# Stored data for newform 385.2.i.a, downloaded from the LMFDB on 19 April 2024. {"label": "385.2.i.a", "space_label": "385.2.i", "level": 385, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 549789368705, "dim": 8, "is_polredabs": true, "nf_label": "8.0.310217769.2", "trace_hash": 1893774478055990250, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 5, 26, 1, 15, -7, 10, -3, 1]]], "qexp_display": "q+(1+\\beta _{1}+\\beta _{2}-\\beta _{5}-\\beta _{7})q^{2}+(-\\beta _{2}+\\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": 1540, "analytic_conductor": 3.074240477819295, "hecke_ring_index": 1, "level_radical": 385, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [385, 3, [232, 276, 211], [3, 2, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [5, 7, 11], "conrey_indexes": [221, 331], "field_disc": 310217769, "field_disc_factorization": [[3, 4], [19, 2], [103, 2]], "field_poly": [1, 1, 5, -4, 15, -2, 4, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.070", "prec": 17}, {"__RealLiteral__": 0, "data": "7.650", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "222.646", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11836.823", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c3", "trace_display": [3, 3, -4, 1], "traces": [0, 8, 3, 3, -3, -4, 14, 1, -18, 1, 3, -4, 3, -12, 1, -6, -5, 3, -1, 3, 6, -18, -6, 6, 4, -4, 5, 6, -20, -16, -7, -10, -4, 3, 20, 1, -16, 9, 23, 13, 9, 30, -16, -4, -3, 1, -16, 15, -2, -19, -6, -1, 3, 30, 13, 8, -24, -12, 1, -17, 3, 0, 32, -11, 10, 6, -7, 25, 19, 12, 1, -26, -26, -3, 16, 3, 80, -2, -10, 4, -5, 16, 27, 36, -24, -6, 10, -20, 9, -25, 2, -3, -52, -10, -23, 3, 7, -46, -60, -2, -3, -18, 17, 4, 70, 0, 44, 5, -7, 5, 3, 4, -4, -92, -14, 6, -22, -15, -50, 9, -8, -4, -22, 30, 22, 8, -61, 30, 9, -5, 5, -5, -6, 19, -28, -3, -13, 24, 33, -26, 4, 12, -25, 6, 38, 8, 60, 33, 68, -3, -7, -11, 8, -4, -2, 20, -7, 37, 15, -3, 8, -31, -20, 24, -24, 3, -26, -12, -20, -16, -10, -3, -25, 25, -8, -2, 10, 55, 39, 29, 8, 36, -19, 50, -11, 9, -25, 3, -80, 36, -46, 24, -21, -2, -6, -26, -87, -12, -1, -59, 9, 28, -14, -15, 46, -15, 73, 11, 13, -6, 8, -64, 41, -9, -30, 2, -14, -3, 78, -20, -3, -7, 25, -102, 58, -2, -47, -2, 34, 16, 32, 18, -28, 39, 19, 15, 5, 4, 5, -24, 1, 46, 3, -11, -38, 14, 14, -21, 3, 12, 3, -66, -46, -12, 56, -1, 7, -34, -90, -3, -6, 9, -31, 48, 4, -60, 49, 6, 0, -1, 13, 3, 14, 4, 2, -4, -37, -48, 8, 22, -30, -194, 39, -12, 41, 6, -10, 58, 66, 45, 1, -9, 40, -68, -25, 34, 25, -3, 20, -6, -6, 94, -70, -47, -6, 0, 3, 80, 16, -86, -16, -23, -14, -13, 76, 31, 64, 24, 41, 8, -5, 92, 24, -68, -40, 6, -16, -21, -94, -44, 14, 74, 64, 25, -54, -50, -74, -20, -64, -42, 19, -10, 40, -14, -134, -6, 13, -44, 25, 72, -2, 58, -4, 14, -21, 13, 162, 11, 228, 16, -26, -13, -35, -6, 42, 6, 20, 0, -27, 20, -32, 84, -18, 7, -10, 3, -55, -32, -56, 8, -40, 13, -24, 26, 74, 1, -28, 56, 3, 4, 5, 74, 75, -32, -68, 4, 8, -49, -234, 66, 10, 24, -28, 50, -61, -32, -3, -18, -11, 3, 27, -61, 206, 85, 24, -18, -2, -40, 23, 34, 9, -36, -10, -8, -117, 3, 16, 33, -28, 13, 10, -10, -56, -122, 28, 40, 57, 51, -9, -34, -18, 4, 8, 4, 2, -25, 17, -132, -30, 48, -1, -15, 52, 14, -12, -39, 30, 2, 24, -16, 26, -10, 8, 74, 5, -10, -59, -44, 56, 159, 46, -25, -13, 2, -45, -6, 13, 76, 11, 3, 7, -23, 114, -69, 6, 23, 0, -47, 26, 22, 60, -50, -11, 25, -41, 1, -126, -80, 70, 2, -3, -43, -87, 56, 46, 36, -16, -84, -99, -36, -34, 0, 66, -1, 17, 4, -28, -30, 157, 98, -35, 22, -27, -37, -156, 18, 98, 9, 1, 28, -22, 34, 88, 30, -103, 5, -156, -78, 0, 5, 14, -40, 10, 47, -7, -10, -22, 14, -59, 23, 3, -51, 56, 66, -76, -2, -56, 7, 48, -8, -55, 2, -65, 17, -41, 46, 204, -71, 184, 30, -14, -114, 3, -126, -82, -12, 9, 58, -28, -14, 44, -42, -16, 30, -17, -15, -60, -46, -96, -106, 25, -10, -80, 91, -26, 15, -52, 107, -18, 35, 4, -90, -118, 184, -56, -4, -4, -2, -98, 55, 44, -33, -25, 9, 38, -60, 54, -2, -8, -9, 22, -26, 44, 151, 98, -4, 108, 6, 51, -4, 41, -36, -27, 9, -48, -15, 60, 81, -2, -50, 9, 101, -13, -152, -45, 10, -43, 49, 35, -17, -10, 98, -42, 15, 78, -5, -105, 26, -39, 60, 3, 99, -21, -19, 78, -5, 150, 29, 65, -79, 14, 0, 76, 50, 69, -3, 44, 18, -190, -59, 26, 45, -16, -27, 57, -48, -38, 40, -160, -84, 33, 51, 150, -20, 158, 13, -2, -11, -11, 106, 16, -4, -53, -61, -5, -6, 148, -205, 52, -25, -25, -36, 81, -48, -34, -12, 150, -34, 35, 62, -76, -48, 30, -74, 117, 8, -7, -106, -2, 40, -30, -28, -17, 16, -18, -12, -16, 25, -52, 38, -34, 60, 95, 42, 72, -3, -121, -37, -38, 121, 14, 38, 21, -64, -11, 22, -106, -40, -66, -6, 8, -53, 140, -48, -222, 2, -53, -59, 78, -50, 1, -94, -42, 24, -124, -10, 156, -23, -110, 2, -7, 13, 38, -94, 16, -74, -79, 49, 126, -7, -30, 5, 52, 50, 73, -3, -127, 58, -50, 82, -4, -11, -69, -3, -78, -1, -196, -40, 176, 57, 10, -38, -29, -90, 16, 24, 36, 2, 4, 27, 48, 138, 77, 34, 36, -6, 64, 160, -20, 11, -26, 53, -114, 78, -112, 6, -40, 66, 39, -192, 37, -68, -151, -74, 29, 8, -48, 1, -180, -61, -10, -14, 5, -2, 23, 6, -1, 62, 5, 23, 50, 0, 94, -24, 31, 25, -23, 38, -78, -8, 4, -131, 22, -35, 132, 1, 8, 46, 36, -86, -5, -50, -7, 184, -11, 55, -38, 46, 146, -39, -78, 16, -113, 42, -1, -58, 72, 80, 11, 7, 8, -30, -54, 175, 198, -18, -75, 1, 33, -172, -19, 78, -69, -18, 39, -25, 136, 0, 58, -22, -11, -67, -8, 42, 15, -18, -2, 14, 44, 17, 50, 174, -130, -90, -2, 3, 40, -68, 198, -36, 40, 54, 41, -19, 84, -51, -20, 11, 66, 49, 23, 116, -124, -262, 68, 24, -56, -20, -160, -186, 42, -4, -98, -7, 40, 4, 15, 252, 9, -63, -6, -7, -56, 81, 168, 13, -19, -14, 122, 50, -12, -100, 10, 49, -55, 6, -12, -33, -104, -71, -1, 5, -84, 46, 104, 118, -21, -39, -39, -44, -18], "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": "385.2.i.a", "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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, -1, 0, -1], [0, 0, -1, 0, 0, 1, 0, 0], [0, 2, 1, 0, 0, -1, 0, 0], [-1, 0, 0, 0, 0, 1, 0, 0], [2, 0, 0, 0, 0, 0, 1, 0], [0, 0, -1, 1, 0, 0, -1, 0], [-2, 2, 0, -2, 0, 0, 1, 0], [0, 0, 0, 1, -1, 0, -1, 0], [0, -1, -1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [1, 0, 0, 1, 1, -1, 1, 0], [-1, 2, 0, -2, 0, 0, 0, -2], [0, 2, 1, 1, -2, 0, 0, 1], [-1, -1, 0, 1, 0, 0, 0, 1], [-1, -2, -2, -1, 3, 1, 3, 2], [0, -1, 0, 0, -1, 1, 0, 0], [0, 3, 1, 0, -2, 0, 0, 0], [0, -2, -2, -1, -1, 0, -1, 2], [1, -1, 0, 1, 0, 0, 0, -1], [-3, 0, 1, 1, 1, 1, -1, -1], [-1, 0, 0, 0, 0, 0, 0, 1], [2, 0, 0, 1, 2, -2, 2, 0], [0, 2, 2, 0, -2, 1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [1, -3, -3, 0, 2, -1, 2, 3], [1, 2, 0, -2, 0, 0, -2, -3], [-3, 2, -1, -1, 1, 1, 3, 3], [-2, -3, 0, 3, 0, 0, 1, 1], [-2, 0, 0, 0, -1, 2, -1, 0], [0, -3, -4, 0, 2, -2, 0, 0], [0, -4, -2, 0, 2, -1, 0, 0], [1, 1, 1, -1, 0, -1, 0, -1], [3, 0, 0, 0, 0, 0, 0, -2], [0, -2, 0, 1, 1, 0, 1, 1], [-2, 3, 0, -3, 0, 0, 2, 2], [2, -3, -3, -1, 2, -2, 2, 3], [0, -3, -1, 0, 0, 6, 0, 0], [0, 2, 3, 0, -2, 3, 0, 0], [2, 0, 0, 2, -1, -2, -1, 0], [4, 2, 0, -2, 0, 0, -3, -4], [-3, -2, -2, 3, -2, 1, -3, 1], [-1, -1, 0, 1, 0, 0, -5, -3], [-1, -1, -1, -1, 0, 1, 0, 1], [0, -1, 0, 0, 1, 0, 0, 0], [0, 2, 3, 0, 1, -5, 0, 0], [4, 0, 0, 2, 1, -4, 1, 0], [1, 2, 0, -2, 0, 0, 4, -1], [-1, 5, 3, -1, 2, -2, 1, -3], [-1, 0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, 0, -2, 1, -2, 1], [0, -4, -3, 0, 2, 1, 0, 0], [0, -2, 1, 0, 1, 7, 0, 0], [3, -1, -1, 3, 0, -3, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0], [-7, -2, 0, -3, 0, 7, 1, 3], [-2, 3, 0, -3, 0, 0, -4, -2], [0, 1, 1, 1, -2, 0, -2, -1], [0, -1, 5, 0, -2, -5, 0, 0], [0, -1, 0, 0, -1, 1, 0, 0], [1, 3, 3, -2, 1, -1, 1, -3], [3, -5, 0, 5, 0, 0, -1, 3], [1, 3, 2, -1, 1, -5, 0, -1], [1, -4, 0, 4, 0, 0, 2, 3], [1, -2, -2, 2, 0, -1, 0, 2], [0, 0, 0, 0, 1, -2, 0, 0], [0, -1, 3, 0, 6, 4, 0, 0], [5, 3, 3, 0, -2, -5, -2, -3], [3, 1, 0, -1, 0, 0, 4, -2], [0, -1, 1, 1, 0, 0, -2, -2], [-3, 1, 0, -1, 0, 0, 4, 3], [-7, -3, -3, -3, 1, 7, 1, 3], [0, -4, -5, 0, 2, 0, 0, 0], [0, -5, 1, 0, 3, 3, 0, 0], [1, 1, 1, -1, 0, -1, 0, -1], [10, -1, 0, 1, 0, 0, -4, -4], [0, 2, 1, -2, -1, 0, 0, -1], [0, 4, 0, -4, 0, 0, 1, -4], [0, 1, 1, -2, -5, 0, -5, -1], [0, 3, 2, 0, -3, -1, 0, 0], [0, 5, 2, 0, -2, 4, 0, 0], [7, 2, 2, 5, -1, -7, -1, -2], [4, 3, 0, -3, 0, 0, 2, 4], [-3, 1, 0, 2, -2, 1, 1, 0], [-1, 1, 0, -1, 0, 0, -1, 0], [1, 0, 0, 9, -6, -1, -6, 0], [0, -3, 1, 0, -1, -5, 0, 0], [0, -2, 0, 0, 1, 2, 0, 0], [-7, 3, 3, -6, -6, 7, -6, -3], [0, -2, 0, 2, 0, 0, -2, -1], [-4, 2, 5, -1, -2, 6, -1, 0], [-7, -1, 0, 1, 0, 0, 2, 4], [-1, 6, 6, -5, 0, 1, 0, -6], [0, 7, 6, 0, -1, -7, 0, 0], [0, 3, 2, 0, 1, 0, 0, 0], [3, 3, 3, -5, 2, -3, 2, -3], [-5, 0, 0, 0, 0, 0, 3, 0], [-6, 0, -2, -1, 2, -5, 1, 5], [0, 1, 0, -1, 0, 0, 1, 0], [-1, -1, -1, -1, 0, 1, 0, 1]]}