# Stored data for newform 126.2.e.c, downloaded from the LMFDB on 18 January 2025.
{"Nk2": 504, "analytic_conductor": 1.0061150654681328, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 63, "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": [126, 3, [29, 73], [2, 2]], "cm_discs": [], "conrey_index": 25, "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": [[5, [9, 18, 33, 12, 7, -1, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007474166202494, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 63, 8, 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": "126.2.e.c", "level": 126, "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": [2, 3, 7], "level_radical": 42, "minimal_twist": "126.2.e.c", "nf_label": "6.0.309123.1", "prim_orbit_index": 8, "qexp_display": "q-q^{2}+(-\\beta _{2}-\\beta _{4})q^{3}+q^{4}+(1-\\beta _{1}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "126.2.e", "trace_display": [-6, 2, 1, 2], "trace_hash": 1223061718509331722, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.911", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "151.625", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7141.386", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.007", "prec": 17}, "traces": [0, 6, -6, 2, 6, 1, -2, 2, -6, 8, -1, -1, 2, 8, -2, 12, 6, -4, -8, -3, 1, -10, 1, -7, -2, 2, -8, -7, 2, -5, -12, -40, -6, -3, 4, -13, 8, 3, 3, -5, -1, 0, 10, -6, -1, 9, 7, 18, 2, 12, -2, 6, 8, 15, 7, -26, -2, 22, 5, 28, 12, -16, 40, -31, 6, 24, 3, -2, -4, 3, 13, 14, -8, 19, -3, 8, -3, 10, 5, -10, 1, 8, 0, 2, -10, -2, 6, -27, 1, -9, -9, -46, -7, -38, -18, 8, -2, 28, -12, -3, 2, -29, -6, 0, -8, 6, -15, 27, -7, -5, 26, 4, 2, -35, -22, 4, -5, -5, -28, -26, -12, 20, 16, -12, -40, -36, 31, 38, -6, 37, -24, -2, -3, 49, 2, 48, 4, 16, -3, 10, -13, -6, -14, 12, 8, 32, -19, 32, 3, 0, -8, 7, 3, -54, -10, -21, -5, -18, 10, -21, -1, 1, -8, 12, 0, -27, -2, 16, 10, -23, 2, 22, -6, -8, 27, 33, -1, -9, 9, 6, 9, -10, 46, 13, 7, 2, 38, -4, 18, -40, -8, -36, 2, 24, -28, 90, 12, -58, 3, 36, -2, 67, 29, 53, 6, -54, 0, 15, 8, 4, -6, 3, 15, -39, -27, -31, 7, 5, 5, -65, -26, -84, -4, 21, -2, 8, 35, 33, 22, 4, -4, 33, 5, -13, 5, -30, 28, -59, 26, -21, 12, 39, -20, 32, -16, -5, 12, 55, 40, -36, 36, -24, -31, 8, -38, 18, 6, -15, -37, -2, 24, 51, 2, 3, 3, 6, -49, -45, -2, -14, -48, 2, -4, -17, -16, -23, 3, -33, -10, -47, 13, -7, 6, -122, 14, -57, -12, 3, -8, 11, -32, 10, 19, -9, -32, -19, -3, 3, 0, -6, 8, -20, -7, -9, -3, 21, 54, -50, 10, -5, 21, -8, 5, 16, 18, -39, -10, 6, 21, 64, 1, 81, -1, 112, 8, 29, -12, -11, 0, 93, 27, -96, 2, 4, -16, 52, -10, -49, 23, -33, -2, 21, -22, -61, 6, 0, 8, 42, -27, 40, -33, 34, 1, -3, 9, 16, -9, 30, -6, 19, -9, -24, 10, -37, -46, 46, -13, 27, -7, -12, -2, 24, -38, -8, 4, 27, -18, 30, 40, 64, 8, 136, 36, 32, -2, 44, -24, 88, 28, 70, -90, 8, -12, -24, 58, -21, -3, -46, -36, 1, 2, 6, -67, -47, -29, 21, -53, 1, -6, -18, 54, -27, 0, 62, -15, 34, -8, -2, -4, 36, 6, -4, -3, -51, -15, 16, 39, -58, 27, 57, 31, 27, -7, -18, -5, 6, -5, -38, 65, -28, 26, -40, 84, 14, 4, 6, -21, 93, 2, 70, -8, -27, -35, 4, -33, -105, -22, -158, -4, 24, 4, -2, -33, 19, -5, -84, 13, 31, -5, -90, 30, -80, -28, -62, 59, -14, -26, -12, 21, 2, -12, -8, -39, 45, 20, -38, -32, 6, 16, -41, 5, -39, -12, 52, -55, -69, -40, -80, 36, -11, -36, 30, 24, -210, 31, -82, -8, -27, 38, -3, -18, 93, -6, -53, 15, 5, 37, 30, 2, -102, -24, -15, -51, 15, -2, 83, -3, 6, -3, 44, -6, 3, 49, 3, 45, 60, 2, 33, 14, -52, 48, 56, -2, -71, 4, 16, 17, 47, 16, 13, 23, -166, -3, -1, 33, 15, 10, 49, 47, 118, -13, 48, 7, -88, -6, 56, 122, -88, -14, 114, 57, -4, 12, 93, -3, -20, 8, 85, -11, -35, 32, 25, -10, 12, -19, 63, 9, -31, 32, -11, 19, 6, 3, 27, -3, 14, 0, -29, 6, -84, -8, -45, 20, 19, 7, 17, 9, 23, 3, 3, -21, -51, -54, 23, 50, -30, -10, 65, 5, 61, -21, 12, 8, -66, -5, 11, -16, -33, -18, -8, 39, 78, 10, 46, -6, 78, -21, -34, -64, 147, -1, -76, -81, 30, 1, -48, -112, 6, -8, 19, -29, 85, 12, -51, 11, 26, 0, 19, -93, 2, -27, -26, 96, 42, -2, 34, -4, -41, 16, -80, -52, -21, 10, -3, 49, -10, -23, -6, 33, -12, 2, -15, -21, -27, 22, -82, 61, -50, -6, 30, 0, 30, -8, 0, -42, -98, 27, -48, -40, 12, 33, 4, -34, 3, -1, -18, 3, 110, -9, 102, -16, 40, 9, 57, -30, -69, 6, -66, -19, 90, 9, 31, 24, 52, -10, 56, 37, 43, 46, 65, -46, 34, 13, 26, -27, 33, 7, -52, 12, -19, 2, -94, -24, -27, 38, -93, 8, -69, -4, 51, -27, -19, 18, -27, -30, 52, -40, -46, -64, 21, -8, -16, -136, 18, -36, 18, -32, 3, 2, 31, -44, -6, 24, 43, -88, 5, -28, 10, -70, 36, 90, -16, -8, -108, 12, -46, 24, -76, -58, 75, 21, 11, 3, 13, 46, 3, 36, 15, -1, 30, -2, -45, -6, 92, 67, -37, 47, -102, 29, -20, -21, -68, 53, -2, -1, -88, 6, -114, 18, -116, -54, 170, 27, 100, 0, -21, -62, -48, 15, -50, -34, -29, 8, -52, 2, 14, 4, 10, -36, 101, -6, -70, 4, 117, 3, 50, 51, 45, 15, -59, -16, -14, -39, -36, 58, 39, -27, 0, -57, -24, -31, 69, -27, -2, 7, -7, 18, 56, 5, 21, -6, 19, 5, 4, 38, -54, -65, 55, 28, -30, -26, -102, 40, 12, -84, 27, -14, 21, -4, -79, -6, -24, 21, 54, -93, -39, -2, -18, -70, 93, 8, 6, 27, 73, 35, -54, -4, 8, 33, -9, 105, 87, 22, 68, 158, -3, 4, 26, -24, -41, -4, -11, 2, 147, 33, -2, -19, 73, 5, -252, 84, 159, -13, -9, -31, 28, 5, -36, 90, -44, -30, 40, 80, 24, 28, -33, 62, -14, -59, 58, 14, -96, 26, -4, 12, 42, -21, 27, -2, -61, 12, 130, 8, 81, 39, -34, -45, 114, -20, -90, 38, -21, 32, 15, -6, 76, -16, -138, 41, 3, -5, 10, 39, 60, 12, -47, -52, 57, 55, -35, 69, 66, 40, -20, 80, -7, -36, 9, 11, 1, 36], "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, 0, 0], [0, 0, -1, 0, -1, 0], [1, 0, 0, 0, 0, 0], [1, -1, 0, 1, -1, -1], [0, 0, 1, 0, 1, 0], [0, 2, 1, -1, 2, -1], [-1, 0, 0, 0, 0, 0], [2, 1, 1, 2, 0, -1], [-1, 1, 0, -1, 1, 1], [0, 0, 1, 0, 0, -1], [0, 0, -1, 0, -1, 0], [3, 2, 1, 2, 3, -1], [0, -2, -1, 1, -2, 1], [2, -2, 0, 1, -3, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 0, 2, -2], [-2, -1, -1, -2, 0, 1], [-2, -3, -3, -3, -2, 3], [1, -1, 0, 1, -1, -1], [-5, 2, 0, -2, -2, 1], [0, 0, -1, 0, 0, 1], [0, -1, 0, 0, 2, 1], [0, 0, 1, 0, 1, 0], [1, -1, 1, -1, 1, -1], [-3, -2, -1, -2, -3, 1], [-1, -2, -2, 2, -3, 2], [0, 2, 1, -1, 2, -1], [-2, -1, 0, -2, 2, 5], [-2, 2, 0, -1, 3, 0], [-7, 1, 2, 0, 1, 0], [-1, 0, 0, 0, 0, 0], [-2, -1, 0, -1, -3, 0], [0, -2, 0, 0, -2, 2], [-2, 1, -2, -2, 4, 2], [2, 1, 1, 2, 0, -1], [1, 0, 0, 0, 1, 0], [2, 3, 3, 3, 2, -3], [-2, -1, -3, 0, -1, 5], [-1, 1, 0, -1, 1, 1], [1, 1, 3, 1, 1, -3], [5, -2, 0, 2, 2, -1], [3, -6, 0, 3, -1, 0], [0, 0, 1, 0, 0, -1], [3, -3, -2, 2, -4, -2], [0, 1, 0, 0, -2, -1], [0, 3, 0, -6, 3, 0], [0, 0, -1, 0, -1, 0], [3, 1, -1, 2, -2, -4], [-1, 1, -1, 1, -1, 1], [-2, 2, 2, 0, -2, 2], [3, 2, 1, 2, 3, -1], [-1, 2, 0, -1, -4, 0], [1, 2, 2, -2, 3, -2], [-6, 2, 1, -3, 2, 0], [0, -2, -1, 1, -2, 1], [6, 3, 2, -1, 6, -5], [2, 1, 0, 2, -2, -5], [3, 2, 1, -3, 2, 0], [2, -2, 0, 1, -3, 0], [-1, -2, -1, 3, -2, 0], [7, -1, -2, 0, -1, 0], [-4, 4, 4, 2, 3, -4], [1, 0, 0, 0, 0, 0], [7, -5, -6, 4, -5, 0], [2, 1, 0, 1, 3, 0], [2, -4, -5, 3, -4, 0], [0, 2, 0, 0, 2, -2], [1, -1, -1, -3, 4, 2], [2, -1, 2, 2, -4, -2], [6, -2, 5, 9, -2, 0], [-2, -1, -1, -2, 0, 1], [-4, 3, 0, -4, -4, 5], [-1, 0, 0, 0, -1, 0], [-2, -1, -1, -4, -4, 0], [-2, -3, -3, -3, -2, 3], [4, 0, -2, 1, 3, 0], [2, 1, 3, 0, 1, -5], [-1, 1, 5, 3, 1, 0], [1, -1, 0, 1, -1, -1], [8, -2, 1, 5, 6, -1], [-1, -1, -3, -1, -1, 3], [-3, 5, 0, -3, 2, 1], [-5, 2, 0, -2, -2, 1], [-2, -2, -4, -2, -2, 4], [-3, 6, 0, -3, 1, 0], [-1, 1, -3, -5, 12, 0], [0, 0, -1, 0, 0, 1], [-2, 4, 3, 4, -2, -3], [-3, 3, 2, -2, 4, 2], [-6, 2, 4, 2, 0, -7], [0, -1, 0, 0, 2, 1], [-5, -1, 5, -2, 6, 1], [0, -3, 0, 6, -3, 0], [1, 2, 5, 1, 2, 0], [0, 0, 1, 0, 1, 0], [2, 0, 0, 2, -10, -4], [-3, -1, 1, -2, 2, 4], [0, 0, 2, 1, -2, -4], [1, -1, 1, -1, 1, -1]]}