# Stored data for newform 630.2.u.b, downloaded from the LMFDB on 19 April 2024.
{"label": "630.2.u.b", "space_label": "630.2.u", "level": 630, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504974050460278, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1358948378204635098, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[11, [0, 1]], [37, [4096, 0, -64, 0, 1]]], "qexp_display": "q+\\zeta_{12}q^{2}+\\zeta_{12}^{2}q^{4}+(1+2\\zeta_{12}-\\zeta_{12}^{2}+\\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": "0.512", "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": "0.070", "prec": 17}, {"__RealLiteral__": 0, "data": "3.776", "prec": 17}, {"__RealLiteral__": 0, "data": "1.337", "prec": 17}, {"__RealLiteral__": 0, "data": "82.189", "prec": 20}, {"__RealLiteral__": 0, "data": "60.888", "prec": 20}, {"__RealLiteral__": 0, "data": "2860.814", "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, 2, 0], "traces": [0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, -2, 0, 0, -4, 4, 0, 0, 0, 0, 6, -4, 0, 0, -4, 0, -20, 0, 0, 8, -16, 0, 0, 0, 0, -4, 12, 0, 0, 0, 0, 2, 0, 0, -22, 16, 0, 0, 0, 0, 0, -10, 0, 0, -4, 0, 18, 0, 0, -4, -8, 0, 0, 0, 0, 2, -24, 0, 0, 16, 0, -8, 0, 0, -20, 2, 0, 0, 0, 0, 16, 10, 0, 0, 14, 0, -20, 0, 0, 16, 4, 0, 0, 0, 0, -6, -30, 0, 0, -8, 0, -24, 0, 0, 10, 0, 0, 0, 0, 0, 4, -2, 0, 0, 4, 0, 22, 0, 0, 20, 44, 0, 0, 0, 0, 4, 40, 0, 0, -28, 0, 4, 0, 0, 32, -20, 0, 0, 0, 0, -2, 40, 0, 0, 30, 0, -12, 0, 0, 0, -40, 0, 0, 0, 0, -8, -8, 0, 0, 6, 0, 18, 0, 0, 36, 4, 0, 0, 0, 0, 8, 0, 0, 0, 52, 0, 20, 0, 0, -2, 32, 0, 0, 0, 0, -16, -40, 0, 0, 0, 0, 4, 0, 0, 24, 8, 0, 0, 0, 0, 6, -22, 0, 0, 0, 0, -72, 0, 0, -14, 20, 0, 0, 0, 0, 0, 8, 0, 0, -2, 0, 20, 0, 0, 20, 4, 0, 0, 0, 0, 32, 4, 0, 0, -40, 0, -36, 0, 0, 36, -26, 0, 0, 0, 0, -4, 40, 0, 0, 16, 0, -2, 0, 0, -64, -16, 0, 0, 0, 0, -48, -4, 0, 0, -10, 0, -12, 0, 0, -64, 0, 0, 0, 0, 0, -8, -72, 0, 0, -12, 0, 0, 0, 0, -26, -4, 0, 0, 0, 0, -8, -16, 0, 0, -4, 0, 50, 0, 0, -4, -18, 0, 0, 0, 0, 40, 12, 0, 0, -48, 0, -40, 0, 0, 0, -2, 0, 0, 0, 0, 16, 24, 0, 0, -64, 0, -28, 0, 0, -18, -56, 0, 0, 0, 0, 8, 0, 0, 0, 20, 0, -24, 0, 0, 36, -30, 0, 0, 0, 0, -12, 28, 0, 0, 28, 0, 30, 0, 0, -4, 80, 0, 0, 0, 0, 32, -12, 0, 0, 0, 0, -16, 0, 0, 8, -4, 0, 0, 0, 0, 0, -80, 0, 0, 36, 0, 8, 0, 0, -16, 20, 0, 0, 0, 0, -12, 6, 0, 0, 30, 0, 8, 0, 0, -34, 12, 0, 0, 0, 0, 36, -4, 0, 0, -160, 0, 124, 0, 0, -12, 16, 0, 0, 0, 0, -10, 64, 0, 0, 100, 0, -10, 0, 0, 16, 0, 0, 0, 0, 0, -14, -16, 0, 0, 92, 0, 0, 0, 0, -48, -16, 0, 0, 0, 0, -4, 56, 0, 0, 2, 0, 28, 0, 0, -14, 32, 0, 0, 0, 0, -24, -16, 0, 0, -36, 0, -32, 0, 0, 44, 0, 0, 0, 0, 0, 8, 72, 0, 0, -8, 0, 40, 0, 0, 32, 22, 0, 0, 0, 0, -60, 0, 0, 0, -70, 0, 20, 0, 0, 24, -44, 0, 0, 0, 0, -4, -36, 0, 0, 80, 0, 84, 0, 0, -44, -12, 0, 0, 0, 0, -28, -14, 0, 0, 0, 0, -10, 0, 0, -4, 20, 0, 0, 0, 0, 0, 4, 0, 0, -104, 0, 16, 0, 0, 40, -4, 0, 0, 0, 0, 40, -32, 0, 0, 36, 0, 20, 0, 0, -24, 16, 0, 0, 0, 0, -4, 90, 0, 0, 20, 0, -48, 0, 0, 80, 8, 0, 0, 0, 0, 20, 60, 0, 0, -72, 0, -88, 0, 0, 12, -22, 0, 0, 0, 0, 72, -32, 0, 0, 38, 0, 0, 0, 0, -40, -20, 0, 0, 0, 0, 14, 16, 0, 0, 64, 0, -96, 0, 0, 44, 32, 0, 0, 0, 0, -4, -70, 0, 0, -10, 0, -8, 0, 0, 0, -24, 0, 0, 0, 0, -40, -6, 0, 0, 120, 0, 82, 0, 0, 36, -8, 0, 0, 0, 0, -14, 0, 0, 0, 4, 0, 18, 0, 0, 0, 8, 0, 0, 0, 0, -128, 74, 0, 0, -24, 0, 40, 0, 0, -84, 16, 0, 0, 0, 0, -32, 4, 0, 0, 0, 0, -24, 0, 0, -18, -24, 0, 0, 0, 0, 0, -52, 0, 0, -40, 0, 88, 0, 0, 10, -6, 0, 0, 0, 0, 20, -20, 0, 0, -92, 0, -4, 0, 0, -64, -32, 0, 0, 0, 0, -30, 16, 0, 0, 56, 0, -8, 0, 0, 4, -24, 0, 0, 0, 0, -8, -100, 0, 0, -80, 0, 18, 0, 0, -136, 0, 0, 0, 0, 0, 60, 0, 0, 0, -12, 0, 0, 0, 0, 26, -96, 0, 0, 0, 0, -80, 100, 0, 0, 64, 0, -24, 0, 0, 64, -8, 0, 0, 0, 0, 2, 80, 0, 0, -50, 0, 24, 0, 0, 0, 48, 0, 0, 0, 0, 12, -84, 0, 0, 22, 0, 20, 0, 0, 68, -18, 0, 0, 0, 0, -36, 0, 0, 0, 128, 0, -112, 0, 0, -36, 18, 0, 0, 0, 0, 12, 16, 0, 0, 18, 0, 14, 0, 0, 0, 40, 0, 0, 0, 0, -48, -28, 0, 0, 0, 0, -28, 0, 0, -8, -20, 0, 0, 0, 0, 0, 12, 0, 0, -8, 0, 6, 0, 0, 80, 56, 0, 0, 0, 0, 104, 8, 0, 0, 20, 0, -24, 0, 0, 40, 10, 0, 0, 0, 0, -8, -32, 0, 0, -64, 0, 40, 0, 0, 52, 2, 0, 0, 0, 0, 128, 50, 0, 0, -54, 0, 52, 0, 0, 2, 0, 0, 0, 0, 0, -32, 28, 0, 0, 8, 0, 0, 0, 0, 40, -16, 0, 0, 0, 0, 40, -20, 0, 0, -32, 0, -138, 0, 0, 36, -160, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 18, 0, 0, 0, -22, 0, 0, 0, 0, -32, -8, 0, 0, 10, 0, 52, 0, 0, 48, 48, 0, 0, 0, 0, -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, 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.a", "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], [1, 2, -1, 0], [0, 0, 0, 0], [0, -1, 0, 3], [0, 0, 0, 1], [0, 0, 0, 0], [0, 1, 2, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [-3, 0, 2, 0], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 2, 0, -2], [0, 0, 0, 0], [-2, 0, 2, 0], [1, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 4, 3, -4], [-2, 0, 2, 0], [0, 0, 0, 0], [0, -3, 0, 2], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, -10, 0], [0, -1, 0, 1], [0, 0, 0, 0], [2, 0, 0, 0], [-6, 2, 4, 1], [0, 0, 0, 0], [0, 8, 0, 0], [0, -2, 0, 2], [0, 0, 0, 0], [-2, 1, 2, 0], [3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 8, 0, 0], [0, 0, 0, 0], [-3, 0, -5, 0], [4, 0, 0, 3], [0, 0, 0, 0], [0, -2, 0, 2], [0, -6, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, -1, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [9, 0, -9, 0], [0, 0, 0, -10], [0, 0, 0, 0], [-1, 0, 0, 0], [-4, 2, 4, 0], [0, 0, 0, 0], [0, -7, 0, 7], [0, 2, 0, 0], [0, 0, 0, 0], [-1, -6, 3, 4], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 10, 0, -10], [0, 0, 8, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-10, 0, 10, 0], [0, -2, 1, 2], [0, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, -9], [0, 0, 0, 0], [4, 0, 0, -2], [5, 0, -5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [7, 0, -7, 0], [0, 0, 0, 0], [-4, 0, -2, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 8, 0], [0, -4, 2, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, -5], [0, 0, 0, 0], [-3, 4, 3, 0]]}