# Stored data for newform 637.2.k.d, downloaded from the LMFDB on 24 April 2024.
{"label": "637.2.k.d", "space_label": "637.2.k", "level": 637, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13511486110433917, "dim": 4, "is_polredabs": true, "nf_label": "4.0.441.1", "trace_hash": 949287619917119317, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 0, 5, 0, 1]], [3, [25, -5, 6, 1, 1]]], "qexp_display": "q+(\\beta _{1}-\\beta _{3})q^{2}+(1-2\\beta _{1}-2\\beta _{2}+\\beta _{3})q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 91, "char_orbit_label": "k", "char_is_real": false, "Nk2": 2548, "analytic_conductor": 5.086470608755561, "hecke_ring_index": 1, "level_radical": 91, "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": "0.177", "prec": 17}, "analytic_rank_proved": true, "char_values": [637, 6, [248, 197], [4, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [7, 13], "conrey_indexes": [459, 569], "field_disc": 441, "field_disc_factorization": [[3, 2], [7, 2]], "field_poly": [4, -2, -1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.037", "prec": 17}, {"__RealLiteral__": 0, "data": "3.993", "prec": 17}, {"__RealLiteral__": 0, "data": "0.256", "prec": 17}, {"__RealLiteral__": 0, "data": "59.012", "prec": 20}, {"__RealLiteral__": 0, "data": "7.372", "prec": 17}, {"__RealLiteral__": 0, "data": "1318.249", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, -1, -3, 0], "traces": [0, 4, 0, -1, -2, -3, 9, 0, 0, -5, 5, 9, -10, 14, 0, -9, 2, 12, -3, 9, 12, 0, -1, 12, 3, -5, -3, 20, 0, 9, -8, -30, 0, -15, 0, 0, -8, 0, 15, -5, -3, 18, 0, -5, 6, 0, 0, -24, -11, 0, -3, -3, -7, 6, 0, -1, 0, 0, -3, 0, 15, 2, -15, 0, 32, -9, 10, -12, -6, 18, 0, 6, -15, 12, -24, 26, -36, 0, 27, 12, 9, 10, 2, 0, 0, -9, 24, -30, 9, 0, -4, 0, -48, 0, 5, -30, 0, -39, 0, 0, -8, -15, 27, 0, 6, 0, -51, -30, -10, 0, 12, -12, 0, -12, 48, -30, 6, -10, -50, 0, 9, -5, 60, 0, 15, 0, 0, 9, 0, -34, 25, 21, -45, 0, 27, -15, 0, 0, 48, -3, 0, 33, 4, 27, -13, 0, 6, 0, 0, -3, 0, 42, -9, -15, 0, 30, -50, -21, 18, 78, -14, 0, 36, -24, 12, -20, 22, 60, 0, 46, 15, 9, -29, -12, 0, 0, 15, 87, -2, 18, 0, 0, 0, -128, 0, 12, -90, 27, -9, 0, 0, 15, 13, -12, 30, -36, 0, -15, -16, -44, -15, -57, -33, 0, -30, -4, 21, 6, 7, 6, 0, -12, -45, -24, 0, -24, 0, 0, -21, 0, 11, 42, -36, -3, 0, -23, 3, 0, 0, -24, 36, 0, 27, -9, -12, 5, 0, 6, 0, 0, 6, 0, 39, 14, 62, 0, 40, 36, 30, -45, -54, -24, 0, 6, -66, -27, -2, -66, 9, 0, 36, 33, 0, 18, 15, 0, 0, 69, 69, 54, 25, 0, 6, 0, -86, 0, -30, -8, 6, 75, 0, 0, -29, -22, 18, -24, -5, 0, -42, -32, 24, -12, -6, -18, 0, 25, 48, 45, -5, 42, 50, 0, 21, 3, -27, 0, -9, 0, 0, -21, 0, 21, 9, 14, 84, 0, -6, 0, 0, 0, -45, -3, 0, 27, -26, -10, -12, 0, -18, 0, 0, -45, 0, 60, 37, 27, 0, -6, -21, -27, 36, -90, 6, 0, 15, -48, -45, -36, -90, 18, 0, 70, 28, -15, -19, 4, 0, 0, 27, 21, -6, 7, 0, -58, 0, -12, 0, -36, -36, -66, 60, 0, 0, -69, -3, 57, -24, 18, 0, -57, 78, 96, 9, 9, 93, 0, -36, 88, 51, -36, -16, 36, 0, 42, -25, -18, 0, 30, 0, 0, -13, 0, -39, -120, 18, -36, 0, -36, 9, 0, 0, 111, -21, 0, 12, -11, 21, -12, 0, 24, 0, 0, -3, 0, 18, -15, 2, 0, 36, -60, -19, -33, 10, -10, 0, -30, 63, 90, 36, 18, -3, 0, -9, 12, -120, 1, -54, 0, 0, -78, 18, 68, -15, 0, 62, 0, -54, 0, 12, 60, 78, -39, 0, 0, 15, 45, 39, 42, -16, 0, -39, -84, -12, -54, 54, 9, 0, -27, -70, -15, 35, -24, -36, 0, 34, 30, 21, 0, 6, 0, 0, -33, 0, 27, 30, 8, -15, 0, 5, 105, 0, 0, -78, -3, 0, 33, -24, -22, -57, 0, -24, 0, 0, 45, 0, -21, -25, -43, 0, 138, -15, 42, -24, -24, 21, 0, 111, -90, -60, 28, 114, -99, 0, 72, 32, 33, -12, 9, 0, 0, 60, 63, -114, 42, 0, 42, 0, 8, 0, 68, -16, 9, -54, 0, 0, -36, -9, 9, 15, -25, 0, -45, -56, -72, 120, -3, -96, 0, 6, 12, -99, 27, 18, -78, 0, 6, -19, 96, 0, 132, 0, 0, -69, 0, -12, 3, 16, -45, 0, -45, 69, 0, 0, -45, -5, 0, 12, 11, -30, 27, 0, -11, 0, 0, -21, 0, -78, -12, -42, 0, -116, -72, -24, -33, 120, -20, 0, -78, 21, 12, -120, 60, 42, 0, -55, 2, 84, 30, 63, 0, 0, 27, -36, 54, -49, 0, -60, 0, 12, 0, 33, 90, -78, -102, 0, 0, 45, 6, -30, 37, -12, 0, 12, 54, -42, 0, 30, -30, 0, -12, 10, -120, 9, -15, 12, 0, -12, 6, -51, 0, -93, 0, 0, 2, 0, -25, -23, -63, -33, 0, -9, -81, 0, 0, 27, 43, 0, 12, -34, 12, -66, 0, -57, 0, 0, -6, 0, 54, -33, -57, 0, 36, -15, 36, 51, 58, 67, 0, 30, 39, -6, -60, -66, -90, 0, -2, -9, 105, -28, 30, 0, 0, 105, 108, -84, 33, 0, 56, 0, -38, 0, -15, -20, -45, -54, 0, 0, 3, -16, -12, -48, 27, 0, 69, -30, 10, 114, 57, 18, 0, -39, 40, -33, 30, -12, -42, 0, -12, 3, 60, 0, -33, 0, 0, 24, 0, 8, 6, -10, 60, 0, -36, -120, 0, 0, 75, -39, 0, 138, 6, 60, 16, 0, 45, 0, 0, 63, 0, 60, -75, -30, 0, -66, 4, -48, -69, 22, -24, 0, -72, -42, -135, 158, 36, 60, 0, -30, -24, 45, -24, -46, 0, 0, 27, -12, 24, -33, 0, 6, 0, 44, 0, -52, 20, 0, 90, 0, 0, 18, 55, -27, -61, 112, 0, -3, -74, -66, -150, -99, 129, 0, 7, 84, 168, -15, -24, 38, 0, -39, 52, -9, 0, -30, 0, 0, 6, 0, 63, 20, -28, 33, 0, -50, 84, 0, 0, 111, 8, 0, 54, 15, -36, 0, 0, 108, 0, 0, -66, 0, -12, 10, 24, 0, -48, -21, -19, -24, -108, -12, 0, -30, 24, 159, -30, -16, -27, 0, 90, 32, -135, -41, 18, 0, 0, 36, -42, 126, 18, 0, 54, 0, -90, 0, -23, 60, 54, 12, 0, 0, -6, -30, -150, 37, 18, 0, 60, -42, 42, 84, -54, 120, 0, -48, -168, 21, -3, -60, 28, 0, -56, -34, -72, 0, 12, 0, 0, 29, 0, 60, 48, 6, 147, 0, 30, 33, 0, 0, -120, -31, 0, -93, 88, -84, 27, 0, -36, 0, 0, -15, 0, -129, 72, 35, 0, -72, 91, 64, -96, -72, 67, 0, -63, 144, -9, 60, 50, -9, 0, -144, 48, -9, 67, 105, 0, 0, 33, -30, -72, -84, 0, 24], "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, 91, 11, 1, 6, 0]], "char_orbit_index": 11, "prim_orbit_index": 11, "minimal_twist": "637.2.q.e", "char_is_minimal": false, "conrey_index": 459, "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], [1, 0, 0, 0], [0, 1, 0, -1], [1, -2, -2, 1], [-1, 1, 0, 1], [-1, 0, 0, 1], [3, 0, -1, -1], [0, 0, 0, 0], [-1, 0, 2, 0], [-3, 1, 4, -2], [1, -2, 1, 1], [3, 0, -2, 1], [0, 0, -5, 0], [4, 0, -1, 0], [0, 0, 0, 0], [-2, 1, -1, 0], [0, 1, 0, 1], [3, 0, 0, 0], [0, -1, -1, 0], [3, -3, 0, 0], [4, 0, -1, -2], [0, 0, 0, 0], [-1, 2, 1, -1], [4, -2, 0, -2], [1, 0, -2, 3], [-3, 1, 4, -2], [-1, 4, 0, -3], [5, 0, 0, 0], [0, 0, 0, 0], [5, -1, -6, 2], [-3, -2, 1, 4], [-5, 0, -5, 0], [-3, -1, 6, 1], [0, -5, -5, 0], [0, 3, 0, -3], [0, 0, 0, 0], [-5, 2, 7, -4], [4, 0, -8, 0], [6, 3, -3, -6], [3, -7, -6, 2], [-1, 2, 0, -1], [2, 2, 4, 0], [0, 0, 0, 0], [3, -6, -7, 3], [2, 0, -3, 4], [-1, 1, 2, -1], [2, 6, -4, -6], [-8, 0, 5, -2], [1, -2, -7, 1], [0, 0, 0, 0], [0, -1, -1, 0], [3, -6, -6, 3], [-3, 2, -1, 5], [1, 4, 3, -8], [0, 5, 0, -5], [0, -1, -1, 2], [0, 0, 0, 0], [-3, -3, 6, 3], [-2, 3, 1, 0], [-5, 8, 10, -8], [5, -5, 0, 0], [4, -6, -10, 12], [-5, -5, 0, 10], [0, 0, 0, 0], [9, -2, 0, -2], [-3, -1, 0, 4], [5, 0, -5, 0], [-4, 0, -1, 6], [-3, 3, 0, 3], [2, -4, 6, 2], [0, 0, 0, 0], [2, 0, -2, 2], [-1, -3, -4, 0], [2, 0, 2, 0], [-8, 4, 0, 4], [5, 3, 0, 3], [-9, 6, -3, 0], [0, 0, 0, 0], [10, 1, -5, -4], [0, 0, 6, 0], [3, 0, -1, -1], [2, -4, 2, 2], [0, 2, 2, -4], [3, -4, -6, 4], [0, 0, 0, 0], [-3, 0, 0, 3], [8, 0, -3, -2], [-5, -5, 0, -5], [-1, 2, 6, -1], [-8, 5, 16, -5], [-1, 0, 0, 0], [0, 0, 0, 0], [-14, 4, 0, 4], [-10, 15, 20, -15], [3, -6, -2, 3], [-9, 3, 0, 3], [0, 0, -5, 10], [-13, 0, 5, 3], [0, 0, 0, 0], [-9, 7, 18, -7], [-5, 2, 7, -4]]}