# Stored data for newform 630.2.u.a, downloaded from the LMFDB on 25 April 2024.
{"label": "630.2.u.a", "space_label": "630.2.u", "level": 630, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1374423089782, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1745298777327659642, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[11, [9, -3, 1]], [37, [1, 0, -1, 0, 1]]], "qexp_display": "q+\\zeta_{12}q^{2}+\\zeta_{12}^{2}q^{4}+(-2-\\zeta_{12}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 35, "char_orbit_label": "u", "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": 12, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [630, 6, [281, 127, 451], [6, 3, 4]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 3, 5, 7], "conrey_indexes": [109, 289], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "3.926", "prec": 17}, {"__RealLiteral__": 0, "data": "2.881", "prec": 17}, {"__RealLiteral__": 0, "data": "97.252", "prec": 20}, {"__RealLiteral__": 0, "data": "153.024", "prec": 24}, {"__RealLiteral__": 0, "data": "3709.551", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, -4, 0], "traces": [0, 4, 0, 0, 2, -4, 0, 0, 0, 0, -2, 6, 0, 0, 10, 0, -2, 0, 0, -10, -8, 0, 0, 0, 0, -6, -10, 0, 0, -16, 0, 4, 0, 0, 8, -10, 0, 0, 0, 0, 2, -12, 0, 0, -6, 0, 14, 0, 0, -4, 16, 0, 0, 0, 0, -24, 8, 0, 0, 8, 0, -12, 0, 0, -4, 10, 0, 0, 0, 0, -4, 24, 0, 0, -2, 0, -20, 0, 0, 28, -4, 0, 0, 0, 0, -8, 4, 0, 0, -4, 0, 40, 0, 0, -14, -20, 0, 0, 0, 0, 6, 0, 0, 0, -20, 0, 36, 0, 0, 4, 6, 0, 0, 0, 0, -14, -8, 0, 0, 4, 0, 4, 0, 0, -4, 8, 0, 0, 0, 0, -20, -2, 0, 0, 8, 0, 4, 0, 0, -64, -8, 0, 0, 0, 0, 16, 64, 0, 0, 36, 0, 12, 0, 0, 24, -16, 0, 0, 0, 0, 4, 70, 0, 0, -6, 0, 12, 0, 0, -48, -8, 0, 0, 0, 0, 8, -12, 0, 0, -26, 0, 104, 0, 0, -14, 2, 0, 0, 0, 0, 20, -40, 0, 0, 24, 0, 22, 0, 0, 36, 8, 0, 0, 0, 0, 12, -16, 0, 0, -60, 0, -36, 0, 0, -32, -4, 0, 0, 0, 0, -12, 20, 0, 0, -2, 0, -28, 0, 0, 32, -56, 0, 0, 0, 0, 14, -8, 0, 0, 80, 0, 18, 0, 0, -24, 52, 0, 0, 0, 0, -22, -20, 0, 0, -14, 0, -2, 0, 0, -10, 20, 0, 0, 0, 0, -36, -10, 0, 0, 20, 0, -48, 0, 0, 32, 18, 0, 0, 0, 0, -20, -36, 0, 0, 12, 0, -60, 0, 0, -26, 8, 0, 0, 0, 0, -32, 2, 0, 0, -70, 0, -16, 0, 0, -10, -24, 0, 0, 0, 0, 4, 12, 0, 0, -36, 0, 56, 0, 0, -24, 4, 0, 0, 0, 0, 40, -24, 0, 0, -70, 0, -10, 0, 0, 30, -8, 0, 0, 0, 0, -4, -12, 0, 0, 8, 0, -18, 0, 0, 48, -24, 0, 0, 0, 0, -24, -8, 0, 0, -32, 0, -12, 0, 0, -10, -64, 0, 0, 0, 0, 8, 18, 0, 0, 12, 0, 14, 0, 0, 116, 20, 0, 0, 0, 0, -24, 40, 0, 0, 12, 0, 56, 0, 0, -10, 56, 0, 0, 0, 0, 12, -30, 0, 0, 0, 0, -40, 0, 0, -28, 6, 0, 0, 0, 0, -12, -10, 0, 0, 140, 0, -80, 0, 0, 18, 16, 0, 0, 0, 0, 8, 4, 0, 0, 16, 0, -4, 0, 0, -56, 12, 0, 0, 0, 0, -8, -16, 0, 0, 20, 0, -18, 0, 0, 24, -100, 0, 0, 0, 0, 14, 128, 0, 0, 8, 0, 16, 0, 0, 4, 56, 0, 0, 0, 0, 60, 20, 0, 0, -72, 0, 10, 0, 0, 8, -24, 0, 0, 0, 0, -22, -96, 0, 0, -50, 0, -8, 0, 0, 8, 4, 0, 0, 0, 0, 0, -42, 0, 0, 68, 0, 32, 0, 0, -12, 16, 0, 0, 0, 0, 20, -54, 0, 0, -4, 0, 0, 0, 0, 52, -36, 0, 0, 0, 0, 32, 4, 0, 0, 66, 0, 32, 0, 0, -4, -16, 0, 0, 0, 0, 24, 40, 0, 0, -8, 0, -32, 0, 0, 40, 2, 0, 0, 0, 0, 28, -56, 0, 0, 30, 0, -64, 0, 0, -30, 112, 0, 0, 0, 0, 32, -48, 0, 0, 32, 0, 18, 0, 0, -40, 8, 0, 0, 0, 0, 32, 72, 0, 0, 24, 0, -88, 0, 0, -12, 8, 0, 0, 0, 0, 24, 70, 0, 0, 44, 0, -6, 0, 0, 38, -8, 0, 0, 0, 0, 14, -44, 0, 0, -8, 0, -72, 0, 0, -4, 14, 0, 0, 0, 0, 2, -10, 0, 0, 56, 0, -20, 0, 0, -24, 60, 0, 0, 0, 0, -4, 6, 0, 0, -144, 0, -32, 0, 0, 24, 10, 0, 0, 0, 0, -8, -72, 0, 0, -20, 0, -24, 0, 0, -96, -16, 0, 0, 0, 0, -32, -34, 0, 0, 90, 0, 88, 0, 0, 48, 64, 0, 0, 0, 0, 40, -104, 0, 0, -6, 0, 96, 0, 0, 24, -12, 0, 0, 0, 0, 60, 26, 0, 0, -52, 0, -80, 0, 0, 52, 24, 0, 0, 0, 0, -64, -8, 0, 0, 52, 0, -28, 0, 0, -58, -2, 0, 0, 0, 0, 72, 52, 0, 0, -160, 0, -56, 0, 0, 40, -48, 0, 0, 0, 0, 10, 2, 0, 0, -80, 0, -42, 0, 0, 116, -60, 0, 0, 0, 0, 12, 48, 0, 0, 30, 0, 36, 0, 0, 26, 36, 0, 0, 0, 0, -56, 112, 0, 0, 28, 0, -36, 0, 0, -56, -8, 0, 0, 0, 0, -28, -40, 0, 0, 10, 0, -132, 0, 0, 6, 24, 0, 0, 0, 0, 24, -36, 0, 0, 16, 0, 32, 0, 0, -52, 24, 0, 0, 0, 0, -30, -30, 0, 0, -136, 0, -52, 0, 0, -18, 48, 0, 0, 0, 0, -12, -14, 0, 0, -12, 0, 32, 0, 0, -24, -8, 0, 0, 0, 0, 18, 56, 0, 0, 168, 0, 20, 0, 0, -140, 88, 0, 0, 0, 0, 12, 60, 0, 0, -20, 0, -60, 0, 0, 56, 8, 0, 0, 0, 0, 104, -10, 0, 0, -16, 0, 36, 0, 0, -56, -104, 0, 0, 0, 0, 10, -8, 0, 0, 20, 0, 64, 0, 0, 40, -28, 0, 0, 0, 0, -16, -34, 0, 0, -42, 0, 130, 0, 0, 68, -12, 0, 0, 0, 0, -14, -56, 0, 0, -16, 0, 24, 0, 0, 160, -40, 0, 0, 0, 0, -80, 40, 0, 0, 16, 0, 54, 0, 0, -18, -40, 0, 0, 0, 0, 48, -66, 0, 0, -128, 0, -12, 0, 0, -24, 8, 0, 0, 0, 0, 10, -32, 0, 0, 28, 0, 16, 0, 0, 60, -144, 0, 0, 0, 0, -44], "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, 5, 2, 1, 2, 0], [1, 1, 7, 3, 1, 3, 0], [1, 1, 35, 10, 1, 6, 0]], "char_orbit_index": 21, "prim_orbit_index": 10, "minimal_twist": "70.2.i.b", "char_is_minimal": true, "conrey_index": 109, "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, 1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [-2, -1, 2, 0], [0, 0, 0, 0], [0, 2, 0, -3], [0, 0, 0, 1], [0, 0, 0, 0], [0, -2, -1, 2], [0, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, 5], [3, 0, -1, 0], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 2, 0, -2], [0, 0, 0, 0], [-5, 0, 5, 0], [-2, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 3], [0, 7, 0, 0], [0, 0, 0, 0], [0, 4, -3, -4], [-5, 0, 5, 0], [0, 0, 0, 0], [0, 3, 0, -1], [-4, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, -1, 0, 1], [0, 0, 0, 0], [2, 0, 0, 0], [-3, 2, 1, 4], [0, 0, 0, 0], [0, -1, 0, 0], [0, -5, 0, 5], [0, 0, 0, 0], [1, -2, -1, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -2], [-3, 0, 3, 0], [0, 0, 0, 0], [0, 0, 7, 0], [0, -7, 0, 0], [0, 0, 0, 0], [3, 0, -8, 0], [4, 0, 0, -3], [0, 0, 0, 0], [0, -5, 0, 5], [0, 9, 0, -9], [0, 0, 0, 0], [-6, 0, 0, -3], [1, 0, 2, 0], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [-6, 0, 6, 0], [0, 0, 0, 2], [0, 0, 0, 0], [-1, 0, 0, 0], [5, -10, -5, 0], [0, 0, 0, 0], [0, 2, 0, -2], [0, 2, 0, 0], [0, 0, 0, 0], [-4, -3, 6, 1], [6, 0, 0, 0], [0, 0, 0, 0], [0, 16, 0, -16], [0, 0, -1, 0], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 9, 0, -3], [0, 0, 0, 0], [14, 0, -14, 0], [0, 1, -2, -1], [0, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [-2, 0, 0, 4], [2, 0, -2, 0], [0, 0, 0, 0], [0, -3, 0, 3], [-2, 0, 2, 0], [0, 0, 0, 0], [5, 0, 10, 0], [0, 0, 0, 7], [0, 0, 0, 0], [0, 0, -7, 0], [0, 5, -10, -5], [0, 0, 0, 0], [0, 0, 0, -12], [0, 3, 0, -8], [0, 0, 0, 0], [3, 4, -3, 0]]}