# Stored data for newform 770.2.i.j, downloaded from the LMFDB on 25 April 2024.
{"label": "770.2.i.j", "space_label": "770.2.i", "level": 770, "weight": 2, "hecke_orbit": 10, "hecke_orbit_code": 40532946435703554, "dim": 6, "is_polredabs": true, "nf_label": "6.0.19683.1", "trace_hash": 2005492044141488755, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, -3, 9, -2, 3, 0, 1]], [13, [136, -24, -6, 1]]], "qexp_display": "q+(1-\\zeta_{18}^{3})q^{2}+(-\\zeta_{18}+\\zeta_{18}^{2}+\\zeta_{18}^{4}+\\cdots)q^{3}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 3080, "analytic_conductor": 6.14848095563859, "hecke_ring_index": 1, "level_radical": 770, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 18, "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": "0.017", "prec": 17}, "analytic_rank_proved": true, "char_values": [770, 3, [617, 661, 211], [3, 2, 3]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 5, 7, 11], "conrey_indexes": [221, 331], "field_disc": -19683, "field_disc_factorization": [[-1, 1], [3, 9]], "field_poly": [1, 0, 0, -1, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "6.013", "prec": 17}, {"__RealLiteral__": 0, "data": "1.709", "prec": 17}, {"__RealLiteral__": 0, "data": "158.305", "prec": 24}, {"__RealLiteral__": 0, "data": "169.369", "prec": 24}, {"__RealLiteral__": 0, "data": "7367.187", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c3", "trace_display": [3, 0, -3, 0], "traces": [0, 6, 3, 0, -3, -3, 0, 0, -6, 3, 3, 3, 0, 12, 0, 0, -3, -12, -3, 6, 6, -15, 6, -6, 0, -3, 6, 6, 0, -12, 0, 0, 3, 0, -24, 0, -6, -18, -6, 18, 3, 48, -3, 12, 3, 3, 6, 12, 0, 0, -6, -3, -6, 0, 3, -6, 0, -42, -6, -12, 0, 6, 0, -3, 6, -6, 0, -15, -12, 12, 0, 0, -3, -3, 18, 0, -12, 0, 36, -12, -3, 9, 24, -48, 12, 24, 6, 15, -3, 12, 6, -36, 12, -3, -12, 6, 0, 36, 0, 6, -3, -27, 3, 24, -12, 3, 0, -18, -3, -21, -3, 6, 0, 60, -21, -6, 6, 24, -24, -12, 0, -3, -6, -6, 0, 6, 12, -6, 3, -18, 6, -18, 0, -69, -30, -3, 12, -6, 6, 30, 0, 84, 0, 6, 3, 6, -6, -33, 36, -12, 0, -24, -6, -12, 0, 0, 18, -18, 12, 0, -6, -42, 18, 12, -24, 0, -24, 24, 15, 90, 12, -9, -6, 36, 30, 0, -6, -12, -12, 0, 3, -24, 18, -6, 6, -18, 3, 12, -24, -9, 12, 21, 0, 24, 18, -36, 0, -12, 3, 12, 3, 0, -54, 60, 6, -24, -24, -24, -6, 12, -12, 84, 0, -9, 18, -6, -6, 15, -42, -24, 3, -6, 3, -36, 0, -6, 30, 24, 21, -42, -12, -12, 12, -12, -24, 12, -12, -24, -15, -12, 0, -42, 3, 21, -12, 0, -12, -24, 0, -12, 3, 48, 15, -12, -3, -3, -3, 18, -36, 33, 12, -21, 18, -12, 0, 0, -39, 12, -15, 6, 3, -6, 24, 24, -12, 3, -6, 36, 15, -42, 0, -36, 42, 36, 0, 21, 12, 30, 6, -3, -6, -12, -3, -12, 6, 24, 18, 3, 12, 60, 0, -72, -48, 0, 6, 6, -6, -36, 0, 12, 0, -12, -18, 12, -36, -12, 24, -18, 0, -6, -3, -36, 42, -42, 9, -6, -12, 12, -48, 66, 0, -30, 24, 30, 12, 30, 3, 48, 45, -30, -12, 0, -18, -111, -12, -6, -36, 18, 15, 18, 0, 120, -3, 24, 12, 0, -24, 60, 0, -18, -3, -69, -12, 0, 54, 6, -3, -6, -6, 12, -36, -9, 6, -54, -12, 0, -12, -24, 36, 48, 6, 0, -21, -18, 0, 0, 48, 24, -18, -18, -18, 108, 0, 54, -6, -12, -3, 33, 24, -72, 6, 24, 0, -36, -27, -18, 75, -36, 3, -6, 24, -42, -48, -48, -48, 24, 6, -36, 6, 36, -15, 84, 42, -42, 0, -12, -18, 39, 36, -18, 6, 24, -3, 72, 66, -30, -21, -48, 24, 6, 6, 33, -12, -12, -3, 12, -18, 24, 0, 30, -3, 24, -30, 36, 48, -18, 42, -24, 42, -3, -6, -36, -15, 156, 6, -3, 12, -42, -48, -18, 24, -21, 12, 6, -12, -12, -3, 18, -6, 42, 0, -54, -84, -6, 6, -18, -21, -42, -6, -108, 0, -24, -6, 9, 24, -3, 0, 18, -24, -30, -3, 24, 24, -138, 3, 54, -6, 0, 3, 0, -6, -60, -6, -57, -18, 24, -18, 24, -6, -72, 6, 3, 21, 24, 36, 12, -24, 21, 0, -111, 0, 24, 30, 24, 6, -18, 15, 0, 12, 0, 6, -24, 6, 36, 12, 42, 30, -60, -6, 18, -3, -132, -12, -24, 72, -3, -15, -60, -21, 24, 0, -6, -18, 18, -42, -30, 72, 57, 0, -42, -21, 18, 6, -24, 6, 12, 3, 42, 3, 30, -12, -48, -24, 0, 3, 24, -6, 156, 39, -156, 12, -66, -18, 6, 6, 15, 24, -72, -60, -60, 0, 144, -90, 6, -24, -3, 0, 48, 12, 15, 12, 168, 6, 6, -18, 12, 0, 72, 6, 66, 0, 12, -24, 84, -36, -3, -12, -21, -18, 120, -15, 48, 12, 45, 18, 3, 0, 90, -12, -9, 3, -12, -18, -132, 84, 36, -21, 84, -9, 12, -12, -69, -24, -42, -12, -18, -24, 18, 114, -60, 0, 6, 30, 84, 48, 39, 60, -108, -12, -12, 15, 12, -12, 96, 24, -3, -45, -12, -60, 6, -24, 60, 0, -102, -9, 12, -60, -72, -6, 18, 6, -78, -72, -15, 36, -15, -15, -108, 9, -12, 0, 12, 60, 87, 3, -42, 48, -18, 24, -24, 0, 18, -12, -264, 75, -12, 0, -84, 18, 0, -6, -6, -138, 36, 12, 6, 0, 120, 36, 60, 3, -6, 3, 12, -12, -6, -12, 15, -12, 57, -18, 60, -27, -48, 3, -12, 54, -12, -24, 18, 0, -48, 12, 12, -12, 48, 45, -90, 24, 6, -6, -42, 0, -6, -42, 6, 18, 48, 0, -60, 0, -36, 24, 30, -24, 0, -36, 39, -36, 42, 18, 0, 54, 78, 0, 36, 27, -6, 6, 60, -24, 42, -6, -42, -33, 0, 12, -66, -27, -36, 3, 21, -24, 3, 0, -42, -72, 24, 27, 0, -9, 132, 15, 108, -18, 12, -3, 156, -12, -42, 48, -21, 42, -42, -24, 0, -60, -168, -24, -18, -24, -66, 12, 6, -72, -12, -6, 9, 18, 42, -3, 150, 42, 54, -42, -45, -84, 0, 0, 6, 12, 42, -9, 12, -30, 18, 18, 72, 18, 36, 12, -150, 48, -30, 3, 36, 36, 54, 51, -24, -15, 6, 21, 12, -96, 0, 48, -30, -6, -30, 3, 108, -6, -180, -6, -12, 12, 24, -6, 0, 24, -9, 18, 96, 12, 0, 0, -192, 15, 120, 3, -9, 48, -12, -60, 12, -36, -54, 24, -18, -54, 24, 21, -24, 24, 3, 84, 45, -6, 78, 6, 24, -18, -72, -3, 36, 78, -36, -6, 0, -6, -96, 24, 87, 42, 12, -24, -36, -54, -144, 12, -48, 21, -108, 24, -36, 12, 12, 12, 66, -6, 126, 12, -72, 9, 21, 6, -15, 84, -78, 0, -21, 54, 54, -42, -48, -102, -72, 3, 111, 18, -42, -42, 126, -84, 18, 6, -18, -54, 24, 0, 18, -12, 48, 6, 6, 18, 84, 48, 132, 3, -51, 0, 48, -9, -24, -12, -24, 30, -9, -6], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "770.2.i.j", "char_is_minimal": true, "conrey_index": 221, "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], [1, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0], [0, -1, 1, 0, 1, -1], [0, 0, 0, -1, 0, 0], [-1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, -1], [0, -3, 0, 0, 1, 0], [-1, 0, 0, 0, 0, 0], [1, 1, 0, -1, -1, -1], [0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, -1, 0, 0, 0], [2, 2, 2, 0, 2, -4], [0, -2, 0, 0, 3, 0], [0, 0, 0, 0, -1, 1], [-1, 0, 0, 1, 0, 0], [0, 0, 1, -4, 1, 0], [0, 0, -1, -1, -1, 0], [2, -2, 5, -2, -3, -3], [1, 0, 0, 0, 0, 0], [-3, 0, 2, 1, 0, -3], [1, 0, 0, 0, 0, 0], [-2, 4, 2, 2, -6, -6], [0, 1, -1, 0, -1, 1], [0, 0, 0, -1, 0, 0], [2, 4, -2, -2, -2, -2], [1, 0, 0, 0, 3, -3], [0, 1, 0, 0, 2, 0], [-2, -5, -5, 0, 5, 0], [0, -1, 1, 0, 0, 0], [0, -3, -2, 0, -2, -3], [0, 0, 0, 1, 0, 0], [0, -1, 1, 0, 0, 0], [-4, 1, 1, 0, 0, -1], [0, 2, 0, 0, -3, 0], [-1, -1, -1, 0, 0, 1], [-6, -1, -2, 6, 3, 3], [0, -5, 2, -2, 2, -5], [0, 0, -2, 6, -2, 0], [1, 0, 0, -1, 0, 0], [8, -2, -2, 0, 0, 2], [-2, 0, -1, 3, 0, -2], [2, 6, 6, 0, -6, 0], [1, 0, 0, -1, 0, 0], [0, 0, 1, 1, 1, 0], [0, -2, -4, 2, -4, -2], [4, 8, -6, -4, -2, -2], [0, 0, 0, 0, -1, 1], [0, 0, 8, 0, 0, -5], [-1, 0, 0, 0, 0, 0], [-1, 5, -5, 1, 0, 0], [0, 2, -4, -2, -4, 2], [0, 1, 1, 0, 1, 1], [1, 3, -3, -1, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 3, 0, 0, -1, 0], [-7, 5, 5, 0, -1, -4], [-2, 0, -5, 2, 5, 5], [0, 0, 4, -4, 4, 0], [0, -1, 1, 0, 1, -1], [2, -3, -2, -2, 5, 5], [0, -5, -5, 0, 3, 2], [-2, -2, -2, 3, 3, 3], [1, 0, 0, 0, 0, 0], [-2, -4, 2, 2, 2, 2], [0, -1, 1, 0, 1, -1], [0, 2, 2, -5, 2, 2], [-4, 1, 0, 4, -1, -1], [2, 2, 2, 0, -8, 6], [0, -1, 0, 0, -2, 0], [0, -1, -1, 0, -1, 2], [-1, -1, 0, 1, 1, 1], [0, -4, 4, -1, 4, -4], [0, 2, 1, 6, 1, 2], [0, 1, -1, 0, 0, 0], [-2, -3, -3, 0, 5, -2], [0, -1, 0, 0, -2, 0], [6, -2, -2, 0, 0, 2], [-4, -2, 2, 4, 0, 0], [0, 0, 0, -1, 0, 0], [0, -1, -5, 3, -5, -1], [8, -2, 0, -8, 2, 2], [-8, 4, 4, 0, -4, 0], [1, 0, -3, 2, 0, 1], [4, -1, -1, 0, 0, 1], [2, 0, 6, -2, -6, -6], [0, -3, -2, 5, -2, -3], [0, 0, 0, -1, 0, 0], [4, -3, -5, -4, 8, 8], [1, 1, 1, 0, 0, -1], [-10, -6, -8, 8, 2, -2], [2, -6, -6, 0, 2, 4], [-1, -2, 5, 1, -3, -3], [0, 6, -8, -4, -8, 6], [0, 5, -2, 2, -2, 5], [0, -1, 1, 0, 0, 0], [6, 0, 0, 0, -2, 2], [0, 0, 3, 0, 0, -8], [1, 1, 1, 0, 0, -1], [-1, 0, 0, 1, 0, 0]]}