# Stored data for newform 637.2.q.a, downloaded from the LMFDB on 19 April 2024.
{"label": "637.2.q.a", "space_label": "637.2.q", "level": 637, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1099545182845, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1658937276552948324, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [3, 3, 1]], [3, [4, -2, 1]]], "qexp_display": "q+(-1-\\zeta_{6})q^{2}+(2-2\\zeta_{6})q^{3}+\\zeta_{6}q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "q", "char_is_real": false, "Nk2": 2548, "analytic_conductor": 5.086470608755561, "hecke_ring_index": 1, "level_radical": 91, "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": "0.180", "prec": 17}, "analytic_rank_proved": true, "char_values": [637, 6, [248, 197], [6, 5]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [7, 13], "conrey_indexes": [491, 589], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "1.947", "prec": 17}, {"__RealLiteral__": 0, "data": "0.187", "prec": 17}, {"__RealLiteral__": 0, "data": "11.375", "prec": 20}, {"__RealLiteral__": 0, "data": "2.027", "prec": 17}, {"__RealLiteral__": 0, "data": "90.845", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c6", "trace_display": [-3, 2, 0, 0], "traces": [0, 2, -3, 2, 1, 0, -6, 0, 0, -1, 3, 0, 4, 5, 0, 6, 5, -3, 0, 6, -3, 0, 0, 6, 6, 4, -3, 8, 0, -3, -6, 0, -9, 0, 0, 0, 1, 15, -12, 14, -6, 9, 0, -8, 0, 3, -18, 0, -10, 0, -6, -12, -2, -6, -12, 0, 0, 0, 9, -12, 0, 1, -6, 0, -2, -9, 0, 6, 3, -12, 0, 6, 3, 0, -15, 4, 6, 0, -24, 8, 15, 11, -9, 0, 0, 9, 0, 6, 0, 12, -6, 0, 12, -12, 6, 6, 0, -12, 0, 0, 2, -3, 18, 20, -9, 0, 9, -6, 4, 0, 0, 30, 0, 15, -12, 18, -6, 2, 24, 0, -6, -11, 0, 18, 6, 0, 0, 2, 21, -32, 21, -36, 0, 0, -6, 0, 9, -27, 0, -4, 0, 12, -12, 0, -10, -9, -3, 0, 0, -33, -12, 0, 6, -3, 0, 12, 10, 26, -12, -6, -9, 0, -33, 36, 0, 0, -24, 24, 0, -1, -18, -6, 8, 6, 0, 0, 0, 0, -12, 0, 3, -22, 0, 4, 18, -15, 12, 0, -6, 0, 0, -18, -2, -9, 24, 6, 0, 24, 0, -2, 0, 12, 9, 0, -6, -9, -30, -12, 35, 0, 0, -10, -3, 0, 18, 24, 0, 0, -24, -6, 0, 6, -60, 18, 0, -2, 0, -42, 12, 0, -18, 0, -9, 12, -9, -12, -12, 8, 0, 0, 30, 3, 0, -10, -1, 0, -36, 24, 12, -48, 21, -18, 0, 0, -6, 0, -19, 3, 48, 0, -12, 6, 54, -12, 0, 0, 0, 24, 0, -6, 12, -36, -30, 0, 54, 0, 12, 7, 0, -6, 0, 0, -12, 4, 6, 24, 0, 0, 9, 8, 9, 0, 3, -9, 0, -12, -15, 0, 66, 42, 8, 0, 30, 6, 0, -3, 9, 0, 0, 20, -18, 60, 6, -20, -39, 0, 4, 0, 18, 0, 0, 12, 0, -18, 22, 10, -72, -48, -9, 0, 0, -48, 24, 0, -24, -6, 0, -46, 24, 60, 9, 0, 6, 0, 24, 36, 0, 30, -6, -24, 0, 20, 0, -57, 24, 6, 0, 0, 0, 0, 3, -7, 33, -44, 0, 6, -6, -22, -30, 0, 45, 0, 0, -19, 0, 42, -12, -21, 0, -42, -6, -4, 0, 36, 42, 0, 9, -8, -12, -18, 12, -36, 0, -36, -24, 0, 0, 24, 0, 0, 10, -3, -24, 18, -6, 33, 0, 0, 0, -27, 27, 0, 10, 0, 18, 48, -36, -16, 0, 18, 0, 0, 30, 6, 0, -6, -12, 0, -12, 0, -48, -12, 20, -17, 0, -18, 24, 0, 6, -28, 0, 0, -27, -24, 30, -12, -18, 0, 0, -12, 0, 0, -15, 60, 84, 0, 24, 3, 0, -12, 0, -39, 0, 0, 15, 12, -18, -24, 7, 0, 18, 26, -12, 0, -24, 12, 0, 3, -36, -42, -36, 15, -6, 0, 11, -12, 0, -12, -3, 0, 0, -12, 18, 18, -30, 0, -30, 0, 48, 0, -21, 48, 0, 36, 0, -9, 0, 44, 4, -33, -18, 0, 0, 24, -9, 0, -16, 0, 0, 24, -15, -18, -9, -16, -18, 0, 36, -18, 0, -13, -9, 12, 0, 9, -48, -18, -6, 0, 0, 0, -12, 0, 36, -22, 27, 48, 0, -44, -27, 1, 0, 0, 36, 0, 0, 30, 4, -27, 12, 16, 0, 0, -39, 0, 0, -45, -12, 0, 6, 42, -36, 80, 0, -72, 0, 12, 1, 0, -24, -18, 0, 0, 24, 0, 6, 12, 18, 36, 0, -12, 0, 48, 75, 0, 0, 0, -33, -8, -72, 60, 12, 25, 0, 0, -30, 33, 0, -34, -18, 0, 6, -18, -6, -21, 30, 18, 0, -39, -60, 0, 6, 24, -90, 0, 20, -22, 30, 0, 13, 0, 0, -84, 0, 20, -9, 6, -12, 0, 0, -6, -21, -33, 0, -24, 0, 0, 18, 18, 33, 0, -6, 0, 36, 30, 48, 0, 45, -3, 0, 12, 0, 81, 96, -30, 48, 0, -15, 18, 0, 36, 18, 0, 0, 19, 69, 16, -23, 12, -90, 0, 9, 0, 0, 42, 0, -27, 0, 0, -80, -15, -72, -24, -6, 0, 0, 12, -18, 0, 24, 12, 0, 36, -12, 60, 0, -12, 57, 0, -24, -9, 0, -4, -12, -36, 0, 0, 0, -72, -12, -48, 0, 0, 21, 0, -11, -6, 66, 64, 0, 26, -9, -24, 2, 0, 66, 0, 0, 0, -9, -36, -30, 36, 0, -60, 12, -33, 0, -24, 0, 0, -42, 16, 30, -72, 36, -60, 0, 26, 42, 0, -18, -60, 0, 0, 18, -9, -72, -48, -76, -12, 0, -6, 0, 60, 24, 0, -12, 0, 27, 36, -18, 0, 54, -12, 0, 0, 108, -66, 0, 24, 12, 0, 0, -2, -48, -18, 2, 42, 0, 18, -18, 0, 3, 0, 12, 0, -42, -24, -9, -33, -33, 0, 0, -72, 0, 36, -30, -48, 54, 0, -18, -72, 54, 4, 0, 0, 0, 0, -6, 25, -72, 28, -5, 0, 24, -24, 0, 0, -54, -78, 0, 20, 27, -78, -20, -45, -12, 0, -15, -8, 0, 90, 12, 0, 0, 6, -18, -6, 0, 28, 24, 0, 12, 0, -36, -18, 0, -16, 0, 0, 36, 6, 48, 12, -36, 0, 0, 21, 84, 0, 0, 27, 0, 20, 21, -48, 36, 36, 30, 0, 36, 0, 0, 12, 66, 0, 0, 24, 24, 18, 2, 9, 0, 0, -45, 0, -60, -28, -42, 6, 0, 0, -60, 0, -3, 0, 0, 0, 0, -22, -18, 60, 78, 24, 0, 30, 24, -10, 0, 81, -36, 0, 6, 60, 36, 0, 12, -14, 0, -20, -6, 0, -78, 54, 0, 0, 0, -30, 16, 9, -24, -18, 0, 6, 0, 54, 36, 0, 42, 0, -6, 38, 30, 12, 3, 9, 0, 0, 33, -36, 0, 6, 10, 0, 24, 28, 10, 75, -72, 0, 0, -24, 36, 0, 18, -24, -27, 0, 6, -96, 0, -2, 18, 0, 0, 6, 0, 17, 54, 60, -42], "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, 13, 5, 1, 6, 0]], "char_orbit_index": 17, "prim_orbit_index": 5, "minimal_twist": "13.2.e.a", "char_is_minimal": true, "conrey_index": 491, "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], [2, -2], [0, 1], [-1, 2], [-4, 2], [0, 0], [-1, 2], [0, -1], [3, -3], [0, 0], [2, 0], [1, 3], [0, 0], [2, 2], [5, -5], [0, -3], [-1, 2], [4, -2], [-2, 1], [0, 0], [0, 0], [6, -6], [2, 2], [2, 0], [2, -7], [4, 0], [0, 0], [-3, 3], [0, -6], [2, -4], [-6, 3], [0, 0], [-3, 6], [0, 0], [1, -1], [5, 5], [-6, 0], [8, -2], [-3, 0], [3, 3], [0, 0], [0, -8], [0, 0], [2, -1], [-12, 6], [-2, 4], [0, -10], [0, 0], [-2, -2], [-6, 0], [-3, 4], [-3, 0], [-4, -4], [0, 0], [0, 0], [4, -8], [6, -3], [-8, 4], [-2, 4], [0, 1], [-6, 6], [0, 0], [-1, 0], [-7, 5], [0, 0], [2, 2], [3, -3], [0, -12], [0, 0], [4, -2], [2, -1], [1, -2], [0, -15], [4, -4], [2, 2], [0, 0], [-10, -4], [4, 0], [5, 5], [11, -11], [0, -9], [8, -16], [0, 0], [6, -3], [-8, 16], [0, 6], [0, 0], [4, 4], [-3, 0], [0, 0], [6, 0], [-4, -4], [6, -6], [0, 6], [-6, 12], [-8, 4], [0, 0], [0, 0], [0, 2]]}