# Stored data for newform 546.2.g.c, downloaded from the LMFDB on 08 May 2024. {"label": "546.2.g.c", "space_label": "546.2.g", "level": 546, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007611605156386, "dim": 12, "is_polredabs": true, "trace_hash": 2148801455089587081, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [4, -32, -7, 46, -18, -2, 1]]], "qexp_display": "q-\\beta _{5}q^{2}+\\beta _{3}q^{3}-q^{4}-\\beta _{4}q^{5}+\\beta _{6}q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 21, "char_orbit_label": "g", "char_is_real": true, "Nk2": 2184, "analytic_conductor": 4.359831950361909, "hecke_ring_index": 4, "level_radical": 546, "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": "0.518", "prec": 17}, "analytic_rank_proved": true, "char_values": [546, 2, [365, 157, 379], [1, 1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7, 13], "conrey_indexes": [209], "field_disc": 203077620922126336, "field_disc_factorization": [[2, 12], [7041271, 2]], "field_poly": [729, -486, 324, 0, -72, 78, -50, 26, -8, 0, 4, -2, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.083", "prec": 17}, {"__RealLiteral__": 0, "data": "10.219", "prec": 20}, {"__RealLiteral__": 0, "data": "0.107", "prec": 17}, {"__RealLiteral__": 0, "data": "612.764", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "54967.314", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "1.2.3.c2", "trace_display": [0, -2, 4, -8], "traces": [0, 12, 0, -2, -12, 4, -2, -8, 0, 4, 0, 0, 2, 0, -10, 4, 12, -12, 8, 0, -4, 0, 0, 0, 2, 20, -12, -8, 8, 0, 14, 0, 0, -46, 0, 22, -4, 16, 8, -2, 0, -28, 2, -8, 0, 0, 24, 68, -2, 26, 0, -50, 0, 0, -16, 0, 10, -28, -24, -8, -4, 0, -16, 2, -12, 0, 12, 8, 12, 24, -28, 0, -8, 0, 0, -92, 0, 8, 2, 36, 4, 16, 0, 32, 0, 0, 0, -8, 0, 48, -2, -10, 0, 8, 0, 0, -2, 0, -16, 0, -20, 0, 0, 0, 12, -16, 0, 0, 8, -32, 108, 66, -8, 0, 28, 0, 0, 8, 0, -44, -14, -68, 8, 20, 0, -84, 14, 52, 0, 26, -4, 36, 46, -36, 0, -16, 0, 0, -70, 0, -22, -44, -36, 0, 4, 0, -16, 38, -16, 0, -10, -8, -8, 66, 20, 0, 2, 0, 0, -96, 0, 24, 16, 64, 28, 8, 0, -36, -2, -12, 0, 28, 8, 72, -20, -72, 0, 40, 0, 0, 0, 0, 8, 10, -24, 28, 30, 0, -68, 56, -24, 0, 2, 8, 24, 14, -26, 0, -10, 0, 0, -58, 0, -60, 50, -56, -20, -78, 0, -32, 24, 16, 0, 0, -56, 76, 16, -36, 0, 44, 0, 0, -50, 0, -10, 146, 80, -48, 28, 0, -24, 2, 24, 0, -4, 52, 8, 48, 6, 0, 4, 0, 0, -102, 0, -56, 30, 8, 16, -64, 0, -96, -2, 72, 0, -68, 12, 52, 28, 98, 0, -36, 0, 0, -12, 0, -52, -96, -8, 80, 44, 0, -12, 2, -52, 0, -24, 0, 96, 98, 28, 0, -4, 0, 0, -52, 0, -16, 8, 36, -80, 56, 0, -120, 46, -16, 0, -40, 60, 24, 92, 100, 0, -26, 0, 0, -12, 0, -8, -60, -72, -40, -2, 0, -24, 110, -36, 0, 20, 64, -4, 32, -16, 0, -16, 0, 0, -36, 0, -190, -104, 40, -32, 60, 0, 16, 0, -60, 0, -56, 0, 88, 40, -32, 0, -24, 0, 0, 8, 0, 12, -16, 0, -28, -36, 0, -48, 60, 8, 0, 2, 8, 60, 82, 10, 0, -52, 0, 0, -138, 0, -116, -8, -8, 0, 56, 0, -24, 118, 72, 0, 40, 16, -80, 2, 20, 0, -6, 0, 0, -4, 0, 16, 110, 72, -48, 0, 0, 92, 4, 20, 0, -60, -16, 0, 96, 4, 0, 0, 0, 0, -68, 0, -20, -24, -48, -12, -22, 0, 4, 16, 24, 0, 18, 0, 320, -22, -32, 0, 12, 0, 0, -8, 0, -72, -12, 32, 172, -50, 0, -108, 74, 12, 0, -66, -128, -60, 114, 8, 0, 72, 0, 0, -108, 0, -28, -28, -184, 44, -116, 0, -100, 28, 40, 0, -4, 8, 208, -8, -64, 0, -74, 0, 0, -18, 0, 44, -28, -4, 116, 14, 0, 88, 24, 68, 0, 18, 8, -8, -80, 42, 0, -20, 0, 0, -140, 0, 14, 76, 16, 84, 0, 0, -128, -14, -112, 0, 2, -52, -36, -18, 24, 0, 104, 0, 0, -26, 0, -72, 116, 4, 4, -60, 0, -36, 220, -32, 0, -46, -84, -40, 104, 36, 0, -24, 0, 0, -42, 0, -44, 16, 32, 4, -50, 0, -164, 0, 4, 0, -100, -84, 60, 70, -84, 0, -26, 0, 0, -136, 0, 22, 120, 24, 180, 44, 0, -44, -70, 36, 0, 68, 172, 0, 56, 72, 0, -4, 0, 0, 68, 0, -124, -46, -152, 16, -2, 0, -48, -38, -8, 0, 22, 16, 96, -24, -14, 0, 12, 0, 0, 10, 0, -6, -88, 8, 144, -36, 0, 8, 96, -92, 0, -66, 104, 128, 100, -20, 0, -48, 0, 0, 32, 0, -196, -2, 324, 56, -40, 0, -196, -24, -168, 0, -194, 36, 56, 96, -16, 0, 80, 0, 0, -56, 0, -24, -12, 4, 56, -16, 0, -20, 156, -64, 0, -14, -64, -28, 90, -64, 0, -8, 0, 0, 0, 0, -16, -8, -124, 36, 68, 0, 112, 2, -76, 0, -176, 12, 88, 18, 76, 0, 116, 0, 0, -28, 0, 16, 8, -8, 0, 32, 0, -72, 80, 120, 0, 20, -120, -36, -42, 72, 0, 8, 0, 0, -166, 0, -48, -40, 48, 64, -10, 0, 60, 72, 108, 0, 8, 136, 80, 0, -52, 0, -96, 0, 0, -24, 0, -8, -116, -24, -100, -10, 0, 96, 220, 24, 0, -20, -152, -28, 28, -68, 0, -30, 0, 0, 4, 0, -8, -18, 44, 68, 54, 0, -228, -56, -56, 0, -110, 24, -116, -54, -10, 0, 84, 0, 0, -2, 0, -160, 62, -8, -28, 52, 0, -24, -70, -56, 0, -14, -64, 60, -8, 26, 0, -80, 0, 0, -120, 0, 4, 10, 8, -40, -116, 0, 24, 76, 152, 0, -84, 136, 112, 58, 140, 0, -10, 0, 0, -22, 0, 60, 12, -72, 160, -50, 0, 40, 14, 56, 0, 16, 108, 20, 34, -24, 0, 78, 0, 0, -48, 0, -142, 80, 44, 32, 144, 0, 4, -24, 96, 0, -44, -16, -4, -74, 168, 0, 94, 0, 0, 0, 0, 0, 12, 56, 176, 46, 0, -76, -56, 44, 0, -16, -136, 80, -56, 36, 0, 132, 0, 0, -94, 0, 142, -44, -56, -84, 96, 0, -4, 56, -232, 0, -76, -8, 16, 50, -36, 0, -56, 0, 0, -132, 0, 10, -70, -84, -104, -146, 0, 4, 68, -80, 0, -78, -100, 48, -220, -22, 0, -28, 0, 0, -48, 0, 152, -88, 156, 24, 100, 0, -36, -2, -256, 0, -24, -24, 252, 24, -80, 0, 80, 0, 0, 4, 0, -72, 102, -52, 8, -52, 0, -8, -58, 132, 0, -48, -16, 56, -62, -6, 0, -32, 0, 0, -168, 0, -140, -4, -152, -16, 140, 0, 120, 6, 88, 0, 168, 16, 68, 102, 92, 0, -10, 0, 0, 4, 0, 56, 60, 248, 52, -30, 0, -4, -124, -8, 0, 168, 132, -16, 110, -16, 0, 64, 0, 0, 32, 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, 21, 3, 1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "546.2.g.c", "char_is_minimal": true, "conrey_index": 209, "id": null, "nf_label": 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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 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], [-1, 0, 0, 0, 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, 0, 1, 0, 0, 0, 0, 0], [-1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 1, -1, 0, -1, 0, -1], [0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1], [0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 1, 1], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [1, -1, 0, 1, 2, 1, 1, 0, 0, 0, 0, -1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0], [1, -1, 0, 0, 1, -1, 1, 0, 1, 0, 0, -1], [-1, 0, 0, 1, -1, 2, -2, 0, -1, 1, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, -1, -2, 0, 1, 1, 1, -1, -1, 0, -1, 0], [0, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0], [1, 1, 1, 0, 1, 0, 3, 0, 1, -1, 0, -1], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [2, -1, -1, -1, 2, 0, 1, -2, 0, 0, 1, -1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, -2, 1, 1, 0, -2, 0, 0], [1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1], [1, 0, 2, 1, 1, -4, 2, 0, 1, -1, 1, -2], [1, 0, -2, -1, 0, 1, 0, 0, 0, 1, -1, 2], [0, -1, 1, -1, 0, -2, -1, 0, 2, 2, -1, -1], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [-3, 0, 2, 2, 1, -1, 1, -1, 0, -2, 1, -3], [1, -2, 1, 0, 1, 0, 0, 0, 1, -1, 0, -1], [3, -2, 0, 1, 3, -3, 0, -1, 1, 0, -1, -2], [-1, 0, 0, -1, -1, 0, -1, 1, 0, 1, 0, 1], [1, 2, -1, 3, 0, 0, -2, -1, 0, 0, -3, -1], [2, -1, 0, 1, 1, 0, 1, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [-2, -1, 1, -1, 0, 0, 1, 2, 0, 0, 1, 1], [0, 0, -1, -1, 0, 0, -1, -1, 1, 1, -2, 0], [-1, -1, -1, 1, 0, 0, 1, 0, 0, 0, -1, -1], [0, 0, 1, -1, 0, -1, 0, 0, 0, 0, -1, -1], [-1, 0, -2, 0, -2, 1, -2, -1, 0, 0, -1, 1], [1, 0, 0, -2, 0, 0, 0, 1, 0, 0, 2, 0], [6, 1, 2, -2, -2, 0, -1, 0, 0, 0, 2, 2], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, -2, 0, 0, 1, -1, 0, -1, 2, -2, 2], [1, -3, 0, -1, 1, -2, -1, 0, 2, 0, -1, 0], [-4, 0, 1, -3, 0, -1, 0, 2, 1, 0, -1, 1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 4, -2], [-3, 1, -2, 1, -1, 2, -1, 0, -1, 1, -1, 0], [-1, 3, 1, 2, -1, 9, 1, 0, -2, 0, 2, -1], [1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0], [-1, -1, -1, 0, 1, 3, -1, -2, 0, 0, -2, 1], [-2, -1, 0, -1, 1, 0, 1, 1, 0, 0, 1, 0], [0, 2, 0, 2, 0, 0, -2, -2, 0, 0, -2, 0], [-1, 1, 0, -1, -2, -1, -1, 0, 0, 0, 0, 1], [2, 0, 3, 1, 2, -3, 4, 0, 2, -2, 1, -3], [-1, 1, 2, -1, -1, 0, -1, 2, 0, 0, 1, 2], [1, -4, 1, -1, 0, 0, 1, 1, 1, -1, -1, -1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1], [2, -2, 0, 1, 3, 3, 2, 0, 1, 0, 0, -2], [-1, 3, 2, -3, -3, 0, -3, 2, 0, 0, 3, 2], [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0], [1, 0, -1, 0, 1, -6, 0, 1, 1, 0, 1, -1], [-2, 0, -1, 0, 0, -1, 0, 1, 1, 1, -1, 2], [-2, 2, -3, -1, -2, 0, -2, 0, -2, 2, -1, 3], [-1, 1, 0, 0, -1, 1, -1, 0, -1, 0, 0, 1], [-3, 3, -3, -2, -3, 2, -3, 0, -3, 3, -2, 3], [0, 2, 1, 2, 0, -2, 2, 0, 1, 1, 2, -1], [-8, -1, 0, -2, -2, -1, -1, 3, 1, 0, -3, 2], [1, 0, 0, -1, 1, -2, 2, 0, 1, -1, -1, 0], [0, -1, 0, 0, 0, 2, -1, -2, -3, -1, 0, -2], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [4, 1, 1, 1, 0, 0, -1, 0, 0, 0, -1, 1], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -2, 2, 1, 1, -2, -1, 5, 0], [-1, 1, -2, -1, -1, 4, -1, 0, -2, 0, -1, 2], [4, -4, 0, -2, 2, 0, 4, 0, 0, 0, 2, 0], [0, 1, 2, 0, -1, -1, -1, 1, 1, 0, 1, 0], [-2, 3, 1, -2, -5, 0, -3, -1, 0, 0, 2, 1], [-1, 1, 0, -1, -1, 1, -1, 0, 0, 2, -1, 0], [-1, 1, -3, 0, 1, -1, 3, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0], [4, 0, 2, -4, 0, 0, 0, 2, 0, 0, 4, 2], [0, 0, 3, 2, -1, -2, 0, 0, 1, 0, 0, -3], [-1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [-1, -1, -1, 0, -1, 0, -3, 0, -1, 1, 0, 1], [-2, 5, -4, 0, -2, 5, -3, -1, -1, 4, -5, 2], [2, -2, 2, 1, 2, -8, 2, 0, 0, -4, 1, -2], [1, -2, 0, 1, 1, -2, 0, 0, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, -1, -1, 0, 2, 1, 0, -2, -2, -1, 1], [-1, 2, -1, -1, -1, -2, 0, -1, 0, 0, -2, 2], [0, -1, -3, -5, 2, 0, 1, 1, -1, -2, 0, 3], [-2, 1, 1, 1, -2, 0, -1, 2, 0, 0, -1, 1]]}