# Stored data for newform 189.2.e.f, downloaded from the LMFDB on 21 May 2025. {"Nk2": 756, "analytic_conductor": 1.5091725982021993, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [189, 3, [29, 136], [3, 2]], "cm_discs": [], "conrey_index": 109, "dim": 6, "field_disc": -309123, "field_disc_factorization": [[-1, 1], [3, 3], [107, 2]], "field_poly": [3, -12, 19, -15, 10, -3, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [9, -9, 15, 0, 7, -2, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22518273048314045, "hecke_ring_generator_nbound": 4, "hecke_ring_index": 3, "hecke_ring_index_factorization": [[3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "189.2.e.f", "level": 189, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 7], "level_radical": 21, "minimal_twist": "189.2.e.e", "nf_label": "6.0.309123.1", "prim_orbit_index": 3, "qexp_display": "q+(1-\\beta _{4}+\\beta _{5})q^{2}+(-\\beta _{1}-\\beta _{2}-\\beta _{3}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "189.2.e", "trace_display": [2, 0, 1, 2], "trace_hash": 387737947683834455, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.652", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "117.962", "prec": 24}, {"__RealLiteral__": 0, "data": "15.880", "prec": 20}, {"__RealLiteral__": 0, "data": "4262.058", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.007", "prec": 17}, "traces": [0, 6, 2, 0, -4, 1, 0, 2, -18, 0, 1, 7, 0, 4, -17, 0, -10, 0, 0, -5, 26, 0, -8, 6, 0, 2, 17, 0, -30, -26, 0, 8, 25, 0, 24, -10, 0, 8, -7, 0, 24, -4, 0, -18, -1, 0, 3, 9, 0, 12, -8, 0, -9, 24, 0, 8, -48, 0, -14, -15, 0, 1, 42, 0, 66, 10, 0, -14, 39, 0, 26, 6, 0, -7, 0, 0, -36, -1, 0, -6, -16, 0, -43, -6, 0, -54, -32, 0, -9, -5, 0, -33, -24, 0, 27, 16, 0, -28, -49, 0, 21, -13, 0, 9, -6, 0, -6, 25, 0, 20, 8, 0, 60, -38, 0, 9, -1, 0, -6, 39, 0, 8, 20, 0, 17, -36, 0, 38, 3, 0, 7, 4, 0, -3, 2, 0, -66, 12, 0, 44, -2, 0, 33, -11, 0, -28, 84, 0, -58, 33, 0, 18, -24, 0, -37, 24, 0, 7, -17, 0, -22, 21, 0, 13, 40, 0, 45, -56, 0, 6, -39, 0, 43, -25, 0, 21, 26, 0, 10, -13, 0, 28, -2, 0, -33, 21, 0, 12, 30, 0, 46, -5, 0, -24, -30, 0, -31, -50, 0, -7, -48, 0, -118, 44, 0, -5, 46, 0, -60, -44, 0, -44, -3, 0, -41, 2, 0, 17, 48, 0, 13, -3, 0, -44, 89, 0, -2, -45, 0, 9, 12, 0, -6, 45, 0, 3, -24, 0, 63, 96, 0, 33, -47, 0, 96, 52, 0, 3, -21, 0, -24, -56, 0, 42, -39, 0, -12, -55, 0, 29, 80, 0, -32, 1, 0, 48, -38, 0, 6, 27, 0, -14, -150, 0, -12, -10, 0, -5, 9, 0, -63, -22, 0, 22, -78, 0, 76, 49, 0, -15, 14, 0, 71, 2, 0, 12, -66, 0, -15, -21, 0, 10, 76, 0, 39, -29, 0, -74, 10, 0, -9, -12, 0, 33, -22, 0, 40, 30, 0, -25, -32, 0, -27, 78, 0, -33, -61, 0, 78, 66, 0, -15, -15, 0, 7, -38, 0, -20, -24, 0, 24, -3, 0, -61, 126, 0, 8, 2, 0, -86, 5, 0, -22, 31, 0, -42, 128, 0, -34, -7, 0, 24, 35, 0, -86, -72, 0, -52, 3, 0, 42, -3, 0, -6, -3, 0, -6, -86, 0, -34, -1, 0, 16, 3, 0, -50, 10, 0, 68, 39, 0, 30, 81, 0, -53, -31, 0, 5, 12, 0, -18, 12, 0, 46, -65, 0, 50, 48, 0, -54, -38, 0, 100, -24, 0, 27, 70, 0, 13, -126, 0, 60, 32, 0, -21, -42, 0, 12, -100, 0, -34, 6, 0, 58, 27, 0, -10, 6, 0, 23, 60, 0, 54, -21, 0, -49, 11, 0, 77, -18, 0, 37, 62, 0, -150, -19, 0, -2, -17, 0, 12, 152, 0, 16, 41, 0, -96, -3, 0, 6, -48, 0, 60, 5, 0, 30, -117, 0, 63, -40, 0, -29, 64, 0, -96, 24, 0, -26, 75, 0, 31, 14, 0, 42, 14, 0, -160, 57, 0, 58, 63, 0, -86, 30, 0, -14, -33, 0, 98, 35, 0, 71, -76, 0, 2, -13, 0, 108, -66, 0, 63, 57, 0, 40, -130, 0, 202, 3, 0, 39, 27, 0, 4, -178, 0, -16, 3, 0, 60, -26, 0, -78, -43, 0, -75, 108, 0, 58, 24, 0, -37, 40, 0, -71, -100, 0, -109, 73, 0, -106, -116, 0, -49, -23, 0, 41, 20, 0, -252, 31, 0, 0, -10, 0, 7, 66, 0, 19, 83, 0, -134, -105, 0, -75, -93, 0, 53, -68, 0, -14, 9, 0, 29, -18, 0, 69, -96, 0, -45, 3, 0, -100, 56, 0, 55, -7, 0, -12, 28, 0, -98, -66, 0, -5, -40, 0, -24, -60, 0, -29, 66, 0, 60, -34, 0, 11, -32, 0, 3, 84, 0, 66, 63, 0, 75, 78, 0, -11, -34, 0, 63, -30, 0, 120, -21, 0, 54, -7, 0, 42, 70, 0, -36, 51, 0, 29, 169, 0, 48, 78, 0, 1, 109, 0, 36, -1, 0, 3, -55, 0, -20, 46, 0, 76, 20, 0, 27, 51, 0, -46, 72, 0, 30, -9, 0, -36, -116, 0, 139, -6, 0, -12, 46, 0, -88, -78, 0, -33, -13, 0, -61, -120, 0, -5, 46, 0, -38, -65, 0, 77, 75, 0, 123, -18, 0, 74, -89, 0, 38, 18, 0, 88, 42, 0, -111, 44, 0, -30, -54, 0, -78, -36, 0, -106, -48, 0, 66, 43, 0, -31, 24, 0, -105, 48, 0, 0, 4, 0, 54, -73, 0, -2, -96, 0, -50, 2, 0, -114, 15, 0, 9, -27, 0, -10, -154, 0, 99, 15, 0, 42, 1, 0, -44, 26, 0, 29, 240, 0, 150, -34, 0, -24, 36, 0, 236, -14, 0, -59, 89, 0, -28, -118, 0, -12, 33, 0, -46, 64, 0, -42, -19, 0, -63, 63, 0, 12, 72, 0, 84, -27, 0, -72, 91, 0, -45, -56, 0, -16, -218, 0, -184, -13, 0, -49, 45, 0, 30, 18, 0, -9, 18, 0, 82, 36, 0, -76, -16, 0, -42, 82, 0, 44, 145, 0, -51, 6, 0, -93, 24, 0, 63, -45, 0, -168, 115, 0, -84, 91, 0, -66, -182, 0, 156, -24, 0, 10, -43, 0, -43, -70, 0, -3, 24, 0, -72, -54, 0, 34, -36, 0, -11, 180, 0, -96, 117, 0, 78, -28, 0, -79, -118, 0, -63, 42, 0, 118, -90, 0, 72, -69, 0, 51, -170, 0, 282, -62, 0, 24, -126, 0, 77, 126, 0, -54, 53, 0, 172, -31, 0, -15, -27, 0, 71, 42, 0, 116, -16, 0, -106, 2, 0, -125, -228, 0, -18, -42, 0, 38, 64, 0, -27, 149, 0, 42, 66, 0, -70, -40, 0, 55, 52, 0, -255, -22, 0, 98, -138, 0, -154, 24, 0, 31, -69, 0, 130, 50, 0, -50, -57, 0, -54, 63, 0, 191, -232, 0, -108, -54, 0, -10, -10, 0, -52, 9, 0, 11, 6, 0, -118, 3, 0, 21, -120, 0, -60, 90, 0, 76, 8, 0, 240], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0], [0, -1, -1, -1, -2, 1], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, -1, 0, 1, -1, 1], [-4, -1, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, -1], [0, -1, 0, 0, 2, 1], [0, 0, 0, 0, 0, 0], [1, 2, 0, -1, 0, 0], [-2, -1, -1, -1, -2, 2], [0, 0, 0, 0, 0, 0], [-5, 0, 1, 0, 5, -4], [0, 1, 2, 2, 1, -1], [0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 1, 1], [5, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 2, 0, -1, 0, 0], [2, 0, -1, 0, -2, -1], [0, 0, 0, 0, 0, 0], [0, -1, 2, 2, 1, 1], [6, 0, -1, 0, -6, 0], [0, 0, 0, 0, 0, 0], [-6, -3, 1, -1, -1, 0], [-4, -1, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, -1, -1, 3, -2], [0, 4, 1, 1, 10, -4], [0, 0, 0, 0, 0, 0], [6, 3, 0, 3, 0, 0], [-3, 1, -1, 1, 4, -1], [0, 0, 0, 0, 0, 0], [3, 0, -2, 0, -3, -1], [0, 0, -2, -2, -3, 0], [0, 0, 0, 0, 0, 0], [9, 0, 0, 0, -9, 3], [-2, -5, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [-4, -3, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 3], [2, 0, -1, 0, -2, -4], [0, 0, 0, 0, 0, 0], [1, -3, -1, -2, 0, 3], [0, 3, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, -3, -3, -3, -5, 3], [0, -2, -1, -1, 7, 2], [0, 0, 0, 0, 0, 0], [1, 1, 0, -2, 0, 0], [-13, 2, 3, 1, 9, -6], [0, 0, 0, 0, 0, 0], [-5, 0, -1, 0, 5, -2], [0, 1, -1, -1, -5, -1], [0, 0, 0, 0, 0, 0], [-1, 0, 2, 0, 1, -2], [8, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [13, 3, 0, 3, 0, 0], [2, 0, 3, 0, -2, -1], [0, 0, 0, 0, 0, 0], [0, 1, 1, 1, -4, -1], [16, 0, -2, 0, -16, 7], [0, 0, 0, 0, 0, 0], [5, 3, -2, 0, 1, -1], [3, 3, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0], [0, 5, 2, 2, 0, -5], [0, -5, -1, -1, -2, 5], [0, 0, 0, 0, 0, 0], [-7, -3, 0, 0, 0, 0], [-1, -2, 3, 2, 2, 4], [0, 0, 0, 0, 0, 0], [-2, 0, 3, 0, 2, 3], [0, -5, -3, -3, -8, 5], [0, 0, 0, 0, 0, 0], [-16, 0, 4, 0, 16, -1], [0, 6, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0], [-9, -3, 0, 3, 0, 0], [-13, 0, 3, 0, 13, -4], [0, 0, 0, 0, 0, 0], [0, 3, -3, -3, -3, -3], [-3, 0, 4, 0, 3, 0], [0, 0, 0, 0, 0, 0], [-1, 3, -1, 1, -6, 0], [-5, -2, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0], [0, -3, 3, 3, 9, 3], [0, 2, -3, -3, 5, -2], [0, 0, 0, 0, 0, 0], [-6, -2, 0, -2, 0, 0], [-10, -1, 1, -4, 0, 0], [0, 0, 0, 0, 0, 0], [8, 0, 0, 0, -8, 3]]}