# Stored data for newform 630.2.j.l, downloaded from the LMFDB on 25 April 2024. {"label": "630.2.j.l", "space_label": "630.2.j", "level": 630, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49540214409921142, "dim": 8, "is_polredabs": true, "nf_label": "8.0.856615824.2", "trace_hash": 577710230856118239, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [19321, 556, 4186, 436, 769, 52, 34, -2, 1]], [13, [324, -648, 1080, -540, 270, -36, 21, -3, 1]]], "qexp_display": "q+(-1+\\beta _{1})q^{2}+\\beta _{6}q^{3}-\\beta _{1}q^{4}+\\beta _{1}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "j", "char_is_real": false, "Nk2": 2520, "analytic_conductor": 5.030575327340665, "hecke_ring_index": 9, "level_radical": 210, "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": "0.012", "prec": 17}, "analytic_rank_proved": true, "char_values": [630, 3, [281, 127, 451], [1, 3, 3]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [211, 421], "field_disc": 856615824, "field_disc_factorization": [[2, 4], [3, 6], [271, 2]], "field_poly": [4, 0, 32, 0, 36, 0, 11, 0, 1], "hecke_ring_index_factorization": [[3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.705", "prec": 17}, {"__RealLiteral__": 0, "data": "0.227", "prec": 17}, {"__RealLiteral__": 0, "data": "246.392", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15641.388", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c3", "trace_display": [-4, -3, 4, 4], "traces": [0, 8, -4, -3, -4, 4, 0, 4, 8, 3, -8, 2, 3, 3, 4, -3, -4, 4, -3, 6, 4, 0, 2, -6, -3, -4, -6, 18, -8, -12, 3, -2, -4, 6, -2, 8, 0, -8, -3, -3, 4, 1, -3, 5, -4, 0, 12, -11, 0, -4, -4, -21, 3, 44, -18, 4, 4, 9, -12, -1, 0, -4, 4, 3, 8, -3, 27, -21, -2, -24, -4, 34, 3, -20, 4, 0, -3, -2, -12, -25, -8, 15, -2, -23, 3, 2, 5, -72, 2, 32, -3, 6, -6, 6, -11, 3, 3, -2, 8, 51, 8, -24, 48, 26, 3, -3, -22, 54, 0, 30, -2, 6, 4, -26, -9, 6, 24, -15, 2, 2, -3, -20, -4, 0, -2, -8, 0, -4, -4, 21, -3, -44, -33, 3, 42, 0, 4, -51, 30, -37, -4, -27, -17, 30, -3, -24, 10, 3, 4, -15, 3, -17, 6, 27, 4, 2, 15, 41, -25, -42, 4, -12, -12, 28, 1, 33, -23, -9, 0, 19, -4, 87, -10, -2, 36, 4, 2, -54, -16, -6, 3, 8, -3, -42, -6, -4, -24, 10, 22, 18, -6, -42, -3, 1, -2, -15, -4, 64, -36, 16, -4, 72, -24, 12, -27, -1, -52, 36, -6, 15, 0, 11, -22, -18, -27, 10, 18, -4, -15, -21, -2, -45, -6, 11, -8, -3, 52, 10, 0, 8, 6, -27, -12, 18, 30, -22, -1, -21, 2, 8, 3, 23, 40, -63, 8, 4, 15, -30, -2, -51, 4, -54, -3, -132, 2, 27, -4, 16, 24, -4, 6, 18, 88, -32, 6, 22, 3, -30, -21, -12, -18, 0, -2, 12, -51, 2, -6, 24, 74, 78, 8, -17, 33, 19, -17, 0, -15, 2, 0, 112, 12, 54, 10, -10, -3, 1, -8, 72, 30, 18, -3, -5, -17, 60, -3, -8, -57, 44, -2, -78, 2, 0, -3, 7, -82, 3, 50, -4, 24, 24, 4, -111, 6, 54, -3, -6, -14, 54, 1, 11, -6, -49, 46, -120, 18, 21, -3, 23, 19, -66, 2, 52, -48, -8, 5, 6, -2, 5, 36, 20, -8, 63, -4, -15, 57, 17, -16, -48, 3, 4, 0, 22, -4, -18, -3, -10, 60, -1, 12, 15, 8, 22, 18, 64, 10, 3, -11, -108, 0, -24, 3, 36, -42, -21, 0, 2, -2, 36, 4, -11, 3, -12, -4, 60, -32, -50, -15, -100, -8, 9, -4, -73, -45, 66, 48, 3, -24, -2, -21, -15, -1, -33, 26, -2, 18, -46, 3, 0, 15, 72, 3, -35, -22, -33, 44, -2, 33, 4, -27, 6, -5, 126, -18, -62, 2, -36, -15, -18, 30, 44, 4, 0, 90, -19, 0, 16, 11, 33, 4, -78, 0, -26, -26, 87, 10, 3, 9, 23, -16, -54, -12, -4, 33, -14, -12, -18, -9, 4, -15, -42, 11, -87, -1, -79, -9, -3, -4, -36, -16, -18, 0, 60, 23, -30, -20, -4, -27, -56, -4, -30, 4, -12, -15, 138, 60, 15, 4, 17, -9, -42, 4, -27, 27, 0, 3, -48, 66, -27, 2, -4, 21, -10, 8, -90, -32, -26, -45, -17, -4, 18, -3, 118, -54, 14, -44, -3, -32, 50, 27, 20, -44, 111, -6, 30, -36, 27, -21, -48, 6, -4, 18, 54, 0, -90, -2, 15, -15, 45, 102, 102, -4, -36, -24, 25, 24, 0, -37, 80, -168, 96, -4, -12, -17, -38, -6, 26, -38, 12, 34, 0, -9, -36, -15, 114, -1, 12, 3, -28, -56, -30, 12, 23, -111, -16, -20, 15, 20, 67, 0, 168, 1, -90, 4, 0, 0, 4, -15, -30, 18, -27, 0, 51, 10, -81, 34, 20, 78, 20, -3, -36, 4, 78, 30, -156, -22, 15, -2, 13, 114, 1, -4, 0, 0, 16, -12, -4, 7, 153, 41, -148, -3, 10, -25, 69, -4, -2, 18, 3, -48, 6, -8, -65, 87, 2, 6, 45, -27, -112, 15, -226, 3, 24, -14, 46, -63, 44, -2, 57, -22, 83, -27, 74, -49, 147, -23, 6, 66, 72, -9, 9, 21, -70, 3, 50, -46, -18, -38, -69, 30, 2, 2, 0, -26, 178, -39, -102, 4, -60, 5, 18, 24, -58, 4, 36, -10, 37, -72, 47, 20, -15, 4, -58, -90, -240, 2, 6, -15, 24, -3, -22, -34, -51, 32, 24, 27, 15, 3, 0, -2, -156, -3, 52, -11, -111, -4, -12, 96, -9, 6, 108, 20, -35, -18, 62, -1, 0, -6, 150, -33, -22, -4, 108, 22, -6, 6, 15, -128, -15, -20, 27, 0, -56, -11, 189, 54, -34, -18, -100, 12, -96, 3, -60, -6, 15, 84, -30, 42, 60, 3, -34, 2, 105, 1, -126, -51, 4, -2, 6, -11, 33, 12, 31, 24, -72, 8, -41, -42, -73, -32, 24, 25, -52, 51, -72, 50, -18, -8, 129, 0, -1, 8, 90, 146, -32, -27, -6, 66, 48, -24, 144, -15, 46, 12, -78, -2, 14, 48, -15, 30, -30, 2, 9, 66, 98, 26, 27, 1, 76, -54, -80, 23, -60, 3, -2, -87, 9, -30, -234, -144, 82, -3, -136, -35, 81, 11, 38, -99, -40, -22, -39, -2, 6, -15, 22, -8, 39, 54, -15, 15, 33, -5, -15, -63, -28, 0, -4, 31, -156, 2, 89, 72, 18, 30, -177, 36, -4, -9, -80, 44, 144, -2, -56, 3, -6, -45, 3, -19, -62, 6, -2, -32, 42, -22, -132, 42, -3, 4, 0, 39, -96, 3, 64, 13, -24, -26, 4, -15, -65, -20, 138, -6, 3, -9, 115, 23, 18, 8, -88, -18, 64, 6, 147, -4, -3, -6, 4, 28, 48, 24, 92, -6, -3, -9, 168, -2, 20, -15, 154, 21, -123, 11, -68, 6, -12, 2, 18, 158, 19, 30, -69, -3, -102, 2, -6, 12, -84, 8, 108, -18, 51, -3, -216, -120, -105, -46, -1, 6, 38, -20, -117, 2, 204, 90, -74, 28, -12, -4, -45, 48, -64, -8, 84, 24, 121, 0, 32, 138, -33, -30, -168, -51, -34, -2, -45, 17, 8, 60, 22, 84, 162, -8], "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": 10, "prim_orbit_index": 3, "minimal_twist": "630.2.j.l", "char_is_minimal": true, "conrey_index": 211, "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], [-1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [1, -1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, -1, 0, 1, 1], [0, 0, 0, 0, -1, 0, -1, 0], [0, 0, -1, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0], [-1, 1, 0, 0, 0, 0, 0, 0], [0, 2, 0, 1, 3, 0, 1, 1], [0, 1, 1, 1, 0, 1, 0, -1], [1, 0, 0, 1, 0, -1, 1, 0], [1, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -1, 1, -1, 1, 0], [0, -1, 0, 1, -1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 1, 0], [-1, 1, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 1, 1, 0, 0, 0], [2, 1, 1, -1, 0, 0, 1, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [-2, 6, 0, 2, 5, 2, 3, -1], [0, 0, 0, 0, 0, 0, -1, 0], [2, 2, 4, 4, 2, 0, 4, -2], [0, -1, 0, 0, 0, 0, 0, 0], [3, -7, -1, -1, -2, -2, 0, 1], [-1, -1, 1, -1, -3, -1, -2, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, -1, 0, 0, 0, 1], [-1, -1, 0, -2, -1, 1, -1, 0], [0, 2, 2, 1, 1, 1, 1, -1], [-1, 4, 1, 2, 2, 0, 2, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0], [2, -2, 1, 0, -2, 0, 1, 1], [-1, 1, 0, 1, 0, 1, -2, -1], [0, 1, 1, 1, 0, 0, 0, -1], [2, -1, 0, -1, 0, -1, 2, 1], [-1, 5, 3, 2, 2, 2, 3, -1], [0, 0, 0, 0, 1, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [2, -6, 3, 1, -1, 1, 1, -2], [1, -1, 1, 0, -1, 0, 0, 0], [5, 1, 0, 0, 1, 1, -1, 0], [-4, 1, -2, -1, 0, 0, -2, 0], [1, -1, 0, -1, 0, -1, 2, 1], [1, -1, 0, 0, 0, 0, 0, 0], [1, -2, 1, -3, -2, -2, 1, 1], [-2, -3, 0, -1, -1, -1, -3, 2], [1, 2, 2, 4, -1, 2, 0, -1], [0, 0, 0, 0, -1, 0, 0, 0], [0, 2, -1, 1, 2, 1, 3, 1], [0, 0, 0, -2, 0, 2, -2, 0], [0, -1, -1, -1, 0, -1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 0, 1, 0, 0, 0], [3, 5, 2, 2, 2, 1, 2, -2], [-1, -6, 0, -2, 1, -2, 0, 1], [1, -1, -1, 0, 0, 1, 1, -1], [-3, -5, -2, -2, -3, -1, -3, 2], [-1, 1, 0, 0, 0, 0, 0, 0], [4, 1, 0, 0, 2, 0, 1, 1], [0, 0, 0, 0, 0, -1, 0, 0], [-3, 2, 0, 2, 2, 0, 0, 0], [0, -2, -3, -1, 0, -1, -1, 1], [0, 0, 0, 0, 1, 0, 0, 0], [-1, -2, -2, -2, -1, 0, -2, 1], [0, 0, 0, 1, -1, 1, -1, 0], [-1, -2, 1, -1, -1, 0, -1, 0], [-7, 7, -1, 0, 2, 0, -1, -1], [-1, 0, 0, 0, 0, 0, 0, 0], [3, 2, -1, 2, 3, 1, 3, -2], [0, -1, 0, -1, -1, 0, 0, 0], [-7, 7, -3, 0, 4, 0, -1, -1], [0, 0, 0, 0, 0, 0, -1, 0], [-1, 1, 1, 0, 0, -1, -1, 1], [0, 0, -1, -2, 1, -1, 1, 0], [-9, 3, 3, 3, 3, 0, 0, -3], [1, -1, 0, 0, -1, 0, 1, 1], [4, 0, 0, 2, -2, 0, -2, -2], [0, 0, 0, 0, 0, 1, 0, 0], [1, -1, 0, -1, -1, 0, 0, 0], [-2, 2, 0, 0, 1, 0, -1, -1], [-2, -2, -2, -6, -4, -2, -4, -2], [-2, -5, -3, -4, -1, -1, -3, 2], [1, 2, 2, 2, 1, 0, 2, -1], [0, 0, 0, 0, -1, 0, -1, 0], [-3, -1, 0, -2, -2, -2, -6, -2], [1, 0, 0, 0, 0, 0, 0, 0], [6, -2, 1, -2, -6, -2, 0, 2], [1, 0, 0, 0, 0, 0, 0, 0]]}