# Stored data for newform 648.4.i.g, downloaded from the LMFDB on 25 April 2024.
{"label": "648.4.i.g", "space_label": "648.4.i", "level": 648, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27022147587146376, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1140207560908794040, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [1, -1, 1]]], "qexp_display": "q+\\zeta_{6}q^{5}+(9-9\\zeta_{6})q^{7}+(-17+17\\zeta_{6})q^{11}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "i", "char_is_real": false, "Nk2": 10368, "analytic_conductor": 38.23323768371992, "hecke_ring_index": 1, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [648, 3, [487, 325, 569], [3, 3, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [217, 433], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.038", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.156", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "109.710", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [0, 0, 1, 9], "traces": [0, 2, 0, 0, 0, 1, 0, 9, 0, 0, 0, -17, 0, 44, 0, 0, 0, -112, 0, -188, 0, 0, 0, -50, 0, 124, 0, 0, 0, -30, 0, 139, 0, 0, 0, 18, 0, -348, 0, 0, 0, 318, 0, 242, 0, 0, 0, -630, 0, 262, 0, 0, 0, -1094, 0, -34, 0, 0, 0, -236, 0, -328, 0, 0, 0, -44, 0, -614, 0, 0, 0, -592, 0, 866, 0, 0, 0, 153, 0, 56, 0, 0, 0, -1225, 0, -56, 0, 0, 0, -3012, 0, 792, 0, 0, 0, -94, 0, -1391, 0, 0, 0, -1665, 0, -1468, 0, 0, 0, -1254, 0, 1220, 0, 0, 0, 1134, 0, 50, 0, 0, 0, -504, 0, 1042, 0, 0, 0, 498, 0, 1010, 0, 0, 0, 515, 0, -846, 0, 0, 0, -6, 0, -636, 0, 0, 0, -1496, 0, -60, 0, 0, 0, -2239, 0, 2695, 0, 0, 0, -139, 0, 1988, 0, 0, 0, -900, 0, -5160, 0, 0, 0, 1878, 0, 261, 0, 0, 0, -2163, 0, -1116, 0, 0, 0, -4362, 0, -2976, 0, 0, 0, -174, 0, 952, 0, 0, 0, 1764, 0, 3547, 0, 0, 0, 9882, 0, -2974, 0, 0, 0, 270, 0, -318, 0, 0, 0, 1598, 0, -442, 0, 0, 0, 484, 0, 2502, 0, 0, 0, -2464, 0, 5096, 0, 0, 0, 5484, 0, 3530, 0, 0, 0, -3260, 0, -1260, 0, 0, 0, -1990, 0, -2214, 0, 0, 0, -262, 0, -4136, 0, 0, 0, 8960, 0, 1700, 0, 0, 0, 2204, 0, -1566, 0, 0, 0, 1942, 0, -547, 0, 0, 0, 15212, 0, 8782, 0, 0, 0, 2108, 0, -7000, 0, 0, 0, 8912, 0, -3614, 0, 0, 0, 5724, 0, -3554, 0, 0, 0, -4194, 0, 236, 0, 0, 0, 2200, 0, -2178, 0, 0, 0, -656, 0, 1680, 0, 0, 0, 606, 0, -2037, 0, 0, 0, 519, 0, -510, 0, 0, 0, 10528, 0, 10912, 0, 0, 0, 5670, 0, -2750, 0, 0, 0, 614, 0, -4410, 0, 0, 0, -4726, 0, 10890, 0, 0, 0, -10911, 0, 4650, 0, 0, 0, 9410, 0, -296, 0, 0, 0, 4260, 0, 3954, 0, 0, 0, 433, 0, -1393, 0, 0, 0, -4923, 0, 2920, 0, 0, 0, -2640, 0, -21560, 0, 0, 0, -3888, 0, -153, 0, 0, 0, 4009, 0, 2800, 0, 0, 0, 112, 0, 1720, 0, 0, 0, 1716, 0, -6116, 0, 0, 0, 2958, 0, 3201, 0, 0, 0, -4248, 0, -2450, 0, 0, 0, 5700, 0, 10312, 0, 0, 0, -6944, 0, 2952, 0, 0, 0, 20708, 0, -21574, 0, 0, 0, 4700, 0, 14715, 0, 0, 0, -6628, 0, -1506, 0, 0, 0, -16244, 0, -10812, 0, 0, 0, 396, 0, 6553, 0, 0, 0, -4079, 0, 12685, 0, 0, 0, -12222, 0, -11052, 0, 0, 0, 4114, 0, -11656, 0, 0, 0, -11254, 0, -7656, 0, 0, 0, -2782, 0, 27872, 0, 0, 0, 6045, 0, 1680, 0, 0, 0, -2664, 0, 19482, 0, 0, 0, -39540, 0, -3330, 0, 0, 0, -11613, 0, 3897, 0, 0, 0, 1468, 0, -10710, 0, 0, 0, 11000, 0, -16048, 0, 0, 0, -7784, 0, 9667, 0, 0, 0, -13992, 0, -627, 0, 0, 0, -8908, 0, -18072, 0, 0, 0, 610, 0, -23456, 0, 0, 0, 2820, 0, -504, 0, 0, 0, -37442, 0, 21296, 0, 0, 0, 1417, 0, -1134, 0, 0, 0, -18596, 0, 3708, 0, 0, 0, -12400, 0, 42988, 0, 0, 0, 11025, 0, 9299, 0, 0, 0, -16049, 0, -13066, 0, 0, 0, 9316, 0, -1008, 0, 0, 0, 26538, 0, -1147, 0, 0, 0, -1042, 0, -26048, 0, 0, 0, -55440, 0, -788, 0, 0, 0, -27822, 0, -21580, 0, 0, 0, -13554, 0, -15251, 0, 0, 0, 19488, 0, 15710, 0, 0, 0, 505, 0, -11528, 0, 0, 0, -30770, 0, 18420, 0, 0, 0, -20896, 0, 8024, 0, 0, 0, 19221, 0, -515, 0, 0, 0, 29649, 0, -4478, 0, 0, 0, -1692, 0, 3000, 0, 0, 0, -5576, 0, 14099, 0, 0, 0, 14782, 0, 12519, 0, 0, 0, 49240, 0, -12, 0, 0, 0, -24068, 0, -30716, 0, 0, 0, 636, 0, -17808, 0, 0, 0, -6294, 0, 32712, 0, 0, 0, 14985, 0, 22660, 0, 0, 0, 6950, 0, -748, 0, 0, 0, -9656, 0, -26424, 0, 0, 0, 3720, 0, 3849, 0, 0, 0, -13552, 0, -11738, 0, 0, 0, 20876, 0, -53648, 0, 0, 0, -68, 0, 2239, 0, 0, 0, -5643, 0, 36039, 0, 0, 0, 5390, 0, 37300, 0, 0, 0, 18848, 0, 5490, 0, 0, 0, 10384, 0, 29215, 0, 0, 0, -53172, 0, 34472, 0, 0, 0, -29892, 0, 5032, 0, 0, 0, -1988, 0, -15520, 0, 0, 0, 20412, 0, -28864, 0, 0, 0, 7477, 0, 35280, 0, 0, 0, -7361, 0, -450, 0, 0, 0, 50564, 0, -71164, 0, 0, 0, -2580, 0, -22748, 0, 0, 0, 37506, 0, -12185, 0, 0, 0, 16256, 0, -79084, 0, 0, 0, -14672, 0, -1878, 0, 0, 0, 40368, 0, 23489, 0, 0, 0, 522, 0, 18756, 0, 0, 0, 8700, 0, 20194, 0, 0, 0, 8664, 0, 15672, 0, 0, 0, 92152, 0, -4326, 0, 0, 0, 952, 0, 27016, 0, 0, 0, 2241, 0, 28926, 0, 0, 0, 20744, 0, -31004, 0, 0, 0, -29524, 0, 4545, 0, 0, 0, 59220, 0, -2181, 0, 0, 0, -8340, 0, 61264, 0, 0, 0, -1488, 0, -27226, 0, 0, 0, -53510, 0, -20825, 0, 0, 0, 9270, 0, -886, 0, 0, 0, -13024, 0, -21576, 0, 0, 0, 27260, 0, -24628, 0, 0, 0, 1904, 0, 42150, 0, 0, 0, 22749, 0, 15900, 0, 0, 0, 36201, 0, 19052, 0, 0, 0, 8856, 0, 3528, 0, 0, 0, 54, 0, 10470, 0, 0, 0, -3547, 0, -26927, 0, 0, 0, 95922, 0, -11448, 0, 0, 0, 16746, 0, 25602, 0, 0, 0, 37146, 0, 4941, 0, 0, 0, -24200, 0, 84158, 0, 0, 0, -1487, 0, -46492, 0, 0, 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, 9, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "216.4.a.b", "char_is_minimal": false, "conrey_index": 217, "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], [1, 0], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [9, -9], [0, 0], [0, 0], [0, 0], [-17, 17], [0, 0], [0, 44], [0, 0], [0, 0], [0, 0], [-56, 0], [0, 0], [-94, 0], [0, 0], [0, 0], [0, 0], [0, -50], [0, 0], [124, -124], [0, 0], [0, 0], [0, 0], [-30, 30], [0, 0], [0, 139], [0, 0], [0, 0], [0, 0], [9, 0], [0, 0], [-174, 0], [0, 0], [0, 0], [0, 0], [0, 318], [0, 0], [242, -242], [0, 0], [0, 0], [0, 0], [-630, 630], [0, 0], [0, 262], [0, 0], [0, 0], [0, 0], [-547, 0], [0, 0], [-17, 0], [0, 0], [0, 0], [0, 0], [0, -236], [0, 0], [-328, 328], [0, 0], [0, 0], [0, 0], [-44, 44], [0, 0], [0, -614], [0, 0], [0, 0], [0, 0], [-296, 0], [0, 0], [433, 0], [0, 0], [0, 0], [0, 0], [0, 153], [0, 0], [56, -56], [0, 0], [0, 0], [0, 0], [-1225, 1225], [0, 0], [0, -56], [0, 0], [0, 0], [0, 0], [-1506, 0], [0, 0], [396, 0], [0, 0], [0, 0], [0, 0], [0, -94], [0, 0], [-1391, 1391], [0, 0], [0, 0], [0, 0]]}