# Stored data for newform 1296.3.q.f, downloaded from the LMFDB on 23 April 2024. {"label": "1296.3.q.f", "space_label": "1296.3.q", "level": 1296, "weight": 3, "hecke_orbit": 6, "hecke_orbit_code": 22519097698813200, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 696079263532549532, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [324, 0, -18, 0, 1]], [7, [16, 4, 1]]], "qexp_display": "q+\\beta _{1}q^{5}-4\\beta _{2}q^{7}+(-4\\beta _{1}+4\\beta _{3})q^{11}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "q", "char_is_real": false, "Nk2": 11664, "analytic_conductor": 35.31344226109448, "hecke_ring_index": 9, "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": [1296, 6, [1135, 325, 1217], [6, 6, 1]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [593, 1025], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [[3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.093", "prec": 17}, {"__RealLiteral__": 0, "data": "3.616", "prec": 17}, {"__RealLiteral__": 0, "data": "2.783", "prec": 17}, {"__RealLiteral__": 0, "data": "78.737", "prec": 20}, {"__RealLiteral__": 0, "data": "132.589", "prec": 24}, {"__RealLiteral__": 0, "data": "2587.468", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, 0, -8], "traces": [0, 4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, -100, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, -352, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 334, 0, 0, 0, 0, 0, -368, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 304, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, -296, 0, 0, 0, 0, 0, 164, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 210, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -928, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, -412, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -396, 0, 0, 0, 0, 0, 592, 0, 0, 0, 0, 0, -704, 0, 0, 0, 0, 0, -872, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, -324, 0, 0, 0, 0, 0, -1520, 0, 0, 0, 0, 0, 656, 0, 0, 0, 0, 0, -416, 0, 0, 0, 0, 0, 508, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, 2080, 0, 0, 0, 0, 0, 188, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 1072, 0, 0, 0, 0, 0, 416, 0, 0, 0, 0, 0, -1312, 0, 0, 0, 0, 0, 476, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, -420, 0, 0, 0, 0, 0, 568, 0, 0, 0, 0, 0, 380, 0, 0, 0, 0, 0, 640, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 584, 0, 0, 0, 0, 0, 704, 0, 0, 0, 0, 0, -736, 0, 0, 0, 0, 0, -2016, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -400, 0, 0, 0, 0, 0, 2168, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 3168, 0, 0, 0, 0, 0, 800, 0, 0, 0, 0, 0, -1208, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 544, 0, 0, 0, 0, 0, -2384, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 448, 0, 0, 0, 0, 0, 504, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, -2880, 0, 0, 0, 0, 0, 2944, 0, 0, 0, 0, 0, -482, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3232, 0, 0, 0, 0, 0, 1072, 0, 0, 0, 0, 0, -608, 0, 0, 0, 0, 0, 1280, 0, 0, 0, 0, 0, 1332, 0, 0, 0, 0, 0, 736, 0, 0, 0, 0, 0, -568, 0, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 1408, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, -316, 0, 0, 0, 0, 0, 664, 0, 0, 0, 0, 0, 2312, 0, 0, 0, 0, 0, 1792, 0, 0, 0, 0, 0, 802, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 528, 0, 0, 0, 0, 0, 1456, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, -124, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, 1340, 0, 0, 0, 0, 0, -1408, 0, 0, 0, 0, 0, 2664, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -1188, 0, 0, 0, 0, 0, -2176, 0, 0, 0, 0, 0, -1936, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 448, 0, 0, 0, 0, 0, -1016, 0, 0, 0, 0, 0, 2288, 0, 0, 0, 0, 0, 1216, 0, 0, 0, 0, 0, -2340, 0, 0, 0, 0, 0, 376, 0, 0, 0, 0, 0, -4960, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, 1820, 0, 0, 0, 0, 0, -1232, 0, 0, 0, 0, 0, -1728, 0, 0, 0, 0, 0, -2720, 0, 0, 0, 0, 0, 1600, 0, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 640, 0, 0, 0, 0, 0, -1280, 0, 0, 0, 0, 0, 664, 0, 0, 0, 0, 0, 2528, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, -1646, 0, 0, 0, 0, 0, -2672, 0, 0, 0, 0, 0, -892, 0, 0, 0, 0, 0, 1456, 0, 0, 0, 0, 0, -2952, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 1820, 0, 0, 0, 0, 0, -4256, 0, 0, 0, 0, 0, 736, 0, 0, 0, 0, 0, -1728, 0, 0, 0, 0, 0, 1944, 0, 0, 0, 0, 0, -3536, 0, 0, 0, 0, 0, 4032, 0, 0, 0, 0, 0, -1520, 0, 0, 0, 0, 0, 476, 0, 0, 0, 0, 0, 1056, 0, 0, 0, 0, 0, -712, 0, 0, 0, 0, 0, 1584, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, -1950, 0, 0, 0, 0, 0, 3400, 0, 0, 0, 0, 0, -2432, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, -1404, 0, 0, 0, 0, 0, 3088, 0, 0, 0, 0, 0, -388, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 2240, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 1892, 0, 0, 0, 0, 0, 2432, 0, 0, 0, 0, 0, 1088, 0, 0, 0, 0, 0, 2824, 0, 0, 0, 0, 0, -4608, 0, 0, 0, 0, 0, -1664, 0, 0, 0, 0, 0, -1184, 0, 0, 0, 0, 0, 784, 0, 0, 0, 0, 0, -1756, 0, 0, 0, 0, 0, -560, 0, 0, 0, 0, 0, -5760, 0, 0, 0, 0, 0, 3016, 0, 0, 0, 0, 0, -3472, 0, 0, 0, 0, 0, -1312, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, -1008, 0, 0, 0, 0, 0, 3104, 0, 0, 0, 0, 0, -3104, 0, 0, 0, 0, 0, -1024, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, 448, 0, 0, 0, 0, 0, -2992, 0, 0, 0, 0, 0, 5120, 0, 0, 0, 0, 0, -1600, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 4672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 840, 0, 0, 0, 0, 0, -792, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 2592, 0, 0, 0, 0, 0, 2096, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, -924, 0, 0, 0, 0, 0, -296, 0, 0, 0, 0, 0, -1456, 0, 0, 0, 0, 0, -10656, 0, 0, 0, 0, 0, -3232, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 5632, 0, 0, 0, 0, 0, 1856, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 6832, 0, 0, 0, 0, 0, 1548, 0, 0, 0, 0, 0, -2000, 0, 0, 0, 0, 0, -1720, 0, 0, 0, 0, 0, 856, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, -6336, 0, 0, 0, 0, 0, 2852, 0, 0, 0, 0, 0, -3800, 0, 0, 0, 0, 0, -7040, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, 2916, 0, 0, 0, 0, 0, 3296, 0, 0, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, -852, 0, 0, 0, 0, 0, 4608, 0, 0, 0, 0, 0, -3760, 0, 0, 0, 0, 0, -1024, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 1240, 0, 0, 0, 0, 0, 4824, 0, 0, 0, 0, 0, 3024, 0, 0, 0, 0, 0, -896, 0, 0, 0, 0, 0, 7408, 0, 0, 0, 0, 0, 5444, 0, 0, 0, 0, 0, -1584, 0, 0, 0, 0, 0, 11520, 0, 0, 0, 0, 0, 4024, 0, 0, 0, 0, 0, 2000, 0, 0, 0, 0, 0, -7136, 0, 0, 0, 0, 0, 3708, 0, 0, 0, 0, 0, -1496, 0, 0, 0, 0, 0, -4736, 0, 0, 0, 0, 0, 3088, 0, 0, 0, 0, 0, 992, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 0, 0, -2432, 0, 0, 0, 0, 0, -5328, 0, 0, 0, 0, 0, 648, 0, 0, 0, 0, 0, -2904, 0, 0, 0, 0, 0, -700, 0, 0, 0, 0, 0, -2528, 0, 0, 0, 0, 0, 324, 0, 0, 0, 0, 0, -2936, 0, 0, 0, 0, 0, 8504, 0, 0, 0, 0, 0, -3168, 0, 0, 0, 0, 0, -3488, 0, 0, 0, 0, 0, -656, 0, 0, 0, 0, 0, 2672, 0, 0, 0, 0, 0, 880, 0, 0, 0, 0, 0, 5688, 0, 0, 0, 0, 0, 2720, 0, 0, 0, 0, 0, -3760, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 2240, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, -3232, 0, 0, 0, 0, 0, -1088, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 18720, 0, 0, 0, 0, 0, -2880, 0, 0, 0, 0, 0, 1472, 0, 0, 0, 0, 0, -8776, 0, 0, 0, 0, 0, 2728, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 994, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 2744, 0, 0, 0, 0, 0, -368, 0, 0, 0, 0, 0, -6336, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, -756, 0, 0, 0, 0, 0, 1888, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 0, 0, 2448, 0, 0, 0, 0, 0, 3548, 0, 0, 0, 0, 0, -10304, 0, 0, 0, 0, 0, -1792, 0, 0, 0, 0, 0, 1816, 0, 0, 0, 0, 0, -3816, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, -2752, 0, 0, 0, 0, 0, 7120, 0, 0, 0, 0, 0, 3356, 0, 0, 0, 0, 0, -4752, 0, 0, 0, 0, 0, -11512, 0, 0, 0, 0, 0, 2432, 0, 0, 0, 0, 0, -2244, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 2968, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, -5632, 0, 0, 0, 0, 0, 498, 0, 0, 0, 0, 0, 2592, 0, 0, 0, 0, 0, 6524, 0, 0, 0, 0, 0, -992, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, 6616, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, -8800, 0, 0, 0, 0, 0, 3040, 0, 0, 0, 0, 0, 5904, 0, 0, 0, 0, 0, 8064, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, 3996, 0, 0, 0, 0, 0, -15840, 0, 0, 0, 0, 0, -5212, 0, 0, 0, 0, 0, 2624, 0, 0, 0, 0, 0, -6840, 0, 0, 0, 0, 0, -3464, 0, 0, 0, 0, 0, -896, 0, 0, 0, 0, 0, 4736, 0, 0, 0, 0, 0, -6912, 0, 0, 0, 0, 0, -1064, 0, 0, 0, 0, 0, 3328, 0, 0, 0, 0, 0, -3104, 0, 0, 0, 0, 0, 1028, 0, 0, 0, 0, 0, 2800, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 17, "prim_orbit_index": 4, "minimal_twist": "18.3.b.a", "char_is_minimal": false, "conrey_index": 593, "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], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, -4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, 4], [0, 0, 0, 0], [-8, 0, 8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -3], [0, 0, 0, 0], [16, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, -7, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, -1], [0, 0, 0, 0], [44, 0, -44, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [-34, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -11, 0, 0], [0, 0, 0, 0], [0, 0, -40, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 20, 0, -20], [0, 0, 0, 0], [33, 0, -33, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 9], [0, 0, 0, 0], [-72, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 8, 0, 0], [0, 0, 0, 0], [0, 0, -50, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -8, 0, 8], [0, 0, 0, 0], [8, 0, -8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 12], [0, 0, 0, 0], [-16, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 16, 0, 0], [0, 0, 0, 0], [0, 0, -76, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -28, 0, 28], [0, 0, 0, 0], [54, 0, -54, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 3], [0, 0, 0, 0], [32, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 16, 0, 0], [0, 0, 0, 0], [0, 0, -176, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}