# Stored data for newform 630.2.i.d, downloaded from the LMFDB on 25 April 2024. {"label": "630.2.i.d", "space_label": "630.2.i", "level": 630, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13511348671480438, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 620591050463695577, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [0, 1]], [13, [16, -4, 1]]], "qexp_display": "q+q^{2}+(2-\\zeta_{6})q^{3}+q^{4}+(1-\\zeta_{6})q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "i", "char_is_real": false, "Nk2": 2520, "analytic_conductor": 5.030575327340665, "hecke_ring_index": 1, "level_radical": 210, "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": "0.020", "prec": 17}, "analytic_rank_proved": true, "char_values": [630, 3, [281, 127, 451], [1, 3, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [121, 151], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.018", "prec": 17}, {"__RealLiteral__": 0, "data": "2.028", "prec": 17}, {"__RealLiteral__": 0, "data": "0.245", "prec": 17}, {"__RealLiteral__": 0, "data": "12.423", "prec": 20}, {"__RealLiteral__": 0, "data": "5.212", "prec": 17}, {"__RealLiteral__": 0, "data": "118.012", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [2, 3, 1, -4], "traces": [0, 2, 2, 3, 2, 1, 3, -4, 2, 3, 1, 0, 3, 4, -4, 0, 2, 0, 3, -2, 1, -9, 0, 3, 3, -1, 4, 0, -4, -6, 0, 4, 2, 0, 0, -5, 3, -2, -2, 12, 1, 6, -9, -11, 0, -3, 3, 6, 3, 2, -1, 0, 4, -6, 0, 0, -4, -6, -6, 24, 0, -14, 4, -15, 2, 8, 0, -14, 0, 0, -5, 0, 3, -2, -2, -3, -2, 0, 12, -8, 1, -9, 6, 12, -9, 0, -11, 0, 0, 15, -3, 4, 3, 6, 6, -4, 3, 10, 2, 0, -1, -3, 0, -17, 4, -6, -6, 0, 0, -2, 0, -6, -4, 6, -6, -3, -6, 24, 24, 0, 0, 11, -14, 18, 4, -2, -15, -26, 2, 0, 8, 0, 0, -2, -14, -9, 0, -12, 0, 4, -5, 9, 0, 0, 3, 6, -2, 15, -2, -15, -3, -2, -2, 0, 0, 2, 12, -44, -8, 0, 1, -15, -9, -20, 6, 0, 12, 3, -9, -3, 0, -12, -11, 48, 0, -1, 0, 36, 15, 18, -3, 4, 4, -21, 3, -4, 6, 0, 6, -18, -4, 36, 3, -44, 10, 12, 2, -24, 0, 4, -1, -21, -3, 30, 0, 12, -17, -9, 4, 0, -6, -8, -6, 0, 0, 11, 0, -8, -2, 0, 0, 0, -6, 19, -4, -6, 6, -24, -6, -29, -3, 0, -6, -18, 24, 3, 24, -12, 0, 24, 0, 19, 11, -27, -14, 13, 18, 8, 4, 0, -2, -24, -15, 0, -26, 0, 2, 18, 0, -2, 8, 18, 0, -9, 0, 6, -2, 45, -14, 21, -9, -20, 0, -12, -12, 0, 0, -32, 4, 6, -5, -21, 9, 22, 0, -6, 0, 6, 3, 17, 6, 0, -2, 30, 15, 12, -2, 0, -15, 24, -3, 55, -2, -9, -2, -7, 0, 40, 0, 0, 2, 0, 12, 52, -44, -3, -8, -36, 0, 0, 1, 0, -15, 0, -9, 4, -20, 0, 6, -12, 0, 52, 12, -12, 3, -7, -9, -32, -3, 18, 0, 0, -12, 20, -11, -9, 48, 54, 0, 7, -1, 36, 0, -24, 36, 0, 15, 0, 18, -6, -3, 15, 4, 0, 4, 2, -21, -17, 3, 36, -4, 30, 6, -14, 0, -3, 6, -48, -18, -8, -4, -39, 36, 21, 3, 0, -44, 33, 10, -27, 12, 0, 2, 0, -24, -4, 0, 28, 4, 6, -1, -15, -21, 8, -3, -18, 30, 0, 0, -2, 12, -36, -17, -48, -9, -12, 4, 12, 0, -36, -6, -17, -8, 9, -6, 0, 0, 28, 0, 0, 11, -30, 0, -8, -8, 18, -2, -12, 0, 16, 0, 39, 0, 0, -6, 30, 19, 0, -4, 30, -6, 0, 6, -6, -24, -16, -6, 52, -29, 0, -3, -27, 0, -5, -6, 0, -18, -15, 24, 28, 3, -66, 24, 0, -12, -2, 0, 18, 24, -18, 0, 8, 19, -18, 11, -10, -27, -20, -14, -60, 13, -12, 18, 0, 8, 0, 4, 0, 0, 28, -2, 9, -24, 0, -15, -6, 0, 0, -26, 18, 0, 10, 2, -18, 18, 17, 0, 0, -2, 72, 8, -27, 18, -29, 0, 3, -9, 0, 0, 14, 6, 36, -2, -24, 45, 0, -14, 0, 21, 0, -9, 25, -20, 6, 0, 2, -12, -8, -12, -21, 0, 24, 0, 16, -32, -6, 4, -6, 6, -88, -5, 0, -21, -18, 9, 12, 22, -9, 0, 12, -6, 64, 0, 54, 6, -6, 3, -20, 17, -66, 6, -60, 0, 0, -2, 12, 30, -45, 15, -4, 12, -36, -2, 0, 0, 0, -15, 0, 24, 12, -3, 10, 55, -21, -2, -11, -9, -32, -2, 36, -7, 12, 0, -38, 40, 18, 0, 6, 0, 10, 2, -27, 0, 15, 12, -1, 52, 0, -44, 0, -3, -32, -8, -24, -36, -13, 0, -44, 0, 0, 1, 15, 0, 43, -15, 33, 0, 0, -9, 0, 4, -18, -20, -30, 0, 0, 6, 6, -12, -24, 0, 10, 52, 0, 12, 8, -12, 18, 3, 0, -7, 0, -9, 28, -32, -9, -3, -24, 18, -50, 0, -72, 0, -51, -12, -24, 20, 0, -11, -48, -9, -92, 48, 0, 54, 8, 0, 0, 7, -54, -1, 60, 36, -4, 0, 0, -24, -3, 36, -38, 0, -12, 15, 6, 0, 0, 18, 72, -6, 30, -3, 85, 15, 57, 4, 12, 0, 7, 4, -54, 2, 0, -21, -8, -17, 24, 3, 0, 36, -32, -4, 0, 30, 0, 6, 15, -14, -36, 0, 0, -3, 22, 6, -36, -48, -4, -18, 28, -8, 0, -4, -15, -39, 10, 36, 0, 21, 48, 3, -5, 0, 0, -44, 18, 33, -2, 10, 6, -27, 12, 12, 0, 0, 54, 2, -22, 0, -2, -24, -27, -4, 6, 0, -28, 28, 18, 4, -18, 6, 0, -1, 90, -15, 0, -21, -3, 8, 0, -3, 39, -18, -32, 30, -60, 0, -40, 0, 44, -2, -48, 12, -6, -36, 16, -17, 0, -48, 24, -9, 25, -12, -96, 4, 0, 12, 6, 0, 0, -36, 18, -6, -7, -17, 0, -8, 3, 9, -55, -6, 33, 0, -12, 0, -8, 28, -6, 0, -30, 0, -26, 11, -18, -30, 21, 0, 24, -8, 51, -8, 0, 18, -28, -2, -30, -12, 4, 0, 34, 16, 90, 0, 66, 39, -86, 0, 0, 0, -9, -6, 52, 30, 0, 19, -6, 0, -18, -4, 36, 30, -12, -6, 0, 0, 66, 6, 2, -6, 4, -24, -18, -16, 42, -6, 0, 52, 0, -29, 0, 0, -56, -3, 60, -27, 0, 0, -2, -5, 51, -6, 30, 0, 22, -18, 0, -15, 0, 24, 88, 28, 78, 3, 30, -66, 36, 24, 9, 0, 90, -12, -16, -2, -54, 0, 36, 18, 18, 24, 0, -18, -12, 0, -54, 8, 0, 19, -22, -18, 1, 11, 0, -10, 0, -27, 4, -20, 0, -14, 72, -60, 0, 13, 6, -12, -24, 18, -12, 0, -27, 8, 33, 0, -56, 4, 78, 0, -4, 0, -14, 28, -18, -2], "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, 63, 8, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 8, "minimal_twist": "630.2.i.d", "char_is_minimal": true, "conrey_index": 121, "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], [1, 0], [2, -1], [1, 0], [1, -1], [2, -1], [-1, -2], [1, 0], [3, -3], [1, -1], [0, 0], [2, -1], [0, 4], [-1, -2], [1, -2], [1, 0], [0, 0], [3, -3], [0, -2], [1, -1], [-4, -1], [0, 0], [3, -3], [2, -1], [0, -1], [0, 4], [3, -6], [-1, -2], [-6, 6], [1, -2], [2, 0], [1, 0], [0, 0], [0, 0], [-3, 1], [3, -3], [0, -2], [0, -2], [4, 4], [1, -1], [0, 6], [-4, -1], [-11, 11], [0, 0], [0, -3], [3, -3], [3, 0], [2, -1], [-3, 8], [0, -1], [0, 0], [0, 4], [-6, 6], [3, -6], [0, 0], [-1, -2], [-2, -2], [-6, 6], [12, 0], [1, -2], [-7, 0], [2, 0], [-9, 3], [1, 0], [4, 0], [0, 0], [-7, 0], [0, 0], [3, -6], [-3, 1], [0, 0], [3, -3], [-2, 2], [0, -2], [-1, -1], [0, -2], [0, 0], [4, 4], [-4, 0], [1, -1], [0, -9], [0, 6], [12, -12], [-4, -1], [0, 0], [-11, 11], [-6, 12], [0, 0], [0, 15], [0, -3], [8, -12], [3, -3], [4, -2], [3, 0], [-2, 0], [2, -1], [10, -10], [-3, 8], [0, 0], [0, -1]]}