# Stored data for newform 354.2.c.b, downloaded from the LMFDB on 23 April 2024. {"label": "354.2.c.b", "space_label": "354.2.c", "level": 354, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503737099878754, "dim": 10, "is_polredabs": true, "nf_label": "10.0.41542366334681088.1", "trace_hash": 1234897093970783939, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [108, 54, -54, -25, 2, 1]]], "qexp_display": "q+q^{2}-\\beta _{6}q^{3}+q^{4}-\\beta _{3}q^{5}-\\beta _{6}q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 177, "char_orbit_label": "c", "char_is_real": true, "Nk2": 1416, "analytic_conductor": 2.8267042315533257, "hecke_ring_index": 3, "level_radical": 354, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [354, 2, [119, 61], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 59], "conrey_indexes": [353], "field_disc": -41542366334681088, "field_disc_factorization": [[-1, 1], [2, 17], [3, 6], [29, 2], [719, 2]], "field_poly": [243, -81, -27, -18, 6, 14, 2, -2, -1, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.018", "prec": 17}, {"__RealLiteral__": 0, "data": "8.964", "prec": 17}, {"__RealLiteral__": 0, "data": "6.532", "prec": 17}, {"__RealLiteral__": 0, "data": "437.803", "prec": 24}, {"__RealLiteral__": 0, "data": "1252.130", "prec": 27}, {"__RealLiteral__": 0, "data": "36649.811", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, "sato_tate_group": "1.2.3.c2", "trace_display": [10, -1, 0, -2], "traces": [0, 10, 10, -1, 10, 0, -1, -2, 10, 3, 0, -4, -1, 0, -2, -7, 10, 0, 3, -6, 0, -3, -4, 8, -1, 4, 0, -10, -2, 0, -7, 0, 10, 0, 0, 0, 3, 0, -6, 4, 0, 0, -3, 0, -4, -11, 8, 0, -1, 8, 4, 2, 0, 0, -10, 0, -2, -3, 0, -20, -7, 0, 0, -19, 10, -16, 0, 0, 0, -14, 0, 0, 3, 0, 0, -4, -6, -48, 4, 6, 0, 7, 0, -12, -3, -4, 0, -15, -4, 16, -11, 0, 8, 52, 0, 0, -1, 0, 8, -2, 4, 12, 2, 0, 0, -17, 0, 0, -10, 0, 0, -4, -2, 20, -3, 0, 0, -14, -20, 0, -7, -2, 0, -9, 0, 0, -19, -42, 10, 58, -16, -44, 0, 30, 0, 70, 0, 0, -14, 20, 0, -14, 0, 0, 3, 26, 0, -18, 0, -8, -4, 0, -6, 52, -48, -24, 4, 0, 6, -5, 0, -16, 7, 24, 0, 2, -12, 0, -3, -26, -4, -21, 0, 20, -15, 28, -4, 55, 16, 64, -11, 14, 0, -6, 8, 56, 52, 0, 0, 58, 0, -12, -1, -2, 0, 90, 8, 0, -2, -70, 4, 54, 12, 0, 2, 46, 0, -42, 0, 60, -17, 0, 0, 48, 0, -4, -10, 0, 0, -56, 0, -52, -4, 8, -2, -18, 20, 52, -3, 0, 0, -56, 0, -12, -14, 0, -20, -31, 0, 0, -7, -2, -2, 49, 0, 0, -9, 0, 0, 76, 0, 0, -19, -116, -42, -20, 10, 0, 58, 0, -16, -11, -44, 0, 0, 30, 30, -62, 0, -12, 70, -90, 0, -8, 0, 56, -14, 2, 20, -12, 0, 0, -14, 0, 0, -15, 0, 0, 3, 46, 26, -48, 0, 0, -18, -22, 0, -46, -8, 0, -4, 0, 0, -62, -6, 76, 52, -90, -48, 62, -24, 0, 4, 0, 0, 55, 6, 0, -5, 0, 0, 55, -16, 0, 7, 0, 24, -56, 0, -112, 2, -30, -12, -14, 0, -20, -3, 0, -26, 32, -4, 0, -21, -22, 0, -50, 20, -76, -15, 0, 28, -30, -4, 8, 55, 80, 16, -14, 64, 0, -11, -100, 14, 61, 0, -96, -6, 0, 8, -43, 56, 0, 52, 40, 0, -57, 0, 64, 58, 62, 0, -73, -12, 0, -1, 0, -2, -44, 0, 0, 90, 0, 8, -70, 0, 0, -2, 0, -70, -81, 4, -24, 54, 8, 12, 27, 0, 0, 2, 0, 46, -59, 0, -68, -42, 0, 0, -64, 60, 44, -17, 0, 0, -46, 0, 0, 48, 0, 0, -58, -4, -124, -10, -130, 0, 41, 0, -132, -56, -24, 0, -62, -52, 120, -4, 0, 8, 136, -2, 0, -18, 0, 20, 48, 52, 168, -3, 0, 0, -62, 0, 0, -56, 0, 0, 76, -12, 88, -14, 0, 0, -36, -20, 0, -31, 84, 0, -57, 0, 0, -7, -76, -2, 138, -2, -128, 49, 118, 0, 120, 0, 0, -9, 116, 0, -46, 0, 0, 76, 114, 0, -17, 0, 136, -19, 0, -116, 165, -42, -48, -20, 0, 10, 12, 0, 20, 58, 100, 0, -90, -16, 0, -11, -42, -44, -84, 0, 96, 0, 146, 30, 109, 30, 104, -62, -26, 0, -82, -12, 48, 70, 0, -90, 105, 0, -128, -8, 16, 0, 170, 56, 0, -14, -50, 2, 130, 20, 0, -12, 48, 0, -58, 0, 60, -14, 0, 0, 37, 0, 52, -15, 0, 0, -60, 0, -124, 3, 126, 46, 11, 26, 104, -48, 0, 0, -98, 0, 124, -18, 0, -22, -48, 0, 0, -46, 44, -8, 125, 0, 0, -4, 0, 0, 158, 0, 0, -62, -142, -6, -113, 76, 0, 52, 0, -90, -95, -48, 0, 62, 126, -24, -80, 0, 56, 4, -142, 0, -6, 0, 68, 55, -64, 6, -20, 0, 0, -5, 0, 0, 22, 0, 0, 55, 170, -16, -60, 0, 0, 7, -52, 0, -108, 24, 0, -56, 0, 0, -84, -112, 80, 2, -126, -30, 114, -12, 0, -14, 0, 0, 102, -20, 0, -3, 0, 0, 2, -26, 0, 32, 0, -4, -100, 0, -232, -21, -118, -22, -100, 0, -52, -50, 0, 20, 170, -76, 0, -15, 52, 0, -94, 28, -84, -30, 0, -4, -46, 8, 8, 55, -54, 80, -107, 16, 0, -14, -36, 64, 45, 0, -188, -11, 0, -100, -93, 14, 0, 61, 152, 0, -78, -96, 32, -6, -4, 0, -70, 8, 0, -43, 0, 56, -66, 0, 0, 52, 0, 40, -142, 0, 0, -57, 0, 0, 3, 64, 200, 58, -78, 62, 72, 0, 0, -73, 0, -12, -84, 0, -100, -1, 0, 0, -21, -2, 76, -44, 0, 0, -104, 0, 0, 90, 0, 0, 38, 8, -120, -70, -100, 0, -13, 0, -260, -2, 80, 0, -5, -70, 92, -81, 0, 4, 190, -24, 0, 54, 0, 8, 90, 12, 92, 27, 0, 0, -143, 0, 0, 2, 0, 0, 138, 46, 112, -59, 0, 0, -6, -68, 0, -42, 70, 0, -107, 0, 0, -64, -90, 60, 184, 44, -148, -17, 20, 0, 191, 0, 0, -46, -10, 0, -54, 0, 0, 48, 70, 0, 9, 0, 88, -58, 0, -4, 209, -124, 4, -10, 0, -130, 77, 0, -64, 41, 8, 0, -112, -132, 0, -56, -138, -24, -121, 0, 136, -62, 86, -52, 189, 120, 24, -4, 82, 0, -166, 8, -12, 136, 0, -2, 188, 0, -128, -18, 0, 0, 214, 20, 0, 48, -10, 52, 188, 168, 0, -3, -44, 0, -110, 0, -44, -62, 0, 0, 41, 0, 232, -56, 0, 0, -86, 0, -156, 76, 12, -12, -17, 88, 4, -14, 0, 0, -58, 0, 92, -36, 0, -20, 6, 0, 0, -31, 260, 84, 180, 0, 0, -57, 0, 0, 218, 0, 0, -7, -178, -76, -97, -2, 0, 138, 0, -2, -72, -128, 0, 49, -140, 118, -62, 0, 200, 120, -164, 0, 104, 0, 8, -9, 0, 116, 26, 0, 0, -46, 0, 0, 107, 0, 0, 76, -26, 114, -62, 0], "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, 177, 4, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 4, "minimal_twist": "354.2.c.a", "char_is_minimal": true, "conrey_index": 353, "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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 1, 0, -1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [-1, -1, 0, 1, 1, -1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, -1], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [2, 0, 0, -1, -1, 1, 1, 0, -1, -2], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, -1, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 2, 0, -1, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 1, 1, 0, 1, -1, 0, 1, 0], [-1, -1, 0, 1, 1, -1, 0, 0, 0, 0], [0, 1, 0, -1, 1, 1, 2, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, 0, 1, 1, -1, 0], [0, 0, 0, 0, 0, -1, 0, 0, -1, 0], [0, -1, 1, 2, 1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 1, -1, 1, -1, 0, 1, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, -1, 0, 2, 0, 1, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, -1, -1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, -1], [0, 0, -2, -1, 1, 0, 3, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [-1, 1, -1, -1, 1, -1, 1, -1, 0, 0], [2, 0, 0, -1, -1, 1, 1, 0, -1, -2], [0, 0, 0, -1, -1, 1, 1, 2, -1, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [1, 0, 0, -1, -1, 1, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, -1, -1, 1, 1, 1, 0, 0, -1], [0, 1, 0, -1, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 2, 0, -1, -1, -1, 0, 0], [0, 0, -1, 1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, -1, 0, 1, 1, -1, -1], [0, 0, 1, 1, 0, 1, -1, 0, 1, 0], [-2, 1, 0, 0, 1, -1, 0, 0, 1, -1], [-1, -1, 0, 1, 1, -1, 0, 0, 0, 0], [0, -1, 1, 3, 1, -2, -1, 0, -2, 0], [0, 1, 0, -1, 1, 1, 2, 0, 1, 0], [-3, 0, 0, 2, 2, 0, 0, 1, 1, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 0, 1, 0, -3, -2, 0, 1], [0, 0, -1, -1, -1, 0, 1, 1, -1, 0], [0, 0, 0, 0, 2, -2, 2, 0, -2, 0], [0, 0, 0, 0, 0, -1, 0, 0, -1, 0], [-2, -1, 1, 0, 1, 1, -1, -1, 1, 2], [0, -1, 1, 2, 1, 0, -1, 0, 0, 0], [0, -1, -1, 2, 2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, -2, 0, -1, 1, 1, -1, 0, 1, 0], [0, 1, 1, 1, -1, 1, -1, 0, 1, 0], [0, 0, 0, -1, -1, 0, 0, 1, -1, -1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-6, -1, 1, 2, 1, -2, 1, -1, 2, 0], [1, -1, 0, 2, 0, 1, 0, 0, 0, -1], [2, 0, 0, -2, -2, 2, 2, 1, -2, -2], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [2, 2, 0, -1, -1, 2, 1, -1, 1, -2], [0, -1, -1, 1, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, 0, 1, -2, -1, -1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, -1, 1, 1, 0, -1, 0], [0, 0, -2, -1, 1, 0, 3, 0, 0, 0], [-3, 1, 1, 1, -1, 0, -1, 2, 1, 2], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 1], [1, -1, 1, 2, 1, -2, 1, -2, 2, -1], [-1, 1, -1, -1, 1, -1, 1, -1, 0, 0], [0, -2, 0, 5, 1, -2, -1, 0, -2, 0], [2, 0, 0, -1, -1, 1, 1, 0, -1, -2], [4, -1, 1, 3, 1, -2, -1, 2, -2, 2], [0, 0, 0, -1, -1, 1, 1, 2, -1, 0], [0, -1, 0, 3, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -3, -1, 1, -1, 0, 1, 0], [1, 0, 0, -1, -1, 1, 1, 1, -1, 0], [1, -1, -1, -2, -1, 1, 1, -2, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]}