# Stored data for newform 95.2.e.b, downloaded from the LMFDB on 24 April 2024. {"label": "95.2.e.b", "space_label": "95.2.e", "level": 95, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538831967, "dim": 6, "is_polredabs": true, "nf_label": "6.0.3518667.1", "trace_hash": 245483191335473910, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [49, 42, 43, 8, 7, 1, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(\\beta _{1}+\\beta _{3}-\\beta _{5})q^{3}+(-3+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "e", "char_is_real": false, "Nk2": 380, "analytic_conductor": 0.7585788192021636, "hecke_ring_index": 1, "level_radical": 95, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [95, 3, [77, 21], [3, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [5, 19], "conrey_indexes": [11, 26], "field_disc": -3518667, "field_disc_factorization": [[-1, 1], [3, 3], [19, 4]], "field_poly": [49, -42, 43, -8, 7, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.629", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "111.289", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3596.607", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, -1, 3, 4], "traces": [0, 6, -1, -1, -7, 3, 6, 4, -12, -4, 1, -10, -8, 15, -7, 1, -3, -1, 28, 0, -14, 12, 8, -4, 21, -3, -10, -16, -11, 2, 12, -2, 6, -11, 25, 2, -3, -4, -19, -10, -6, 2, 23, 1, 18, -8, -48, -6, -1, -14, 2, 6, 35, -11, -10, -5, 30, -19, -14, -6, -4, 9, 13, -9, -16, 30, -29, 20, 68, -10, 7, 29, -11, 22, 7, 2, -19, -32, -30, 24, 3, 21, -31, -6, -56, 1, 32, 24, -18, 14, 14, 10, -41, -6, 42, 0, 34, -7, -23, 13, -7, 3, -80, 20, -30, -12, -18, 20, 25, 1, -8, -50, -2, 10, 0, -8, 11, 20, -21, -7, -21, -24, 70, 26, -4, -6, 44, -12, -3, -6, -5, -8, 64, -38, 12, -8, 21, 13, 46, 1, -22, 4, 16, -25, -30, 4, -18, 34, 49, 6, 6, -74, -57, -48, 37, -1, -20, -14, 46, 96, 12, -9, 26, 34, -22, 11, -37, -28, 14, -36, 50, 38, 46, 0, -23, -2, 5, -2, -60, -84, 3, -7, -70, -6, 27, -2, -2, 8, 5, 2, -38, -36, -48, 31, -34, -5, 10, 44, -72, -9, 6, 12, 74, 14, -43, -2, 22, 20, -30, 38, 46, 28, 6, -22, -16, -1, 70, -14, -44, 1, 36, -10, -99, -3, 23, -4, 30, 24, 76, 18, -24, -39, 15, -20, 70, -12, -10, 8, -15, 66, -2, 36, -34, -17, 59, -7, -30, 0, -34, 20, 1, 9, -40, 13, 160, 12, 59, -25, -34, -104, -35, 9, 29, -20, -35, -22, 38, -60, 72, -29, 10, 10, -58, 120, -72, 5, -39, 24, -26, 14, 15, -14, -7, -16, -186, 19, 80, -24, 8, -38, -7, -15, -166, 40, 24, 6, -106, 14, 2, 20, 4, 7, 63, -116, 57, 18, -11, -31, 50, 41, -13, -8, 210, 72, -11, -18, -36, 13, -54, -16, -8, -35, 44, 95, -60, 15, -31, 70, -61, -4, -58, 14, 26, 9, 6, 40, -7, 46, -12, 49, 34, 16, -38, 26, 36, -5, -19, -1, -28, -16, 14, -40, -29, -122, 14, -29, -18, -15, 14, 37, -22, 0, 182, 61, 55, -22, -56, -35, 122, 58, -7, 37, 66, -10, -10, 1, -7, -10, 6, -78, 19, -68, -70, -29, -77, -16, -15, -66, -56, 31, 30, 180, 142, -66, -77, -24, 43, -10, 44, 0, 6, -41, -78, -5, -12, -21, -60, 108, 7, -18, -62, -72, -93, -4, -25, -3, -30, -26, -19, -142, -28, 41, -16, -27, 79, 2, 230, 6, 21, -110, 64, 36, 27, -23, 15, 12, 46, -76, 164, -19, -9, -16, -125, -2, 132, 28, 94, 21, -112, 76, -14, 22, -94, -13, -4, 20, 0, 2, 16, 28, 41, -14, -89, 64, -4, 6, -127, -22, -30, 26, 21, -11, -7, -8, 20, 0, -18, -2, 27, 110, 17, -10, -100, 6, 9, 7, -14, -154, -56, -50, 23, 84, 86, -14, 95, 26, -18, 51, -6, -15, 7, 44, 108, -49, -39, 6, 4, -12, 10, -1, -40, 21, 50, -19, 80, 10, -71, 10, 106, 38, -60, -40, 22, 3, -26, -24, -70, -25, 8, -25, -9, 54, 76, 20, 48, 10, -40, 33, 79, -40, 50, 7, 16, -46, -80, -1, -115, 83, -33, -26, -16, -19, -56, 16, -80, 50, -23, -41, -22, 10, 2, 9, 98, 34, 46, 5, 39, 14, -20, -36, -57, 22, -90, 44, -46, -4, 17, -42, -190, 4, -11, 34, 86, -26, -63, -20, 6, -40, -146, 19, -42, 18, 40, -18, 4, 7, 10, 44, -120, -11, -42, 20, 15, 14, 61, -12, 70, 24, 0, 54, 35, 30, 37, -14, -42, 52, -88, 66, 134, 62, -8, 36, 71, -16, 5, -3, -200, 19, 40, 83, 22, -26, -10, 60, 4, -24, -55, -35, 74, -90, 3, -15, -56, 48, -2, -12, 133, -42, -23, 10, 5, -23, 30, 98, -186, 8, 40, -8, 28, 22, 32, -24, 42, -30, 126, -19, -120, 9, -59, -77, 6, -15, 86, -2, -48, 8, 168, 46, 143, 8, -21, -4, -28, -158, 0, 26, 2, -79, -56, 55, -46, -44, 38, 53, -70, 2, 28, 45, 47, 63, -11, -67, -100, 152, 128, 2, -5, -55, 46, 22, 32, -140, -28, -24, 48, -50, 79, 46, 101, 25, -15, 102, -133, 52, 47, 2, 52, 25, 75, -40, -36, -82, 64, -142, -154, -34, 46, -46, -16, -35, 98, -190, -126, -39, -7, -6, 46, -34, -50, -50, -6, 30, -64, 70, -35, -37, 4, -73, 70, 4, 0, 6, 24, -69, 80, -24, 98, -60, -52, -23, -37, -34, -208, -46, 11, 1, -5, -65, 220, -19, -40, -80, 103, 1, 26, 14, 158, -118, -7, 44, 92, 108, 50, -45, 41, 48, 17, 170, -133, -110, 6, 44, 56, -43, -14, -18, 130, -73, -101, 38, 52, 41, 39, -3, -113, 17, 178, 76, -216, 45, -11, -16, 69, -68, -2, 22, -14, 31, -68, 54, 37, 110, -40, 15, 36, -56, -57, -20, 11, -19, -14, 73, -18, -54, -80, 36, -28, 98, -16, 1, 25, 85, -83, 74, -42, 19, -78, 52, 145, -31, 23, 49, -62, 50, -16, 0, -124, 266, 29, -40, 23, -100, -116, 82, -114, -4, 15, 74, 38, 25, -5, 16, -2, 63, 170, -4, -214, 46, -14, -46, -30, -35, 52, 57, -52, -42, 74, -25, 0, -7, 6, -94, 77, -42, 18, -14, -74, 54, -28, -34, -35, -42, -76, -28, -165, -3, 36, 58, -111, 16, 54, 53, -49, 290, 258, 2, 2, 12, -23, 39, -4, -95, -8, -24, 67, -8, 55, -8, -144, -10, -5, -8, -18, -94, 32, 1, -47, -68, -108, 220, -19, -72, 14, -49, -7, -18, -172, -78, -86, -23, 48, -160, 70, -26, 84, -31, -1, 146, 238, -114, -68, -42, -141, -12, 13, 5, -170, 36, -80, 2, 20, 86, 28, 29, -14, 22, 15, -86, -190, 162, -36, -28, -2, -53, 131, -18, -182, -5, 52, -2, 12], "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, 19, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "95.2.e.b", "char_is_minimal": true, "conrey_index": 11, "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], [0, -1, 0, 0, 0, 0], [0, 1, 0, 1, 0, -1], [-3, 0, 1, -2, 1, -1], [0, 0, 0, -1, 0, 0], [3, -1, -1, 1, -2, 2], [1, 0, 0, 0, -1, 0], [-2, 0, 1, 0, -1, 0], [-1, 1, -1, -1, 0, 0], [0, -1, 1, 0, 0, 0], [-2, 0, 0, 0, 1, 0], [-1, 0, -2, 0, 1, 0], [5, 0, 0, 5, 0, 0], [0, -2, 0, 1, 0, 2], [0, 1, 0, 1, 1, -1], [0, 1, 0, 1, 0, 1], [0, 1, 0, 0, 0, 2], [5, 0, 0, 0, -1, 0], [-1, -1, 1, 0, 2, -1], [-3, 0, 1, 0, 1, 0], [0, 2, 0, -3, 0, -1], [0, 3, 0, -1, 0, -2], [-3, -1, 3, -1, 2, -2], [0, 0, 0, -7, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, -5, 0, 0, 0], [-3, 0, 1, 0, 0, 0], [-4, 3, -1, -2, 2, -2], [1, -1, 0, 0, -1, 1], [3, 0, -1, 0, -2, 0], [0, 0, -1, 0, 0, 0], [3, -1, -1, 1, -2, 2], [0, -3, 0, 2, 0, 2], [9, 4, -3, 10, 1, -1], [0, 1, 0, 0, 0, -1], [0, -4, 0, -1, 0, 2], [-3, 0, 2, 0, 5, 0], [-7, 1, 2, -5, 0, -3], [0, 0, 0, 0, -5, 0], [0, 2, 0, 3, 0, -1], [0, -3, 0, -2, 0, 1], [8, -5, 2, 5, -3, 3], [0, 2, 0, 0, 0, 1], [7, -3, 0, 4, -3, 3], [-1, 0, -1, 0, 0, 0], [-9, 0, 4, 0, -1, 0], [-1, 1, -2, -2, -1, 1], [-2, -1, 3, 0, 2, -2], [-2, 0, 1, 0, -2, 0], [0, 0, 1, 0, 0, 0], [-1, -1, 5, 3, 4, -4], [0, 0, 0, -10, 0, -5], [-2, -3, -1, -6, -4, 4], [0, 3, 0, 4, 0, 1], [0, -1, 0, 1, 0, 1], [5, 0, 1, 0, -1, 0], [2, -2, -3, 5, -3, 2], [-3, 0, 0, 0, 2, 0], [0, -1, 0, 2, 0, -1], [0, -3, 0, 0, 0, 1], [5, 2, -4, 3, -2, 2], [0, 0, 0, -4, 0, -1], [-4, 3, 0, -1, 3, -3], [-5, 0, 2, 0, 5, 0], [5, 0, 0, 0, 0, 0], [-11, 6, -1, -6, 5, -5], [8, 0, -2, 6, -2, 2], [14, 0, -7, 0, -1, 0], [1, 0, -5, 0, -3, 0], [3, -2, 0, 1, -2, 2], [0, 2, 0, -8, 0, -3], [-6, 1, 3, -2, 4, -4], [0, -1, 0, -7, 0, -2], [0, 8, 0, 3, 0, -8], [0, 0, 0, 0, 1, 0], [-1, -2, 5, 5, -2, 2], [-6, 0, -1, 0, 3, 0], [0, -5, 0, 5, 0, 10], [0, 2, 0, -8, 0, 2], [2, 1, -2, 1, -1, 1], [0, 1, 0, -7, 0, 1], [-13, 0, 4, -9, 4, -4], [-2, 0, 3, 0, 0, 0], [-11, 0, -1, 0, 6, 0], [2, 1, -3, 0, -2, 2], [12, 2, -3, 11, -1, 1], [4, 0, 1, 0, -1, 0], [-3, 0, -2, 0, 2, 0], [2, 0, 4, 6, 4, -4], [0, 1, 0, -4, 0, -1], [5, -5, 0, 0, -5, 5], [0, 6, 0, 15, 0, 2], [0, -1, 0, 1, 0, 2], [7, 0, 0, 0, 0, 0], [-1, -2, 2, -1, 1, 1], [5, 0, 3, 0, -1, 0], [0, -1, 0, 3, 0, -3], [0, 0, 0, 6, 0, 5], [5, -4, 1, 2, -3, 3], [0, 0, 0, 2, 0, 1]]}