, 0, -15136, 0, 4776, 0, -14736, 0, -10032, 0, 7176, 0, 14356, 0, -58608, 0, -17648, 0, 54920, 0, -1584, 0, -74052, 0, -49952, 0, 58844, 0, 13960, 0, 22336, 0, 11864, 0, -32556, 0, 18876, 0, 31072, 0, 75448, 0, 3960, 0, 47984, 0, -15764, 0, 9656, 0, -27544, 0, -15796, 0, -25220, 0, -49704, 0, 6012, 0, 48688, 0, 62976, 0, -30648, 0, -35650, 0, 6840, 0, 107076, 0, 24328, 0, 46200, 0, -24880, 0, -23476, 0, -26888, 0, 9876, 0, -14596, 0, 26400, 0, -21056, 0, -5496, 0, -89524, 0, 21856, 0, 56408, 0, 19772, 0, 12384, 0, -40948, 0, -59656, 0, -50972, 0, 1604, 0, -65584, 0, -71112, 0, -12416, 0, -9844, 0, -29536, 0, 51288, 0, -104032, 0, -31488, 0, 16680, 0, -26400, 0, 23816, 0, 19564, 0, 47724, 0, -18384, 0, 42360, 0, -40304, 0, 36624, 0, 20664, 0, -15960, 0, 44592, 0, 22964, 0, 91976, 0, 42204, 0, 10212, 0, 91696, 0, -125584, 0, -28324, 0, -89240, 0, 15532, 0, -12624, 0, -68288, 0, -79516, 0, -50552, 0, -67560, 0, -104044, 0, 54464, 0, 38544, 0, 2000, 0, 38722, 0, -91780, 0, 26312, 0, -21560, 0, -16720, 0, 7276, 0, -25616, 0, -7480, 0, -39012, 0, 15176, 0, -19572, 0, -15784, 0, -5048, 0, -1408, 0, -9840, 0, 34528, 0, -44392, 0, -29584, 0, -7380, 0, 24272, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "128.4.a.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [2, 1], [0, 0], [-2, 2], [0, 0], [4, -2], [0, 0], [25, 4], [0, 0], [46, -1], [0, 0], [-50, -6], [0, 0], [92, 2], [0, 0], [46, -12], [0, 0], [2, -7], [0, 0], [-88, 0], [0, 0], [-4, 18], [0, 0], [71, -8], [0, 0], [188, 6], [0, 0], [-42, 10], [0, 0], [192, -16], [0, 0], [44, 44], [0, 0], [-200, 12], [0, 0], [86, -14], [0, 0], [-388, -62], [0, 0], [-150, -8], [0, 0], [150, -5], [0, 0], [334, 42], [0, 0], [8, 44], [0, 0], [-135, -16], [0, 0], [-484, 22], [0, 0], [6, -14], [0, 0], [-188, 94], [0, 0], [-332, -12], [0, 0], [-322, -33], [0, 0], [-146, -70], [0, 0], [-284, -34], [0, 0], [-476, -88], [0, 0], [-86, -83], [0, 0], [856, 32], [0, 0], [-204, -42], [0, 0], [206, 52], [0, 0], [-242, 55], [0, 0], [280, -96], [0, 0], [200, -36], [0, 0], [-11, 92], [0, 0], [474, 13], [0, 0], [-1244, 116], [0, 0], [396, -22], [0, 0], [286, 116], [0, 0], [376, 76], [0, 0], [-384, 160], [0, 0], [-676, 18], [0, 0], [1102, -92], [0, 0], [958, 159], [0, 0]]}