# Stored data for newform 684.3.y.c, downloaded from the LMFDB on 24 April 2024.
{"label": "684.3.y.c", "space_label": "684.3.y", "level": 684, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9008848572514988, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1387045512082141702, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [0, 1]], [7, [11, 1]]], "qexp_display": "q-11q^{7}+(30-15\\zeta_{6})q^{13}+(-21+\\cdots)q^{19}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "y", "char_is_real": false, "Nk2": 6156, "analytic_conductor": 18.637650082244306, "hecke_ring_index": 1, "level_radical": 114, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.592", "prec": 17}, "analytic_rank_proved": true, "char_values": [684, 6, [343, 533, 325], [6, 6, 5]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 4, "level_primes": [2, 3, 19], "conrey_indexes": [145, 217], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.043", "prec": 17}, {"__RealLiteral__": 0, "data": "1.951", "prec": 17}, {"__RealLiteral__": 0, "data": "0.512", "prec": 17}, {"__RealLiteral__": 0, "data": "16.991", "prec": 20}, {"__RealLiteral__": 0, "data": "6.109", "prec": 17}, {"__RealLiteral__": 0, "data": "181.839", "prec": 24}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.1.d6", "trace_display": [0, 0, 0, -22], "traces": [0, 2, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -83, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -121, 0, 0, 0, 0, 0, 231, 0, 0, 0, 0, 0, -143, 0, 0, 0, 0, 0, 153, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -495, 0, 0, 0, 0, 0, 336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -242, 0, 0, 0, 0, 0, 360, 0, 0, 0, 0, 0, 286, 0, 0, 0, 0, 0, -229, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -193, 0, 0, 0, 0, 0, -598, 0, 0, 0, 0, 0, 506, 0, 0, 0, 0, 0, -275, 0, 0, 0, 0, 0, 312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -525, 0, 0, 0, 0, 0, 109, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 87, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -255, 0, 0, 0, 0, 0, 818, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -93, 0, 0, 0, 0, 0, -225, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -242, 0, 0, 0, 0, 0, -244, 0, 0, 0, 0, 0, -458, 0, 0, 0, 0, 0, 289, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 913, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, -142, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1131, 0, 0, 0, 0, 0, -506, 0, 0, 0, 0, 0, 1342, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, -491, 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, -431, 0, 0, 0, 0, 0, 1575, 0, 0, 0, 0, 0, -912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1320, 0, 0, 0, 0, 0, 1331, 0, 0, 0, 0, 0, -1221, 0, 0, 0, 0, 0, -897, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1534, 0, 0, 0, 0, 0, -794, 0, 0, 0, 0, 0, -2541, 0, 0, 0, 0, 0, -925, 0, 0, 0, 0, 0, 1485, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 851, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1573, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1161, 0, 0, 0, 0, 0, 529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 241, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, -1683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -362, 0, 0, 0, 0, 0, -1924, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1126, 0, 0, 0, 0, 0, 1898, 0, 0, 0, 0, 0, -625, 0, 0, 0, 0, 0, 587, 0, 0, 0, 0, 0, 3240, 0, 0, 0, 0, 0, 1237, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2636, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1584, 0, 0, 0, 0, 0, 457, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1429, 0, 0, 0, 0, 0, 2068, 0, 0, 0, 0, 0, -109, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2583, 0, 0, 0, 0, 0, -673, 0, 0, 0, 0, 0, -792, 0, 0, 0, 0, 0, 863, 0, 0, 0, 0, 0, -2625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5445, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1008, 0, 0, 0, 0, 0, -913, 0, 0, 0, 0, 0, 1058, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -841, 0, 0, 0, 0, 0, 2662, 0, 0, 0, 0, 0, 1177, 0, 0, 0, 0, 0, -1549, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3465, 0, 0, 0, 0, 0, 531, 0, 0, 0, 0, 0, 443, 0, 0, 0, 0, 0, -3960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3674, 0, 0, 0, 0, 0, -2475, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, -1847, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5428, 0, 0, 0, 0, 0, 1787, 0, 0, 0, 0, 0, 2519, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1647, 0, 0, 0, 0, 0, 1487, 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, 3, 2, -1, 2, -3], [1, 1, 19, 4, -1, 6, 0], [1, 1, 57, 6, 1, 6, 0]], "char_orbit_index": 25, "prim_orbit_index": 4, "minimal_twist": "684.3.y.c", "char_is_minimal": true, "conrey_index": 145, "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, 0], [0, 0], [-11, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [30, -15], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-21, 16], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 25], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-35, 70], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-33, 66], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-83, 83], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [72, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -121], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [154, -77], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-143, 143], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [51, 51], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-330, 165], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [112, 112], [0, 0], [0, 0], [0, 0]]}