# Stored data for newform 273.2.i.b, downloaded from the LMFDB on 03 December 2023.
{"label": "273.2.i.b", "space_label": "273.2.i", "level": 273, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504149416739089, "dim": 6, "is_polredabs": true, "nf_label": "6.0.19683.1", "trace_hash": 112402481033725853, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, -3, 9, -2, 3, 0, 1]]], "qexp_display": "q+(-\\zeta_{18}+\\zeta_{18}^{2}+\\zeta_{18}^{4}-\\zeta_{18}^{5})q^{2}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 1092, "analytic_conductor": 2.1799159751809545, "hecke_ring_index": 1, "level_radical": 273, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 18, "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": "0.019", "prec": 17}, "analytic_rank_proved": true, "char_values": [273, 3, [92, 157, 106], [3, 1, 3]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 7, 13], "conrey_indexes": [79, 235], "field_disc": -19683, "field_disc_factorization": [[-1, 1], [3, 9]], "field_poly": [1, 0, 0, -1, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.517", "prec": 17}, {"__RealLiteral__": 0, "data": "1.121", "prec": 17}, {"__RealLiteral__": 0, "data": "122.907", "prec": 24}, {"__RealLiteral__": 0, "data": "21.111", "prec": 20}, {"__RealLiteral__": 0, "data": "5309.113", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 3, -3, 0], "traces": [0, 6, 0, 3, 0, -3, 0, 0, 6, -3, -6, 3, 0, 6, -15, -6, 6, -9, 0, -3, 6, 0, 6, 0, 3, 6, 0, -6, -12, 12, 6, -12, 9, -3, 6, -15, 0, 3, -12, 3, 3, 0, -12, -12, 3, -3, 9, -6, 12, 0, 30, 9, 0, 3, 0, 0, -12, -6, -18, 3, 3, -15, 0, 0, -6, -3, 3, 9, -6, 0, -9, 42, -3, 0, -3, -6, 12, 15, 0, 24, 9, -3, -18, -24, 3, 24, -3, 6, 6, -15, 12, 0, 36, 12, 12, -15, -9, 42, -33, -6, -12, -39, 3, -33, 6, -12, -6, 18, 0, -3, 6, 6, -6, 36, 12, 9, 9, -3, -60, -12, 6, 24, -39, 0, -9, -12, 3, -18, -3, -6, -6, -3, 6, -30, 30, 3, -6, -30, -9, 84, 27, -12, -12, 3, 6, -24, -48, 0, 12, -42, 15, -12, 9, 18, -9, 24, 0, -15, 12, -3, -48, 45, 0, 39, -9, 0, -3, -18, 3, 6, -27, -3, 12, 3, -36, -6, 36, -3, 15, 6, -3, 24, -15, -30, -9, 0, 0, 12, 24, 0, 48, -9, -3, -3, 27, -6, 33, 60, -3, 24, 21, -9, -12, 0, -12, -18, -6, 0, 6, 6, 18, -42, -3, 21, 9, 3, -6, -27, -18, 0, 3, -9, 3, -12, -21, -12, 63, 0, 6, 21, 18, 12, -24, -9, 0, 6, 51, 48, 48, -18, -9, -9, 12, 3, 12, -33, -36, -3, -12, -12, 15, -6, 15, -54, -39, 12, -36, -30, -6, -3, 6, -6, 45, -21, -6, -12, -21, -30, 15, -33, 6, 6, -66, 0, 6, -9, 18, 18, -24, 24, 3, 24, -12, -3, -33, 15, 6, 36, -18, 18, -21, 21, 39, 72, -39, -66, 6, -3, -6, 0, -24, -21, 72, 39, 12, -54, -3, -78, 0, -66, -33, 0, 3, 18, -60, 3, -66, 9, -3, -21, 18, 36, 63, 30, 0, 6, 36, 3, -36, 48, 12, -21, 3, 3, 30, 12, 33, -90, 0, 18, -18, 21, 24, 51, -18, -9, 48, -9, -9, 78, 18, -6, 3, -18, -30, -33, -42, 3, -54, 39, 3, 30, 75, 48, -12, -48, 39, 21, 63, 0, 6, -15, -18, -45, -9, -6, -18, 12, 15, -6, -21, -9, 60, 18, -6, -12, -66, 6, 18, 0, 6, 36, -39, -6, 6, 36, 3, 33, -42, -24, -18, -33, 15, -12, 3, 6, 15, 0, 6, 6, -27, 30, 24, 93, -18, 9, 9, 42, 15, -6, 9, -54, -48, -6, 0, 6, -24, -111, 0, -3, 21, -30, -6, -24, 57, -48, -45, 18, -24, 6, 12, 0, 6, 30, 6, 0, 54, -84, -3, -60, -15, -9, 36, 12, 84, -15, 18, -21, 0, 9, -9, 60, 18, -42, -33, 12, -33, 39, 0, 75, 24, 15, -27, -21, -12, 48, -21, -6, 63, 45, -24, 3, -60, -27, 6, 6, 0, -15, 24, 78, 27, 24, 9, -9, -12, 0, -102, 78, -6, 42, -6, -9, -6, 6, 15, 66, -36, 3, -15, 15, -54, 69, 36, 3, -15, -39, -12, -60, 0, 6, 3, -27, -18, -18, -108, 33, -30, -45, 18, -57, 6, -6, 39, 0, -15, 27, 24, -6, -102, -39, -6, -45, 33, 12, 30, -12, -12, -6, -6, -15, 24, -42, -18, 3, -66, 0, -3, -51, 0, -12, 12, 24, -15, -12, 12, 45, 114, 0, 18, 15, 24, -45, 3, -18, -9, 0, 3, -36, -21, 3, 30, -3, 54, 3, -24, -3, -36, -114, 39, 24, 87, 30, 9, -21, -6, 63, -48, -24, 9, -66, -21, 72, 69, -18, -36, 36, -6, 24, -78, -63, 150, -6, -6, -6, 9, -36, 33, 0, 6, 6, -21, 0, -18, 24, 12, -9, 63, 3, -21, -6, 27, 12, 12, -21, -3, -30, -6, 0, -78, -21, -33, 69, -9, 126, -63, 6, -51, -6, -3, -24, 30, -9, -18, 12, -9, 42, 9, 0, 66, 132, -3, 12, 93, 9, -30, -15, 6, 117, -12, -6, 18, 36, -42, 6, -18, -6, 0, -39, 126, -63, -30, 0, -21, -63, -6, 66, 0, 42, -51, 3, 9, -15, -120, -3, -126, -66, -12, -9, 9, -18, -36, 12, 0, -3, 18, -6, -60, -3, 102, -72, -87, 24, -30, 90, -12, 0, 81, -9, 21, -75, -18, -6, 72, 9, 51, -15, -12, 42, -12, 6, 63, 30, 6, 21, 240, -39, 90, -39, -18, 21, -6, -6, -15, 126, 12, -48, 30, 12, -18, 27, 30, 27, 60, -3, -18, 96, 12, -108, 93, -27, 9, -51, -78, -153, -114, -12, -39, 3, 36, 240, 3, -60, 57, -30, -3, 15, 96, -15, -42, -36, 3, 42, 36, -12, 84, -30, -45, 96, 21, 21, -186, -135, -12, -15, -42, -6, 15, -288, 21, 60, 15, -15, 24, -15, 30, -9, 0, 33, -45, 24, -6, -186, -69, 12, 3, 75, -33, 0, -18, 0, 54, -57, 3, -45, -27, -18, -123, -36, -18, -87, 24, -18, -6, 33, -48, 39, 3, 12, -48, 156, 15, 102, 78, 12, -60, -3, -24, 39, -12, 3, -54, -18, 33, -42, -90, 30, 9, 0, 3, -75, -30, -9, -12, 99, -9, 51, -75, 36, -21, 90, 21, 9, -12, -21, 54, -3, 78, -84, -33, 36, -3, -72, -6, -54, -6, -33, -45, -45, 12, 69, -12, 3, -9, 18, 6, -66, -102, 0, -3, 12, -12, 6, -54, -42, 162, 63, 36, 72, 6, 78, -9, -114, -12, -18, 48, 54, 72, 81, -6, 3, 18, -39, 27, 42, 0, 36, 15, -33, 81, -69, -66, -66, -12, 0, 48, 3, -3, -150, -21, 36, -6, -117, -30, 27, 258, 15, -48, -33, -33, 0, -15, 18, -24, 36, 3, 51, 36, 21, 126, -12, 36, 27, -3, 18, -39, -60, 63, 96, 12, 15, 3, 33, 0, 30, 12, -6, 9, 93, -36, -18, 45, 6, -111, 114, -18, -24, 156, -12, 12, 72, 6, 36, 27, -42, -192, -90, -3, 9, 60, -3, 18], "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, 7, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "273.2.i.b", "char_is_minimal": true, "conrey_index": 79, "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, 1, 0, 1, -1], [1, 0, 0, -1, 0, 0], [0, 1, 0, 0, -1, -1], [0, -1, 1, -1, 1, -1], [0, 0, 0, 0, 1, -1], [0, -2, 0, 0, -1, 0], [1, 0, 0, 0, 1, -1], [0, 0, 0, -1, 0, 0], [-2, 2, -1, 2, -1, -1], [1, 0, -1, -1, 1, 1], [0, 0, -1, 0, -1, 0], [1, 0, 0, 0, 0, 0], [-2, 0, 3, -1, 0, -2], [-1, 0, 0, 0, 1, -1], [0, -1, -2, 2, -2, -1], [-3, 1, 0, 3, -1, -1], [0, 1, -1, 0, 0, 0], [0, -2, 2, -1, 2, -2], [1, -1, -1, 0, -1, 2], [0, -3, 0, 0, 2, 0], [1, -1, -1, 0, 2, -1], [0, 4, 1, 0, 1, 4], [1, 1, -1, -1, 0, 0], [2, 3, -2, -2, -1, -1], [0, -1, 1, 0, 1, -1], [-1, 0, 0, 0, 0, 0], [-3, 0, -3, 2, 0, 2], [2, 4, 4, 0, -5, 1], [0, 1, -2, 2, -2, 1], [-4, 1, 1, 4, -2, -2], [3, -2, 3, -3, -1, -1], [0, 1, 0, -1, 0, 1], [1, 0, 0, 0, -4, 4], [-2, -1, 3, -1, 3, -2], [0, -1, -1, 0, 0, 1], [0, 0, 1, 1, 1, 0], [-4, 3, -1, 4, -2, -2], [1, 0, 0, -1, 0, 0], [0, 0, -1, 1, -1, 0], [0, 0, 0, 0, -3, 3], [-3, 0, 1, 2, 0, -3], [-2, 3, 3, 0, -2, -1], [0, 0, 0, 1, 0, 0], [-1, 1, -1, 1, 0, 0], [3, 1, -5, -3, 4, 4], [0, 4, 0, -2, 0, 4], [2, -3, -3, 0, 1, 2], [0, 0, 3, 0, 0, 5], [5, -2, -2, 0, 1, 1], [0, 0, -1, 3, -1, 0], [0, 1, 0, 0, -1, -1], [1, 0, 1, -1, -1, -1], [0, 1, -1, 0, -1, 1], [0, 0, 0, 0, 1, -1], [-3, -2, 1, 2, -1, -3], [-1, 0, 0, 0, 2, -2], [0, 2, 3, -6, 3, 2], [1, -9, 1, -1, 8, 8], [1, -2, 1, -1, 1, 1], [0, -8, 5, -5, 5, -8], [0, 1, 1, 0, -6, 5], [0, -1, 0, 0, 3, 0], [-1, -3, -3, 0, 4, -1], [0, -1, 1, -1, 1, -1], [1, 1, -2, -1, 1, 1], [3, 0, -5, -3, 5, 5], [0, -1, 3, -2, 3, -1], [0, 5, 5, 0, -4, -1], [-4, 6, -5, 5, -4, 1], [7, -6, -6, 0, 1, 5], [0, 1, -1, -1, -1, 1], [0, -7, 1, 0, 6, 6], [-1, 0, 0, 1, 0, 0], [0, 2, -3, -2, -3, 2], [2, -1, -1, 0, -2, 3], [2, -3, 1, 1, 2, -3], [0, 0, 0, 0, 1, -1], [0, -1, -5, 8, -5, -1], [3, -6, 4, -3, 2, 2], [-1, 0, 0, 1, 0, 0], [0, 0, 3, -6, 3, 0], [-4, 1, 1, 0, -1, 0], [-1, 0, -1, 3, 0, 3], [4, -1, -1, 0, -4, 5], [0, 5, -3, -1, -3, 5], [2, -1, 5, -2, -4, -4], [2, 1, -3, -2, 2, 2], [0, 1, -4, -5, -4, 1], [2, -1, -1, 0, -1, 2], [0, -2, 0, 0, -1, 0], [6, 5, 5, 0, -1, -4], [0, -1, -1, 4, -1, -1], [4, 2, -6, -4, 4, 4], [-5, 5, -3, 5, -2, -2], [0, -3, 2, -3, 2, -3], [7, 1, 1, 0, 4, -5], [-3, 3, 0, -5, 5, 0], [-1, 1, 1, 0, -1, 0], [0, -3, 0, -4, 0, -3]]}