# Stored data for newform 722.2.c.e, downloaded from the LMFDB on 19 April 2024. {"label": "722.2.c.e", "space_label": "722.2.c", "level": 722, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014535981990610, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1871634110687843293, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [1, 1, 1]], [5, [0, 1]], [7, [1, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{2}+(-1+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "c", "char_is_real": false, "Nk2": 2888, "analytic_conductor": 5.765199025936444, "hecke_ring_index": 1, "level_radical": 38, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [722, 3, [363], [2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 19], "conrey_indexes": [429, 653], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.009", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.910", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "106.655", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, -1, 0, -2], "traces": [0, 2, 1, -1, -1, 0, 1, -2, -2, 2, 0, -12, 2, -5, -1, 0, -1, -3, 4, 0, 0, 1, -6, -3, 1, 5, -10, -10, 1, -9, 0, -8, 1, 6, 3, 0, 2, 4, 0, 10, 0, 0, -1, -8, 6, 0, -6, 0, -1, -12, 10, -3, -5, 3, -5, 0, 2, 0, -18, -9, 0, 10, -4, -2, 2, 0, -6, -5, 6, 6, 0, 6, -2, 7, 2, -10, 0, 12, 5, 10, 0, -1, 0, -12, -2, 0, 8, 18, 12, 12, 0, 5, -3, 4, 0, 0, -2, 10, -6, -12, 5, -18, -6, 28, 5, 0, 6, -18, 5, -11, 0, -2, 1, 12, 0, 0, -9, 10, 9, 3, 0, 50, 20, 0, 4, 0, -4, -2, 1, -8, 0, 0, -12, 0, -10, 0, 3, 9, 3, 4, 0, 0, -6, 30, -4, 0, -7, 6, -2, 0, -5, -20, 0, -12, 6, 0, -5, 22, -10, -6, 0, 3, 1, 40, 0, 0, -6, -12, -1, -12, 0, 0, 16, -6, 9, -5, 6, -9, 24, 0, 0, -2, 10, -20, 3, 0, -4, 18, 0, 10, 0, 6, -1, -14, -10, 0, 6, 0, -24, -11, -5, 10, -36, 9, -3, 0, 14, 6, 10, 0, 0, -5, 3, 6, -9, 0, 10, 8, 11, 7, 0, 30, 2, -26, -1, -10, 6, -30, 0, -44, 0, -6, 9, 6, -10, 0, 18, 10, -3, -42, 0, -8, 25, -16, 10, 0, 0, 0, 8, 6, 0, -6, -2, 18, -4, 0, -1, -12, -16, -4, 0, 18, 0, -24, -6, 0, 0, -24, -5, 6, 0, -11, -3, -10, 18, -30, -3, 16, 8, -8, 0, 0, 0, 22, -12, 0, 60, 0, -2, 8, 0, 10, -14, -42, -6, 0, -4, 60, 0, -15, 5, 8, -10, 36, 0, 0, -6, -20, -6, -14, 0, -42, -10, 19, -22, 0, -20, 9, -3, 54, 0, 9, 6, 0, 2, 25, 20, -11, 0, 0, 0, -2, 6, 4, -24, 0, 1, 4, 12, -6, 0, 48, 0, 26, 8, 0, 6, -18, -9, -20, -10, 25, -6, -30, -18, 0, 12, 3, 0, -21, 0, 0, -4, -25, 5, 0, -10, 28, 6, 0, 0, -3, -8, 46, -18, 0, 0, -45, 5, -14, 0, 4, 3, -18, 1, 0, 14, -32, -20, -18, 0, 18, 12, 0, 0, 0, -12, -20, -22, 0, -10, 0, 5, 20, -18, 0, 18, -24, 3, -32, 0, -18, -14, 9, -6, 0, 5, -8, 0, -24, 0, -17, 5, 0, -3, -30, 12, -10, 9, -60, 0, -6, 5, -2, 4, 0, 22, 0, 14, 28, 0, -12, 15, 18, 4, 0, 26, 0, -2, -36, 10, 0, -6, 10, -15, 0, 0, 34, -22, 15, 0, 12, 6, -8, 18, 0, -6, 36, -20, 5, 0, 22, 9, 48, 20, 0, -6, -6, -21, -36, 0, -10, -16, -6, -25, 0, -32, 4, -10, -20, 0, 36, 0, 54, 0, 0, 4, -6, -6, 4, 0, 24, -12, 21, 2, 0, 36, -12, -2, -30, 0, -7, -2, 0, -24, 0, -8, 0, -2, -6, 0, -72, -18, -11, 0, 10, 24, 12, 6, 14, 0, -36, 0, 0, -12, 0, 5, 0, -6, 72, 0, -2, 11, 4, -6, 0, -5, -44, 9, -20, -60, 0, -6, -10, 8, 0, 4, -24, -16, 80, 0, 18, 0, -24, 0, 0, -22, 1, -6, -48, 0, -8, 30, -3, 0, 15, 2, 22, 16, -14, 0, 12, 20, -18, -7, 0, -21, 12, -12, 0, 0, 0, -2, 30, 30, 0, 0, 22, 15, 24, 10, -56, -8, 10, 10, 0, 18, -44, 0, -18, 0, 0, 6, -2, 20, 0, -12, 6, 14, -20, 0, 15, -21, -12, -5, -25, 38, 0, -44, -6, 0, 16, -10, -5, 18, 0, 3, 30, 108, 24, 0, -6, -9, 22, 3, 0, 0, 54, 1, 54, -25, -4, -20, 48, -22, 0, 0, 28, 0, 45, 0, 13, -1, -15, 12, 0, 8, -27, -12, -26, 0, -60, 2, 88, -4, -25, 24, -66, 6, -10, 0, 15, 24, 72, 0, 0, 13, 22, -8, 15, 0, -20, 12, 12, 18, 0, -18, 0, -10, 6, -5, -12, 50, 0, -12, 0, -15, 18, -9, 10, 0, 40, -12, 12, 6, 0, 0, 21, 21, -39, 0, -28, 0, 16, -2, 45, 25, 37, -5, 26, 0, -24, 10, 64, 56, 0, 3, 30, 0, 16, 0, 0, -6, 36, -4, 0, 23, -12, -36, 18, 0, 40, 0, 12, 45, 0, -5, -2, -7, -36, 0, -42, 2, 11, -3, 0, 18, 90, 2, -5, 0, 24, 28, -51, -16, -20, -10, 2, -36, 0, 0, -36, 9, 45, 6, 0, 0, -62, 0, -24, 0, -12, 12, 50, 20, 0, -11, -78, 0, 0, -5, -24, 0, -42, -5, 0, 40, 6, 18, 18, 0, -11, 9, -11, -12, 0, 6, 0, -64, -10, 0, 0, -9, -41, -28, 60, -9, -33, -12, 22, 0, -8, -5, 18, -4, 0, 0, 40, -12, 48, 0, -52, 17, 0, 10, 0, 0, -50, -6, 22, -15, -6, 6, 46, -20, 0, 18, 12, -30, -14, 0, 0, -12, -36, -5, 0, -4, -16, -4, -60, 0, -25, 11, 40, 0, 0, 7, -23, -28, 21, 0, -36, -24, 34, -15, 0, 36, 42, 2, 2, 0, 6, 52, 0, 0, 0, -1, -15, -18, 36, 20, -18, 0, 8, -12, 0, -10, 37, 15, 36, 0, 96, 0, 72, 17, 0, 22, 0, -15, -14, 0, -20, -12, -60, 12, 10, -4, 28, 9, -33, 0, 0, -12, 21, 18, 0, -10, 7, 10, -38, 0, -21, 44, 0, -9, 0, -48, 48, 10, -70, 0, -18, -3, -30, 6, 0, 21, -108, -72, -9, 0, -30, -20, -18, -8, 0, -3, -32, -50, 0, 0, -12, -16, -4, 2, 25, -20, -24, 20, -72, 0, -44, -36, 30, 0, 0, 27, 0, 0, 48, 0, -20, -4, 1, 6, 0, -12, -8, -4, -20, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "38.2.a.a", "char_is_minimal": false, "conrey_index": 429, "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], [1, 0], [1, -1], [-1, 1], [0, -1], [0, 0], [0, 1], [-1, 0], [-1, 0], [0, 2], [0, 0], [-6, 0], [1, 0], [0, -5], [-1, 1], [0, 0], [-1, 1], [-3, 3], [2, 0], [0, 0], [0, 0], [1, -1], [-6, 6], [0, -3], [1, -1], [0, 5], [-5, 0], [-5, 0], [0, 1], [0, -9], [0, 0], [-4, 0], [0, 1], [6, -6], [0, 3], [0, 0], [2, -2], [2, 0], [0, 0], [5, 0], [0, 0], [0, 0], [0, -1], [-8, 8], [0, 6], [0, 0], [-3, 0], [0, 0], [0, -1], [-6, 0], [5, 0], [0, -3], [-5, 5], [0, 3], [-5, 5], [0, 0], [1, 0], [0, 0], [-9, 0], [-9, 9], [0, 0], [0, 10], [-4, 4], [0, -2], [1, 0], [0, 0], [0, -6], [0, -5], [3, 0], [3, 0], [0, 0], [6, -6], [0, -2], [7, -7], [2, -2], [-5, 0], [0, 0], [6, 0], [5, -5], [10, -10], [0, 0], [-1, 1], [0, 0], [-6, 0], [-1, 0], [0, 0], [0, 8], [9, 0], [6, 0], [0, 12], [0, 0], [0, 5], [-3, 3], [4, -4], [0, 0], [0, 0], [-1, 0], [10, -10], [-6, 6], [0, -12], [5, -5]]}