# Stored data for newform 770.2.n.a, downloaded from the LMFDB on 16 April 2024. {"label": "770.2.n.a", "space_label": "770.2.n", "level": 770, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 893386752770, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 2003258240196912731, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, 2, 4, 3, 1]]], "qexp_display": "q+(-1+\\zeta_{10}-\\zeta_{10}^{2}+\\zeta_{10}^{3})q^{2}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "n", "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": 10, "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": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [770, 5, [617, 661, 211], [5, 5, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5, 7, 11], "conrey_indexes": [71, 141, 421, 631], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.933", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "50.175", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1270.241", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [-1, -3, -1, -1], "traces": [0, 4, -1, -3, -1, -1, 2, -1, -1, 4, 4, 1, 2, -2, -1, -3, -1, -1, -1, 8, -1, 2, -9, 16, 2, -1, -7, -9, -1, 10, -3, 2, 4, 8, 14, -1, -1, 12, -2, 9, -1, -20, 2, 4, 1, -6, 6, 20, -3, -1, -1, -13, -7, 8, -4, -4, 4, -6, 10, -2, 2, -10, -8, -1, -1, 18, 8, 4, -1, -22, -1, -18, 4, -14, 12, 2, -12, 1, 14, -10, -1, 16, 20, -10, -3, -6, 4, -20, 11, 28, 4, -7, -14, 6, -5, 8, -3, 7, 4, 11, 4, -2, -13, -16, -2, 2, -12, 8, -9, 32, 1, -24, -1, -4, 14, 6, -5, -2, -2, -1, 2, 19, -20, 0, -8, -1, 4, 16, -1, -8, -2, 8, -12, -12, -6, 11, -6, 16, 8, -20, -1, -15, 2, -43, -6, -5, -14, -3, -18, -10, -3, -20, -2, -16, 11, 12, 9, 18, 5, 4, -1, -14, 16, -36, 0, 3, 50, -20, -3, -31, -1, -2, -6, 39, -5, 4, -4, 4, -22, 32, -1, 0, -2, 30, -14, -18, 16, -4, -30, -9, 8, -5, 2, 16, 2, -16, -1, -8, 1, -8, -1, 2, 8, -5, 7, -20, -16, -4, 18, -38, 2, 10, -12, 16, 18, 4, 11, -8, -18, 28, -9, 68, 6, 24, -1, 4, 16, -3, 14, 14, 16, -12, -10, -34, -2, 20, -12, 5, -6, -13, 2, 12, 19, -20, -10, -1, -20, -14, 2, -40, -1, -8, -6, -46, 36, 7, -1, 34, 2, -18, -7, -5, -32, 84, -7, 8, -2, -6, 4, 2, -9, -40, -6, 9, -64, 11, 28, 30, -20, 2, -1, 54, 35, 24, -18, -16, 7, 0, 4, -14, 10, -9, 21, 42, -3, -12, 12, -36, 70, 32, -3, -6, -25, -6, 8, 20, 9, -22, -4, 32, 2, -24, -16, 46, -7, -1, 5, 40, 24, -10, 4, -26, -14, 38, -14, -2, 34, -14, 20, -30, 8, -30, -10, -18, -20, -6, 2, -8, -31, -12, 14, -32, 8, -1, -6, -22, -46, 32, 15, 38, -1, -38, 1, 14, 14, 17, 8, 7, -13, -47, -1, 35, 0, -38, 18, 21, 30, -45, 6, -40, 12, -12, 6, 52, -9, 2, -5, 55, 11, -27, -2, -52, -5, 2, 2, -9, 16, -6, 2, 41, 9, 26, -1, 24, -28, 10, -14, -82, -18, 14, -1, 33, 2, -46, 8, -14, -10, -12, 12, 2, -20, 48, 29, -12, 6, -15, -2, 40, -8, -8, 2, 21, -25, -5, 8, -6, 16, -10, -52, 36, 4, -17, 11, -11, 2, -5, 2, 72, -7, 20, 1, -6, 3, 18, 6, -22, 4, -60, -1, -42, -6, 20, -24, 45, -3, -7, -6, 14, -16, 46, 6, 20, -7, -12, -5, -14, 36, -18, 13, 4, 20, -11, 28, -24, -10, -2, -6, 8, 2, -30, -3, 54, -18, 28, -1, -18, 25, 2, 20, 2, -1, -12, -20, -20, -64, -14, 12, -18, -40, 40, -1, 40, 2, -55, 4, -12, -46, 62, 16, 42, -13, 21, -1, -48, 34, 29, 12, -95, 12, 7, -7, 74, 5, -59, 28, -3, -36, 52, 3, 52, 8, -12, 8, 80, 14, 8, 4, -19, 52, -4, -4, -10, -40, 0, -1, -18, -16, 36, 16, 0, -4, 60, 8, 5, -30, 6, 20, 76, 2, 18, 4, 13, -16, -9, 35, -4, -11, -14, 17, -34, -6, -162, 52, 10, 20, -14, -1, 41, 21, -32, 10, -10, -4, -28, -14, 13, 42, -43, 2, -16, -2, 36, -18, 10, 49, 14, -10, 26, -78, 81, 2, 8, -6, 14, 90, -41, -16, -59, 8, 15, -10, -35, -1, 34, -57, 40, 1, -60, -13, 16, -8, -26, 26, 8, -16, -1, -24, 46, -22, -48, -1, -44, -10, 15, -40, -34, 4, 18, -35, -38, -1, -25, 34, 26, 6, -8, 38, -27, -4, 2, 18, 6, 34, 6, 16, -32, -20, 21, -5, 106, 8, -40, 10, -71, -15, -2, 42, 80, -20, -28, 4, -40, 2, 48, -8, 11, 14, -91, 8, 2, -1, 6, 8, -76, -2, 16, -1, 2, 4, -64, -22, 12, 14, -14, 32, 20, 15, -80, -2, -2, -1, -34, -38, 24, -9, -40, -66, 8, -16, -54, -18, -10, 8, 28, 12, -8, -38, 11, -47, 60, 4, 29, -25, 6, 0, -10, -18, 126, -2, -53, -14, 14, -10, 21, -45, 2, 16, 26, 40, 20, 12, 78, 8, -46, -14, -25, -48, -70, -34, -52, 2, 36, 20, 6, -25, -20, 11, -38, 78, 92, -12, -62, -52, 2, 10, 9, -13, -24, 2, -60, 1, -68, 16, -63, 4, 2, 7, 6, 41, -40, 14, -72, 76, 15, -1, 18, 4, 34, 32, -48, -10, -24, 16, -120, -2, -16, 22, 58, -6, 95, -1, 58, -142, 14, -8, 6, -46, -54, -2, -70, 16, -4, -5, 80, 18, 4, 7, 28, -8, 13, 20, -46, 48, -32, -26, -7, 28, 4, 6, -52, -10, 0, -7, -6, 0, 80, 22, -52, 22, 28, -3, 49, -14, -38, -25, 14, 20, -1, 8, -13, -6, 48, 1, 46, 20, -2, 18, 80, -59, 168, 4, -20, 28, 0, -9, 39, -11, -7, 12, -15, -20, -22, 2, 7, -28, -1, -7, -68, -40, -84, 11, -20, 4, 46, -37, 14, 8, -40, 6, 16, 28, -16, -56, 40, -60, 32, -1, 46, 43, 50, 4, 48, 80, 12, 16, 0, -65, -42, -18, -2, -7, 73, -16, -40, -56, -10, -16, 28, -29, 9, -14, 79, 40, -26, 3, 12, -22, 29, 10, 88, 6, 8, 36, -2, 82, 41, -22, -82, 4, -22, -5, 8, 29, -120, -12, -4, -14, 68, 5, -63, 8, 0, -1, 14, 8, 10, 22, 45, -60, 16, -3, -13, -66, -62, 12, -24, 8, -44, 4, -76, 7, -70, -15, 20, -48, -16, 20, 128, -68, 82, 4, 52, -12, 48, 0, -28, 45, 35, -14, 56, 11, -86, 2, 20, 17, -18, 25, -30, 40, -42, 4], "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, 11, 3, 1, 5, 0]], "char_orbit_index": 14, "prim_orbit_index": 3, "minimal_twist": "770.2.n.a", "char_is_minimal": true, "conrey_index": 71, "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], [-1, 1, -1, 1], [0, -1, 1, -1], [0, 0, 0, -1], [0, -1, 0, 0], [1, -1, 1, 0], [0, 0, 0, -1], [0, 0, 1, 0], [2, -1, 1, -2], [1, 0, 0, 0], [1, 1, 1, -3], [0, 0, -1, 1], [-4, 5, -5, 4], [0, 0, 1, 0], [-1, 1, 0, 0], [0, -1, 0, 0], [1, -4, 1, 0], [-1, 1, 0, 2], [0, 2, -4, 2], [-1, 1, -1, 1], [0, 0, -1, 1], [-2, 0, 2, 1], [2, 0, -4, 4], [0, 1, -1, 0], [0, 0, 1, 0], [-1, 1, 0, -4], [-4, 3, -4, 0], [0, -1, 0, 0], [3, -3, 0, 1], [0, -1, 1, -1], [-2, 4, -4, 2], [1, 0, 0, 0], [1, -1, -3, 2], [3, 0, -1, 1], [-1, 1, -1, 1], [0, -1, -1, -1], [6, -6, 0, -6], [-2, 4, -2, 0], [5, -6, 5, 0], [0, 0, 0, -1], [0, -8, 4, -8], [0, 1, -1, 0], [0, 0, -2, 2], [2, -4, 1, -2], [-2, 0, -1, 1], [-2, 6, -6, 2], [0, 5, -10, 5], [-1, 1, 0, 0], [0, -1, 0, 0], [0, -1, 0, 0], [-4, 4, 0, -1], [0, -1, 5, -1], [0, 4, -4, 0], [1, 0, 4, -4], [-3, 2, -4, 2], [1, 0, 0, 0], [2, -6, 6, -2], [0, 3, -4, 3], [2, -2, 0, -8], [1, -1, 1, 0], [-6, 8, -6, 0], [-2, 2, 0, -2], [0, -1, -1, -1], [-1, 1, -1, 1], [4, 0, -1, 1], [0, 4, -3, 1], [2, 0, 2, -2], [-3, 4, -4, 3], [0, -6, 10, -6], [0, 0, 0, -1], [-7, 3, -7, 0], [1, 1, 1, 0], [-7, 7, 0, 7], [0, 6, 0, 6], [0, 1, -1, 0], [-2, 0, 2, -2], [2, -4, 1, -2], [1, 0, -5, 5], [-4, 1, -1, 4], [0, 0, 1, 0], [6, -6, 0, -2], [8, -4, 8, 0], [1, -13, 1, 0], [-1, 1, 0, 0], [0, -1, 4, -1], [0, 2, -2, 0], [-3, 0, 4, -4], [2, 1, 0, 2], [10, 0, 6, -6], [2, -1, 1, -2], [0, -1, 5, -1], [-4, 4, 0, -2], [4, -6, 4, 0], [-5, 10, -5, 0], [2, -2, 0, 2], [0, -1, 1, -1], [5, -4, 4, -5], [1, 0, 0, 0], [5, -3, 0, -6], [1, 0, 0, 0]]}