# Stored data for newform 24.4.f.b, downloaded from the LMFDB on 25 April 2024. {"label": "24.4.f.b", "space_label": "24.4.f", "level": 24, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503943291863064, "dim": 8, "is_polredabs": true, "trace_hash": 88262027369693602, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [26112, 0, -324, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(-2+\\beta _{4})q^{3}+(3+\\beta _{2})q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 24, "char_orbit_label": "f", "char_is_real": true, "Nk2": 384, "analytic_conductor": 1.4160458401377747, "hecke_ring_index": 256, "level_radical": 6, "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": "0.758", "prec": 17}, "analytic_rank_proved": true, "char_values": [24, 2, [7, 13, 17], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [11], "field_disc": 23886991554624, "field_disc_factorization": [[2, 6], [3, 6], [11, 6], [17, 2]], "field_poly": [4096, 0, -640, 0, 120, 0, -10, 0, 1], "hecke_ring_index_factorization": [[2, 8]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.040", "prec": 17}, {"__RealLiteral__": 0, "data": "7.099", "prec": 17}, {"__RealLiteral__": 0, "data": "10.003", "prec": 20}, {"__RealLiteral__": 0, "data": "500.948", "prec": 24}, {"__RealLiteral__": 0, "data": "1491.764", "prec": 27}, {"__RealLiteral__": 0, "data": "50218.794", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "3.2.3.c2", "trace_display": [0, -12, 0, 0], "traces": [0, 8, 0, -12, 20, 0, 0, 0, 0, -48, -24, 0, 36, 0, 0, 0, -280, 0, 264, 184, 0, 0, -176, 0, 264, 296, 0, -324, 528, 0, -624, 0, 0, -264, -176, 0, -516, 0, 0, 0, -1248, 0, 1320, -152, 0, 0, 1440, 0, 1080, -952, 0, 1056, 2112, 0, -1584, 0, 0, 1176, -2616, 0, -2640, 0, 0, 0, -1360, 0, 792, -1496, 0, 0, 3696, 0, 2640, 1072, 0, -708, 1912, 0, -3696, 0, 0, -504, -2816, 0, -4224, 0, 0, 0, -1232, 0, 4104, 3168, 0, 0, 4800, 0, 4752, -3872, 0, 2112, 476, 0, -528, 0, 0, 528, -5208, 0, -2196, 0, 0, 0, -4224, 0, 2904, -5952, 0, 0, -704, 0, 3456, 8712, 0, -7392, 4752, 0, -3168, 0, 0, -4920, -3168, 0, 0, 0, 0, 0, -3872, 0, 1536, 14008, 0, 0, 2400, 0, -2280, -2352, 0, 7500, 2112, 0, -528, 0, 0, 2112, 4752, 0, 1056, 0, 0, 0, -1536, 0, 1584, -11528, 0, 0, -5456, 0, -3168, -5656, 0, -9816, -5528, 0, 3792, 0, 0, 2904, 9328, 0, 6336, 0, 0, 0, 3072, 0, -6072, 704, 0, 0, -15072, 0, -3504, 304, 0, 20064, 3692, 0, -2112, 0, 0, 3432, 7656, 0, 5280, 0, 0, 0, 19008, 0, -11616, -12440, 0, 0, 6688, 0, -16632, 2640, 0, -21144, -9504, 0, 14256, 0, 0, -192, 10912, 0, 2280, 0, 0, 0, 7584, 0, -12672, 28032, 0, 0, -8448, 0, -14784, -6224, 0, 29268, -27456, 0, 15840, 0, 0, -5544, 4752, 0, 17424, 0, 0, 0, 32, 0, -10296, -32736, 0, 0, -18656, 0, 5808, -6000, 0, -29568, -2552, 0, 14832, 0, 0, 10560, -12320, 0, 14784, 0, 0, 0, 35904, 0, -18816, 25336, 0, 0, 1056, 0, -5280, 29448, 0, 17688, -16856, 0, 12144, 0, 0, -11880, 32808, 0, 1068, 0, 0, 0, 8080, 0, 5808, -17624, 0, 0, -2640, 0, -12672, -13376, 0, -44352, -33264, 0, 8208, 0, 0, -13992, -6336, 0, 8244, 0, 0, 0, -13376, 0, -5808, 60280, 0, 0, -30624, 0, -2112, 7552, 0, 38016, 16896, 0, -2640, 0, 0, -11136, -8568, 0, -528, 0, 0, 0, 13024, 0, -792, -57792, 0, 0, 14080, 0, -2016, -18696, 0, -7524, 23232, 0, -5808, 0, 0, 33792, 32736, 0, -2112, 0, 0, 0, -37632, 0, 15048, 9064, 0, 0, 18048, 0, 15840, 30624, 0, 31800, 2200, 0, -10560, 0, 0, 22968, -47256, 0, -1056, 0, 0, 0, -13000, 0, 2376, -43296, 0, 0, -27984, 0, -7392, -18800, 0, -51744, 46992, 0, -30816, 0, 0, -20616, 7568, 0, -20064, 0, 0, 0, 16416, 0, 26496, 66528, 0, 0, 51936, 0, -2520, -56096, 0, 46560, 48576, 0, -39072, 0, 0, -30720, 38016, 0, -34848, 0, 0, 0, -71808, 0, 11352, -37312, 0, 0, 51568, 0, 43824, 13072, 0, -15840, -34944, 0, -20064, 0, 0, 40656, -56144, 0, -38016, 0, 0, 0, -12848, 0, 42504, 1000, 0, 0, -27456, 0, 31872, 48576, 0, 40128, 27324, 0, -4752, 0, 0, 30360, -57864, 0, -12672, 0, 0, 0, 33792, 0, 21912, -18968, 0, 0, 13552, 0, 50688, 17424, 0, -55932, 68112, 0, -29568, 0, 0, -37944, -12320, 0, -5832, 0, 0, 0, -71808, 0, 16488, 21160, 0, 0, 65376, 0, 15840, -27448, 0, 8448, -63360, 0, 1584, 0, 0, -44616, -91896, 0, -30096, 0, 0, 0, -34496, 0, 30624, 44344, 0, 0, -8624, 0, 8064, -18480, 0, -15840, 35416, 0, -28512, 0, 0, -2112, -27632, 0, -46464, 0, 0, 0, 52992, 0, 3072, -16520, 0, 0, 107712, 0, 41424, 39040, 0, -21048, 37152, 0, 23760, 0, 0, 38016, 75240, 0, 1788, 0, 0, 0, -52800, 0, -3960, 25344, 0, 0, 46464, 0, 2904, 89776, 0, 1848, -79728, 0, -16368, 0, 0, -86064, -66528, 0, 14784, 0, 0, 0, -40128, 0, 9768, 39928, 0, 0, -128352, 0, 27456, -149992, 0, 8448, 78144, 0, 14256, 0, 0, 44136, -58680, 0, 1584, 0, 0, 0, 131328, 0, -6072, -106952, 0, 0, -21472, 0, -22176, 176, 0, 32736, -15752, 0, 4752, 0, 0, 110784, 122496, 0, 40128, 0, 0, 0, -43472, 0, -12672, -74304, 0, 0, -7392, 0, -59136, 59872, 0, -6444, -78556, 0, -70752, 0, 0, 34584, 6864, 0, -42360, 0, 0, 0, -46160, 0, -40128, 91000, 0, 0, -22352, 0, -54144, 36608, 0, 61248, 33264, 0, 87120, 0, 0, -132864, 54208, 0, 15840, 0, 0, 0, 152416, 0, -4224, 14784, 0, 0, 41952, 0, -50688, -113520, 0, -36600, 6336, 0, 11088, 0, 0, -73008, 192144, 0, 93984, 0, 0, 0, -51456, 0, -52800, 50920, 0, 0, -59664, 0, -28512, -48240, 0, 65472, 704, 0, 51744, 0, 0, 147576, -58080, 0, 50688, 0, 0, 0, 6144, 0, -99000, -106656, 0, 0, -213120, 0, -92448, 67120, 0, -124608, -19832, 0, 25872, 0, 0, 82368, -6168, 0, 99264, 0, 0, 0, 94040, 0, 33000, -17288, 0, 0, 18480, 0, -16368, 86592, 0, 95328, -16368, 0, 39072, 0, 0, -111936, 121264, 0, -5544, 0, 0, 0, -32736, 0, -93528, -108248, 0, 0, 36960, 0, -10560, -116752, 0, -110880, -215424, 0, 88704, 0, 0, -12408, -20592, 0, 50688, 0, 0, 0, 71808, 0, 792, 145728, 0, 0, -137456, 0, -71808, -20632, 0, 95040, -5624, 0, 40896, 0, 0, 50040, -3344, 0, 120384, 0, 0, 0, 94864, 0, -8448, 93544, 0, 0, -3648, 0, 17424, 175440, 0, -71628, 43296, 0, 86064, 0, 0, -48048, 114432, 0, -14712, 0, 0, 0, 4224, 0, -67848, 218680, 0, 0, 1936, 0, -12672, 61776, 0, 50688, -282480, 0, -8688, 0, 0, -198528, -27632, 0, -13548, 0, 0, 0, 33088, 0, -55704, -253208, 0, 0, -162624, 0, -47760, -54736, 0, -153120, 82368, 0, 23760, 0, 0, -37848, 46728, 0, -51744, 0, 0, 0, 119808, 0, -32736, 111688, 0, 0, 158224, 0, -12672, -178784, 0, 68376, -20736, 0, 78672, 0, 0, 264528, -37840, 0, 14784, 0, 0, 0, -8448, 0, 28872, -256512, 0, 0, 74112, 0, 0, 154376, 0, -80256, -61496, 0, -21120, 0, 0, 82368, -107184, 0, 73764, 0, 0, 0, -31680, 0, 26136, 15488, 0, 0, -142208, 0, 124608, 110352, 0, 181632, 141504, 0, 57024, 0, 0, -129096, -154176, 0, 10560, 0, 0, 0, 103488], "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, 3, 2, -1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 24, 6, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "24.4.f.b", "char_is_minimal": true, "conrey_index": 11, "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], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 1, 0, 0, 0], [3, 0, 1, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, 0, -1, -1], [1, -1, 0, -1, 1, 2, 0, 1], [-2, 0, -2, 0, 0, 0, 1, -1], [1, 2, 0, 2, -1, 1, 1, 1], [-6, -3, 0, -3, -3, -3, 0, 0], [-1, 0, 2, 0, -5, -5, -1, 1], [-1, 2, 0, 2, 1, -1, 0, 0], [0, 2, -3, -4, 3, -1, 3, 1], [0, 0, -4, 0, 4, 4, -2, 2], [5, 0, 0, -2, -5, 5, -3, -3], [2, -10, 6, 2, -4, -4, 3, 1], [-36, 0, 2, 0, 2, 2, 2, -2], [4, 2, 0, 2, -4, 4, 0, 0], [27, -9, -6, 6, 3, -3, -3, -3], [23, 0, 0, 0, 11, 11, 0, 0], [-10, -8, 0, 12, 10, -10, -2, -2], [8, 23, 12, -7, -4, -4, -3, 1], [-19, 0, 4, 0, 3, 3, -1, 1], [0, 28, 0, -12, 0, 0, 4, 4], [35, 6, -6, -6, 11, 21, -3, -3], [37, 0, 0, 0, -2, -2, 0, 0], [-14, 8, 0, -20, 14, -14, 2, 2], [-39, 18, 0, 18, -12, -9, 0, 0], [66, 0, 4, 0, -30, -30, 2, -2], [0, -45, 0, 13, 0, 0, 3, 3], [-77, -8, -12, 22, 1, 19, 3, -1], [-2, 0, -10, 0, 8, 8, -3, 3], [18, -36, 0, 4, -18, 18, 2, 2], [-29, -9, 0, -9, 1, 9, 0, 0], [-24, 0, 4, 0, -12, -12, 4, -4], [2, -42, 0, -42, -2, 2, 0, 0], [-63, 36, 3, -12, 0, -12, -12, 0], [-16, 0, -12, 0, -4, -4, 10, -10], [11, 34, 0, -22, -11, 11, 11, 11], [4, -74, 0, 34, 4, 4, -18, -10], [-140, 0, 8, 0, 20, 20, -12, 12], [-28, 32, 0, 32, 28, -28, 0, 0], [169, -8, 18, 28, 1, -11, 9, 11], [-19, 0, 0, 0, -39, -39, 0, 0], [0, -20, 0, 0, 0, 0, 8, 8], [-24, 75, -24, -27, 0, 0, 15, -9], [180, 0, 8, 0, 20, 20, 4, -4], [0, 72, 0, -8, 0, 0, -24, -24], [146, 52, 6, -44, -40, -20, 12, 8], [-119, 0, 0, 0, 46, 46, 0, 0], [-2, 35, 0, 4, 2, -2, -2, -2], [136, 6, 0, 6, 16, 24, 0, 0], [268, 0, -16, 0, 52, 52, -12, 12], [0, -89, 0, 25, 0, 0, 7, 7], [-192, -51, 36, 21, 6, -15, -9, -12], [20, 0, 28, 0, -8, -8, -6, 6], [-12, 32, 0, 72, 12, -12, -28, -28], [119, -33, 0, -33, 23, -33, 0, 0], [-349, 0, -38, 0, 15, 15, 3, -3], [11, 8, 0, 8, -11, 11, 0, 0], [-322, -64, 12, -40, -34, -10, 6, -14], [48, 0, 76, 0, -28, -28, -10, 10], [-23, 16, 0, -42, 23, -23, 1, 1], [-18, -36, -42, -12, 24, 24, 33, 39], [-208, 0, -36, 0, -44, -44, 20, -20], [76, 36, 0, 36, -76, 76, 0, 0], [91, -28, -18, -10, -17, -7, 9, 1], [-187, 0, 0, 0, 9, 9, 0, 0], [20, -40, 0, 40, -20, 20, -12, -12], [8, 32, -24, -16, 32, 32, -12, 28], [418, 0, -84, 0, -6, -6, 2, -2], [0, 68, 0, -52, 0, 0, 44, 44], [315, -66, 36, 6, 33, -57, -9, 15], [134, 0, 0, 0, -148, -148, 0, 0], [54, -8, 0, 4, -54, 54, -26, -26], [-104, 6, 0, 6, 37, 6, 0, 0], [212, 0, -10, 0, 22, 22, 22, -22], [0, 70, 0, -6, 0, 0, -26, -26], [-478, 8, -12, -16, -46, -94, -6, 22], [14, 0, 70, 0, -56, -56, 21, -21], [-56, -128, 0, -48, 56, -56, 40, 40], [9, -18, 0, -18, 0, 144, 0, 0], [-292, 0, 64, 0, 84, 84, -28, 28], [-21, 62, 0, 62, 21, -21, 0, 0], [-526, 152, 0, 44, 62, 74, 18, 10], [0, 0, -32, 0, 32, 32, -16, 16], [-39, -58, 0, 78, 39, -39, -39, -39], [-38, 46, -18, 10, -20, -20, -9, -67], [-180, 0, -36, 0, 40, 40, 8, -8], [-112, -106, 0, -106, 112, -112, 0, 0], [591, 0, 42, -24, -45, 75, -33, -39], [396, 0, 0, 0, 116, 116, 0, 0], [56, 192, 0, -16, -56, 56, 24, 24], [16, -125, 12, 61, 4, 4, -39, -19], [680, 0, 112, 0, -120, -120, -24, 24], [0, -276, 0, 100, 0, 0, -12, -12], [558, 100, -12, 76, 30, 10, -6, -46], [-484, 0, 0, 0, 90, 90, 0, 0], [46, -73, 0, -92, -46, 46, 46, 46], [255, 24, 0, 24, -39, -57, 0, 0], [85, 0, 43, 0, -4, -4, -4, 4]]}