# Stored data for newform 363.3.h.d, downloaded from the LMFDB on 24 April 2024. {"label": "363.3.h.d", "space_label": "363.3.h", "level": 363, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13511279968780651, "dim": 8, "is_polredabs": true, "nf_label": "8.0.228765625.1", "trace_hash": 1080333227279246180, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [14641, 0, -1331, 0, 121, 0, -11, 0, 1]], [5, [3748096, 0, -85184, 0, 1936, 0, -44, 0, 1]], [7, [4096, 512, 64, 8, 1]]], "qexp_display": "q+\\beta _{7}q^{2}+3\\beta _{4}q^{3}-7\\beta _{2}q^{4}+(-2\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 10, "char_parity": -1, "char_degree": 4, "char_conductor": 33, "char_orbit_label": "h", "char_is_real": false, "Nk2": 3267, "analytic_conductor": 9.891033596278778, "hecke_ring_index": 16, "level_radical": 33, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [363, 10, [122, 244], [5, 8]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 8, "level_primes": [3, 11], "conrey_indexes": [245, 251, 269, 323], "field_disc": 228765625, "field_disc_factorization": [[5, 6], [11, 4]], "field_poly": [81, -27, -18, 15, 1, 5, -2, -1, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.613", "prec": 17}, {"__RealLiteral__": 0, "data": "3.495", "prec": 17}, {"__RealLiteral__": 0, "data": "776.866", "prec": 24}, {"__RealLiteral__": 0, "data": "624.724", "prec": 24}, {"__RealLiteral__": 0, "data": "122776.934", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c10", "trace_display": [0, -6, 0, -16], "traces": [0, 8, 0, -6, 14, 0, 0, -16, 0, -18, -176, 0, -168, 8, 0, 0, -10, 0, 0, -12, 0, 192, 0, 0, 0, 38, 0, -54, 112, 0, 132, 52, 0, 0, -352, 0, 126, -60, 0, 24, -132, 0, 0, -336, 0, 0, -44, 0, -30, -30, 0, 0, -56, 0, 0, 0, 0, -36, -264, 0, 0, 24, 0, -144, -194, 0, 0, 16, 0, 0, 352, 0, 0, -148, 0, 114, -336, 0, 0, -80, 0, -162, 88, 0, 336, 176, 0, 0, 0, 0, 396, 64, 0, 156, -572, 0, 0, -124, 0, 0, 1064, 0, 264, -148, 0, 0, 396, 0, 378, 1600, 0, 720, -80, 0, 0, -88, 0, 72, -440, 0, 1584, 0, 0, 0, -364, 0, 0, 376, 0, 252, -176, 0, 0, 384, 0, 0, -264, 0, -132, -148, 0, 0, -1584, 0, 360, -528, 0, -90, 420, 0, 0, -320, 0, 0, 0, 0, -168, -364, 0, 0, -308, 0, 0, 580, 0, 0, 1056, 0, 0, 306, 0, -108, -588, 0, -792, -1216, 0, 0, 792, 0, 0, -20, 0, 72, 132, 0, 0, 0, 0, -432, 264, 0, -582, 596, 0, 0, 210, 0, 0, -336, 0, -12, 704, 0, 0, 176, 0, 0, -160, 0, -4224, 492, 0, 0, -264, 0, 0, 416, 0, 1776, 0, 0, 0, 604, 0, 342, 264, 0, 252, -300, 0, 0, -3168, 0, 0, -1144, 0, -240, 704, 0, 0, -1040, 0, 1944, -168, 0, 264, 48, 0, 0, 264, 0, -4032, 0, 0, 528, 742, 0, 0, -480, 0, 0, 264, 0, 0, -3168, 0, 0, 28, 0, 1188, -896, 0, 192, 2816, 0, 0, -520, 0, 468, -1056, 0, -1716, -100, 0, 0, 0, 0, 0, -226, 0, -372, 1036, 0, 0, -880, 0, 0, 2464, 0, -798, 672, 0, 0, -60, 0, 792, -688, 0, 1776, -1144, 0, 0, -196, 0, 0, 560, 0, -4752, 0, 0, 0, -352, 0, 1134, -152, 0, -1200, -264, 0, 0, -1744, 0, -540, -1584, 0, -240, 556, 0, 0, 4928, 0, 0, 544, 0, -264, 1320, 0, 0, 648, 0, -864, 0, 0, -1320, 792, 0, 0, -1320, 0, -1188, 650, 0, 0, 1792, 0, 0, 556, 0, 0, 1320, 0, -1092, 544, 0, 0, 1716, 0, 0, -1340, 0, 1128, 748, 0, 0, 0, 0, 756, 868, 0, -528, -176, 0, 0, 880, 0, 0, -688, 0, -288, 190, 0, 0, -208, 0, 0, 8448, 0, 3168, 1020, 0, 0, 1036, 0, -396, -528, 0, 1776, 0, 0, 0, 340, 0, 0, -1188, 0, 1188, 192, 0, 0, 7392, 0, -270, 1084, 0, -1584, 2800, 0, 0, -2624, 0, 1080, -352, 0, 1260, 1584, 0, 0, -1552, 0, 0, 0, 0, -960, -1320, 0, 0, 684, 0, 0, 616, 0, 0, -688, 0, 0, -2904, 0, -504, -32, 0, -1092, -5280, 0, 0, 228, 0, 0, 0, 0, -924, 240, 0, 0, 0, 0, 0, -892, 0, 1740, 660, 0, 0, -1056, 0, 0, -1040, 0, -792, 116, 0, 0, -1936, 0, 0, -5632, 0, -3672, -2632, 0, 0, -1184, 0, -324, -3256, 0, 7056, 0, 0, 0, 528, 0, -2376, -284, 0, 912, 1496, 0, 0, 3880, 0, 0, 672, 0, 2376, -528, 0, 0, 1936, 0, 0, 800, 0, -60, -616, 0, 0, 340, 0, -864, 0, 0, 396, -640, 0, 0, 1036, 0, 0, -336, 0, 0, 5280, 0, 0, 528, 0, -1296, -1188, 0, 792, 5648, 0, 0, 704, 0, -1746, 1476, 0, 1788, 3696, 0, 0, 0, 0, 0, 3168, 0, 630, 312, 0, 0, -300, 0, 0, -5632, 0, 252, 176, 0, 0, 1084, 0, -36, -8960, 0, -8448, -1400, 0, 0, -528, 0, 0, 1528, 0, -2112, 0, 0, 0, 1484, 0, 0, -132, 0, 120, 1478, 0, 0, -10192, 0, 3168, 820, 0, 1476, -2068, 0, 0, -480, 0, 0, 3036, 0, -792, -1780, 0, 0, 528, 0, 0, 0, 0, 1248, -4060, 0, 0, 528, 0, -1332, -4576, 0, 0, -5968, 0, 0, 792, 0, 0, 528, 0, 1812, -352, 0, 0, -1268, 0, 1026, -2142, 0, 792, -992, 0, 0, 0, 0, 756, -1408, 0, -900, 420, 0, 0, -916, 0, 0, -8800, 0, 2376, 352, 0, 0, -2128, 0, 0, 1440, 0, 13728, -2640, 0, 0, 1124, 0, -720, -2376, 0, -8448, 0, 0, 0, -2024, 0, 0, -1184, 0, 780, 140, 0, 0, -336, 0, -1458, 3256, 0, -504, -1248, 0, 0, -1232, 0, -3168, 1372, 0, 144, 3168, 0, 0, -1232, 0, 0, 0, 0, 792, -188, 0, 0, 1056, 0, 3024, -2236, 0, 0, 3168, 0, 0, -3200, 0, 1584, 220, 0, 2226, -10192, 0, 0, -4172, 0, 0, -988, 0, -1440, 2772, 0, 0, 0, 0, 0, -150, 0, 792, 596, 0, 0, 1760, 0, 0, 384, 0, 2376, -588, 0, 0, -2288, 0, 0, -6688, 0, -336, -704, 0, 0, -2112, 0, 3564, -364, 0, 10752, 0, 0, 0, 504, 0, 576, -1232, 0, -2112, 492, 0, 0, 14080, 0, 0, -500, 0, -1560, 776, 0, 0, 12672, 0, -5616, 3520, 0, -3168, 1486, 0, 0, -3444, 0, 20592, 0, 0, -300, -1672, 0, 0, 112, 0, 0, 792, 0, 0, 10224, 0, 0, 1848, 0, 0, 2640, 0, -678, 11648, 0, 0, 16, 0, -1116, -264, 0, 3108, 912, 0, 0, 0, 0, 0, 2188, 0, -2640, -880, 0, 0, 3008, 0, 0, 16912, 0, -1848, -2640, 0, 0, 2992, 0, -2394, -6336, 0, -8064, -792, 0, 0, -372, 0, 0, -1408, 0, 720, 0, 0, 0, 2100, 0, 2376, -856, 0, 516, -528, 0, 0, -4560, 0, -1332, 1848, 0, -3432, -180, 0, 0, -15840, 0, 0, 580, 0, -588, 8008, 0, 0, -176, 0, 0, 0, 0, 1680, 592, 0, 0, -2112, 0, 3564, 1496, 0, 0, -5984, 0, 0, 570, 0, 0, -1820, 0, -1056, -3680, 0, 0, 2728, 0, 3402, -1184, 0, -456, 120, 0, 0, 0, 0, -3600, -4664, 0, -792, 1760, 0, 0, -336, 0, 0, 6704, 0, 1308, 3168, 0, 0, -104, 0, -1620, 3168], "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, 3, 11, 3, 1, 5, 0], [1, 3, 33, 8, -1, 10, 0]], "char_orbit_index": 8, "prim_orbit_index": 8, "minimal_twist": "33.3.b.a", "char_is_minimal": false, "conrey_index": 245, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 3, 0, 0, 0], [0, 0, -7, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, -2, -2, -2], [0, -3, 0, 0, 0, -3, -3, -3], [0, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -3, 0, 0], [0, 0, 0, -9, 0, 0, 0, 0], [-22, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-21, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0], [-5, 0, -5, 5, -5, 0, 0, 0], [0, -4, 0, 0, 0, -4, -4, -4], [0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -14], [24, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, -19, 0, 0, 0], [0, -4, 0, 0, 0, 0, 0, 0], [-27, 0, -27, 27, -27, 0, 0, 0], [56, 0, 56, -56, 56, 0, 0, 0], [0, -12, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -66, 0, 0, 0], [0, 0, 0, 26, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -7, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-44, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 16], [0, 0, 0, 0, -63, 0, 0, 0], [0, 0, 30, 0, 0, 0, 0, 0], [0, -6, 0, 0, 0, -6, -6, -6], [12, 0, 12, -12, 12, 0, 0, 0], [0, 0, 66, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 24], [-42, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 18, 0], [0, 0, 0, -22, 0, 0, 0, 0], [0, 0, 0, 0, 0, -26, 0, 0], [0, 0, 15, 0, 0, 0, 0, 0], [-15, 0, -15, 15, -15, 0, 0, 0], [0, 19, 0, 0, 0, 19, 19, 19], [0, 12, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 28, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 18], [0, 0, 0, 0, 0, 0, 27, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -24, 0], [0, 0, 0, -18, 0, 0, 0, 0], [0, 0, 0, 0, 132, 0, 0, 0], [0, -20, 0, 0, 0, 0, 0, 0], [0, 42, 0, 0, 0, 42, 42, 42], [12, 0, 12, -12, 12, 0, 0, 0], [0, -26, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 72, 0, 0, 0], [0, 0, 0, -97, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -28], [0, 0, 0, 0, 0, -6, 0, 0], [0, 0, -176, 0, 0, 0, 0, 0], [0, -18, 0, 0, 0, -18, -18, -18], [0, 27, 0, 0, 0, 27, 27, 27], [0, 0, 74, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 30, 0, 0], [0, 0, 0, 57, 0, 0, 0, 0], [-42, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -12, 0], [0, 0, 0, -40, 0, 0, 0, 0], [0, 0, 0, 0, 0, 10, 0, 0], [0, 0, 81, 0, 0, 0, 0, 0], [44, 0, 44, -44, 44, 0, 0, 0], [0, 12, 0, 0, 0, 12, 12, 12], [0, 0, -168, 0, 0, 0, 0, 0], [0, 0, 0, 0, -88, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -42], [0, 0, 0, 0, 0, 0, -36, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 36, 0], [0, 0, 0, 198, 0, 0, 0, 0], [0, 0, 0, 0, -32, 0, 0, 0], [0, 14, 0, 0, 0, 0, 0, 0], [78, 0, 78, -78, 78, 0, 0, 0], [-286, 0, -286, 286, -286, 0, 0, 0], [0, 12, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -21, 0, 0], [0, 0, 0, -62, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 15, 0], [0, 0, 0, 0, 0, 0, 0, 0], [133, 0, 0, 0, 0, 0, 0, 0]]}