# Stored data for newform 384.5.e.d, downloaded from the LMFDB on 24 April 2024.
{"label": "384.5.e.d", "space_label": "384.5.e", "level": 384, "weight": 5, "hecke_orbit": 4, "hecke_orbit_code": 13511073843904896, "dim": 16, "is_polredabs": true, "trace_hash": 878508417822656521, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [-519546316544, -271760728576, -22111959680, -12942592, 29617840, 186176, -9800, -40, 1]], [13, [115283511800064, 1020751011717120, -13278939766016, -218176770048, 3129196896, 4006400, -107088, 0, 1]]], "qexp_display": "q+(1-\\beta _{3})q^{3}+\\beta _{6}q^{5}+(5+\\beta _{1}+\\beta _{3}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "e", "char_is_real": true, "Nk2": 9600, "analytic_conductor": 39.69406582419622, "hecke_ring_index": 1063732217586401673216, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [384, 2, [127, 133, 257], [2, 2, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [257], "field_disc": 519974478131531886628415509334134358016, "field_disc_factorization": [[2, 44], [3, 4], [41, 2], [61967, 2], [237763, 2]], "field_poly": [21479188203, 25672770504, 12462543468, 866573964, 385003542, 210288484, 45109352, -2262056, 724325, 391324, 22064, -8992, 1348, 356, -32, -4, 1], "hecke_ring_index_factorization": [[2, 54], [3, 10]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.089", "prec": 17}, {"__RealLiteral__": 0, "data": "12.407", "prec": 20}, {"__RealLiteral__": 0, "data": "4.062", "prec": 17}, {"__RealLiteral__": 0, "data": "772.866", "prec": 24}, {"__RealLiteral__": 0, "data": "15.851", "prec": 20}, {"__RealLiteral__": 0, "data": "67398.950", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "4.2.3.c2", "trace_display": [0, 8, 0, 80], "traces": [0, 16, 0, 8, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 416, 0, 0, 0, -816, 0, -608, 0, 0, 0, -2000, 0, -280, 0, 0, 0, 592, 0, -496, 0, 0, 0, -2240, 0, -16, 0, 0, 0, -368, 0, -800, 0, 0, 0, 3984, 0, 352, 0, 0, 0, 1920, 0, 560, 0, 0, 0, 3520, 0, -816, 0, 0, 0, 3536, 0, 10784, 0, 0, 0, 3680, 0, -5112, 0, 0, 0, -14448, 0, -624, 0, 0, 0, 11136, 0, -14944, 0, 0, 0, 22944, 0, -13760, 0, 0, 0, 3264, 0, 26976, 0, 0, 0, 15632, 0, 8800, 0, 0, 0, -18880, 0, 40688, 0, 0, 0, -56448, 0, -2528, 0, 0, 0, -32656, 0, -39488, 0, 0, 0, -22576, 0, -848, 0, 0, 0, 7296, 0, -38752, 0, 0, 0, 19600, 0, 8128, 0, 0, 0, 19680, 0, 31896, 0, 0, 0, 88720, 0, -40384, 0, 0, 0, -25600, 0, 68256, 0, 0, 0, -60656, 0, -24160, 0, 0, 0, -28624, 0, -108176, 0, 0, 0, -121456, 0, 43344, 0, 0, 0, -2816, 0, -149520, 0, 0, 0, 211776, 0, 10336, 0, 0, 0, 36448, 0, 235264, 0, 0, 0, 195984, 0, -58416, 0, 0, 0, -12096, 0, 207936, 0, 0, 0, -213744, 0, 82784, 0, 0, 0, 85856, 0, -302288, 0, 0, 0, -376688, 0, 71072, 0, 0, 0, 161536, 0, -348224, 0, 0, 0, 299136, 0, 448, 0, 0, 0, -32032, 0, 360488, 0, 0, 0, 300000, 0, 97008, 0, 0, 0, 1984, 0, 474560, 0, 0, 0, -532960, 0, -76384, 0, 0, 0, -46560, 0, -334176, 0, 0, 0, -335984, 0, -95744, 0, 0, 0, -44992, 0, -479984, 0, 0, 0, 576208, 0, -144800, 0, 0, 0, -51056, 0, 497584, 0, 0, 0, 679872, 0, -4624, 0, 0, 0, -254464, 0, 619232, 0, 0, 0, -569520, 0, 3424, 0, 0, 0, -122048, 0, -901504, 0, 0, 0, -796672, 0, -139184, 0, 0, 0, -154560, 0, -733264, 0, 0, 0, 695248, 0, 268896, 0, 0, 0, 50944, 0, 922560, 0, 0, 0, 978784, 0, -60352, 0, 0, 0, 485504, 0, 913328, 0, 0, 0, -1182720, 0, 76544, 0, 0, 0, 656, 0, -1037720, 0, 0, 0, -978736, 0, 68416, 0, 0, 0, -246016, 0, -1282176, 0, 0, 0, 1229072, 0, -359808, 0, 0, 0, 196800, 0, 1290544, 0, 0, 0, 1408128, 0, 160560, 0, 0, 0, 16832, 0, 1444768, 0, 0, 0, -974304, 0, 40000, 0, 0, 0, 186272, 0, -1428608, 0, 0, 0, -1854720, 0, 91536, 0, 0, 0, -79744, 0, -1550080, 0, 0, 0, 1808672, 0, 482912, 0, 0, 0, -163904, 0, 1694208, 0, 0, 0, 1106448, 0, 62688, 0, 0, 0, 665664, 0, 1462304, 0, 0, 0, -1875200, 0, -226912, 0, 0, 0, 291872, 0, -1399904, 0, 0, 0, -1679024, 0, -106656, 0, 0, 0, 142912, 0, -1692304, 0, 0, 0, 1636944, 0, -554016, 0, 0, 0, -622656, 0, 1656064, 0, 0, 0, 1636176, 0, 186672, 0, 0, 0, -981120, 0, 2150848, 0, 0, 0, -2190576, 0, 139616, 0, 0, 0, 7200, 0, -1896424, 0, 0, 0, -1333280, 0, -325072, 0, 0, 0, 585600, 0, -1581344, 0, 0, 0, 1595600, 0, 1140960, 0, 0, 0, 32144, 0, 1703456, 0, 0, 0, 2802240, 0, -142800, 0, 0, 0, 400960, 0, 1566768, 0, 0, 0, -1576496, 0, -847648, 0, 0, 0, 439776, 0, -2714752, 0, 0, 0, -1725600, 0, 61504, 0, 0, 0, -1252992, 0, -2525232, 0, 0, 0, 2374736, 0, -1213312, 0, 0, 0, -248192, 0, 2499824, 0, 0, 0, 2533248, 0, -293056, 0, 0, 0, -1578048, 0, 2821600, 0, 0, 0, -2564736, 0, 1033760, 0, 0, 0, -489632, 0, -2035280, 0, 0, 0, -3659312, 0, 247456, 0, 0, 0, 1034176, 0, -2449152, 0, 0, 0, 2211664, 0, 1665248, 0, 0, 0, -190736, 0, 2182688, 0, 0, 0, 1415888, 0, -186544, 0, 0, 0, 2749632, 0, 1888832, 0, 0, 0, -1843120, 0, -1339680, 0, 0, 0, -160928, 0, -2188384, 0, 0, 0, -1694016, 0, 220416, 0, 0, 0, -1161280, 0, -1722304, 0, 0, 0, 1758080, 0, -2090816, 0, 0, 0, 1226304, 0, 2143848, 0, 0, 0, 2089632, 0, -384080, 0, 0, 0, -1716288, 0, 1455536, 0, 0, 0, -2315632, 0, 1532736, 0, 0, 0, 1022208, 0, -889952, 0, 0, 0, -1424160, 0, 946304, 0, 0, 0, 1462848, 0, -1217968, 0, 0, 0, 2640768, 0, 2529856, 0, 0, 0, 290464, 0, 1592688, 0, 0, 0, 545424, 0, 1164288, 0, 0, 0, 2963200, 0, 1703328, 0, 0, 0, 58000, 0, -652064, 0, 0, 0, -1725024, 0, -1399008, 0, 0, 0, -554608, 0, -319600, 0, 0, 0, -390272, 0, -1607104, 0, 0, 0, 709792, 0, -3814400, 0, 0, 0, -100128, 0, 382528, 0, 0, 0, 746512, 0, 105088, 0, 0, 0, -4751296, 0, 992288, 0, 0, 0, -2273776, 0, 1117792, 0, 0, 0, -571200, 0, -475008, 0, 0, 0, -1965312, 0, -1727360, 0, 0, 0, 1412736, 0, -1067680, 0, 0, 0, -370736, 0, 3819456, 0, 0, 0, 300960, 0, 440864, 0, 0, 0, 1531088, 0, -1179888, 0, 0, 0, 2498560, 0, 191216, 0, 0, 0, -394368, 0, -783488, 0, 0, 0, -332752, 0, -1418912, 0, 0, 0, 1740880, 0, -451568, 0, 0, 0, -2076032, 0, 653504, 0, 0, 0, -220528, 0, -5832640, 0, 0, 0, 383328, 0, -375672, 0, 0, 0, 1431648, 0, 825056, 0, 0, 0, -6166528, 0, -939936, 0, 0, 0, 2594256, 0, 2301856, 0, 0, 0, 130528, 0, 368064, 0, 0, 0, -543168, 0, 720320, 0, 0, 0, 1654656, 0, 1868576, 0, 0, 0, -599664, 0, 6063200, 0, 0, 0, 207264, 0, -854912, 0, 0, 0, -2729648, 0, 20112, 0, 0, 0, 8159872, 0, -1381872, 0, 0, 0, -1092624, 0, -2492128, 0, 0, 0, 841856, 0, 2604176, 0, 0, 0, 2798848, 0, 1227040, 0, 0, 0, -926208, 0, 2150240, 0, 0, 0, -3870336, 0, -7693600, 0, 0, 0, -515568, 0, -3020128, 0, 0, 0, -2838832, 0, -932416, 0, 0, 0, -6647488, 0, -2100368, 0, 0, 0, 4379456, 0, 2371040, 0, 0, 0, -2152032, 0, 4287104, 0, 0, 0, 4161296, 0, 1317456, 0, 0, 0, 3262656, 0, 2853296, 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, 3, 2, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "384.5.e.a", "char_is_minimal": true, "conrey_index": 257, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [26, 1, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-51, 1, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-36, 2, 0, -4, 1, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 1, 9, 0, 1, 4, -2, 0, 0, 1, 1, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-128, -4, 1, 1, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-17, 1, -1, 0, 0, 0, 4, 0, -2, 0, 2, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -2, -1, -13, -1, -1, -1, 1, 1, -3, -3, -1, 0, -1, -2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [35, -1, 0, 11, -1, -2, 0, -5, 3, -1, -3, -2, -1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-34, -6, -2, 0, 1, 3, 1, 2, -3, -4, 1, 1, -2, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -2, -1, 0, -1, 12, 8, 0, -1, -4, -2, -2, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-125, -15, 3, -44, -1, 1, 0, 1, 4, -1, 1, -1, 2, 1, 2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, -3, 7, 2, 3, -19, 0, 1, 4, 3, 5, -1, 0, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, 4, -1, -26, 2, -4, 5, 1, -2, -7, 1, 1, 0, 2, 4, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-31, -5, -2, -5, 3, 4, 0, 13, 1, 0, 4, 6, -2, 0, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-45, -19, -3, -38, 0, -3, -4, -1, -2, 12, 6, 1, 3, -3, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9, 2, -1, 11, 1, -1, -30, 15, -1, -1, 2, -3, -4, 1, 6, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [272, 28, -1, -5, -1, 5, 0, 0, -5, -3, -4, 0, -4, 3, -4, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [19, -2, 1, 10, 1, -6, -40, -1, 5, -4, 2, -5, -2, 5, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-22, -4, 4, 42, -2, 6, -1, 4, 2, 8, -14, -4, 4, -2, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [106, 2, 0, 18, -1, 2, 0, 19, -5, -5, 1, 6, -5, 5, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [13, 38, -3, 71, 6, -6, 11, 0, -2, 9, 13, 5, -6, 0, 4, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-22, 4, -2, 71, 2, 7, -60, -18, -2, 2, 0, 10, -8, 2, 12, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [173, 33, 5, 126, -7, -17, 0, -9, 10, 1, -1, -7, 6, -1, 6, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-62, 9, -7, 24, 9, -3, 72, 3, -7, 3, -16, -1, -6, 1, 4, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-82, 8, 1, 192, 4, 18, -3, 1, -4, 7, -7, 5, -8, 4, 16, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [204, 8, -10, 69, 0, -1, 0, -16, -12, 0, -12, -2, -10, 0, -10, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [692, 41, 2, 23, -7, 24, 1, -2, 1, 1, 21, 2, 5, -8, -4, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-16, 10, -12, 56, 5, 4, 102, -15, -5, -13, 39, 10, -5, 5, 15, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [97, -44, -7, 219, -7, -23, 0, 3, -3, -5, -11, 1, -12, 5, -12, -7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-354, 25, 6, 108, 3, 6, 124, -3, 5, -9, 32, 10, -12, 6, 8, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [122, -4, 16, -270, -2, -26, 8, -16, 2, 4, -30, 0, 12, -2, -16, -12], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-897, 17, -2, 25, 11, 2, 0, -13, -17, -7, -9, 0, -9, 7, -9, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-49, -54, -2, -6, 6, 30, -12, 3, 10, 0, 43, 7, -6, 8, 8, -14], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-20, 20, 8, 46, 10, -2, 152, 14, -10, -7, -20, 4, -6, 10, 26, -28], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [898, -44, -2, -378, -10, 30, 0, -34, -6, 10, -6, -14, 8, -10, 8, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-967, 15, 1, 72, 7, 3, -143, 17, -18, -37, -42, 7, -14, 5, 4, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [110, 0, -4, -236, 0, -30, -52, 3, 0, 12, -45, 7, -24, 0, 24, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1405, 69, -10, 134, 1, 3, 0, 7, -21, -4, -8, 6, -14, 4, -14, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-873, -71, 27, -88, -5, -51, 23, -3, 16, -25, 41, -13, 10, -3, -2, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [19, 16, -9, -33, 8, -9, -172, 2, -8, -16, 75, 7, -7, 8, 23, -7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [432, 48, -2, -368, 14, 52, 0, 5, 30, -6, -1, 7, -8, 6, -8, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1642, 51, -19, 154, 0, 15, -192, 8, -34, 3, 62, 11, -24, -5, 4, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}