# Stored data for newform 637.2.a.j, downloaded from the LMFDB on 08 December 2025. {"Nk2": 2548, "analytic_conductor": 5.086470608755561, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[7, -1], [13, 1]], "atkin_lehner_string": "-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [637, 1, [248, 197], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 316, "field_disc_factorization": [[2, 2], [79, 1]], "field_poly": [2, -4, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [2, -4, -1, 1]], [3, [8, -6, -2, 1]], [17, [4, -10, 4, 1]]], "hecke_orbit": 10, "hecke_orbit_code": 40532396679889533, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "637.2.a.j", "level": 637, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [7, 13], "level_radical": 91, "minimal_twist": "91.2.a.d", "nf_label": "3.3.316.1", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{1}q^{2}+(1-\\beta _{1}+\\beta _{2})q^{3}+(1+\\beta _{2})q^{4}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "637.2.a", "trace_display": [1, 2, -2, 0], "trace_hash": 973744459687226268, "trace_moments": [{"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "2.856", "prec": 17}, {"__RealLiteral__": 0, "data": "0.163", "prec": 17}, {"__RealLiteral__": 0, "data": "20.407", "prec": 20}, {"__RealLiteral__": 0, "data": "2.558", "prec": 17}, {"__RealLiteral__": 0, "data": "215.130", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "traces": [0, 3, 1, 2, 3, -2, -4, 0, 3, 7, 8, 2, 12, -3, 0, -6, -1, -4, -15, 4, 2, 0, -4, 10, 12, -5, -1, 8, 0, 24, 20, 4, 7, 16, -14, 0, -1, 0, 10, -2, 2, -2, 0, 10, 12, -22, -18, 8, -20, 0, -15, -8, -3, 8, -32, -6, 0, -2, 12, 4, -8, 6, 2, 0, -17, 2, -12, -12, -22, 6, 0, -6, -1, 10, 30, 16, 8, 0, 4, -14, 14, 3, -10, 12, 0, -10, -26, 26, 12, -2, 28, 0, -12, -22, 10, 6, 4, 10, 0, 14, 1, -32, -20, 16, -3, 0, 8, 0, -8, 0, 20, -4, 0, 12, 12, -28, 38, -7, -32, 0, -8, -17, 2, 28, -20, 0, 0, 0, -41, -14, -8, -16, 8, 0, -40, -40, -22, -8, -56, 18, 0, 50, 20, -2, -29, -12, 28, 0, 26, 20, -20, 10, 8, 16, 0, -2, -12, -4, 26, -34, -26, 0, -35, 0, 18, -28, 66, 16, 0, 3, -16, -8, -40, -8, -24, 0, -20, -28, -36, 34, -30, -24, 0, 4, -12, 30, -4, -8, 60, 0, 6, -4, -12, -22, 12, 6, 0, 2, -44, -6, 1, 60, -6, 0, -16, -8, 24, 66, 1, -2, 0, 2, -26, -28, 8, -36, -8, 0, -38, 42, -8, 4, 60, 20, 0, 15, 24, 32, 16, 10, 26, 0, 38, 32, 15, 2, -60, -38, 0, -28, 48, -6, -23, 46, 6, 0, -16, -4, -20, -74, -34, 26, 0, 6, 52, -12, -1, 12, -72, 0, -2, 48, 20, -6, 8, 0, 0, 42, 20, -2, 40, -64, -6, 0, -14, 16, 40, -4, -32, 8, 0, 0, 4, 0, -8, 14, 4, 0, 59, -15, 74, 2, 70, 18, 0, -36, 26, 24, -6, -10, -20, 0, 60, -36, 12, -4, 18, -60, 0, -48, -14, -18, -12, 36, -74, 0, -12, 30, 0, 26, -10, 20, 0, -18, 35, 5, 44, -16, 18, 0, 52, 8, -8, -60, -2, -28, 0, -12, 1, 58, -28, -22, -2, 0, -40, -62, 22, 28, 96, 2, 0, -8, 4, 62, -72, 26, 6, 0, 86, 6, -30, -43, -22, -2, 0, 18, -8, -18, -24, 14, -4, 0, 16, 14, -20, -6, 60, -24, 0, -2, 20, -28, -28, 52, -28, 0, 2, 82, 14, 10, -20, 30, 0, 0, 38, 40, 28, 38, 72, 0, -31, -6, -56, -4, -42, -38, 0, -4, -16, -2, 24, -60, -24, 0, -70, 54, -7, -4, 12, 14, 0, -12, 58, 4, -26, 14, 52, 0, 28, -16, 6, 68, -56, -10, 0, -50, -54, -8, 36, -48, -8, 0, 14, 42, 0, -34, 22, 8, 0, -34, -27, 28, 82, -36, 36, 0, 16, -64, -58, 40, -36, -78, 0, 18, -14, 18, 24, 54, 1, 0, 66, 0, -60, -14, 80, -20, 0, 8, 0, 16, -56, 0, 24, 0, -25, 2, 20, 72, 6, -48, 0, 20, -8, -50, -10, -58, 24, 0, 108, -22, -40, -34, -48, 52, 0, 26, -56, 2, 24, -74, -12, 0, -9, -24, 78, 8, 40, 50, 0, -128, -2, -50, -136, -24, 20, 0, 46, 18, -32, 29, -18, 76, 0, 2, -68, 8, 20, -54, 70, 0, -64, -12, -56, 28, 34, -38, 0, -38, -74, 14, -20, 36, 40, 0, -24, 64, -36, -42, 30, -10, 0, 4, -82, 100, 32, 12, 76, 0, -8, -4, 0, -50, -12, 36, 0, 4, 3, -46, 63, -44, 24, 0, 4, -34, 70, 22, 4, 0, 0, 6, -20, -116, 34, 30, -80, 0, 2, -56, 18, -54, -20, -54, 0, 44, 24, -6, 52, -58, -12, 0, 16, -8, 34, -26, -46, -44, 0, -26, 16, 4, 4, 112, -44, 0, 20, -9, -18, 4, -74, -56, 0, -76, -12, -66, 2, 52, 32, 0, -24, -58, 6, -20, 16, 0, 0, -58, -44, -10, 35, -28, 15, 0, -4, 26, -76, 36, -38, -26, 0, -10, -24, 10, 32, 8, -8, 0, 38, 58, -36, 78, 36, 4, 0, 28, -104, 40, 3, -32, 24, 0, -28, 32, -4, -48, -32, -6, 0, 64, -12, -8, 108, -32, -106, 0, -76, -50, 96, -8, 32, 2, 0, 44, 32, 30, -12, -46, -22, 0, 16, 8, -40, -94, 6, 36, 0, 6, 32, -48, 12, 30, 86, 0, 7, -18, 6, -34, -12, 68, 0, 7, 62, 66, 24, -38, 44, 0, 88, 60, -58, -46, 60, 2, 0, 40, 16, -26, 10, -96, -16, 0, -68, 18, -40, 60, -12, 50, 0, -28, -52, 96, 20, -10, 104, 0, 8, 2, -8, -4, 36, -6, 0, -44, -42, 34, -38, -32, 14, 0, 42, -12, 8, -28, 40, 48, 0, -70, 72, -72, -78, -42, -66, 0, 28, -6, -48, 34, 16, -34, 0, -70, 9, 66, -10, 42, -48, 0, -2, -88, -42, -56, 76, -92, 0, -24, 60, 44, -24, -16, 68, 0, -20, 30, -12, 28, -24, 0, 0, -8, 60, 60, -50, 46, 17, 0, -100, -18, 16, 8, 40, 28, 0, 119, 38, 32, -8, -2, -122, 0, 42, 32, 38, -86, -24, -14, 0, 6, 28, 22, 12, 24, -52, 0, -20, -40, 104, 30, -62, 2, 0, -38, 172, 12, -54, 6, -10, 0, 40, -52, -12, 86, 48, -34, 0, -76, 22, -44, 34, 100, 0, 0, 38, 70, 100, 18, -52, 52, 0, -6, 22, 8, 61, 18, -16, 0, 82, 2, 100, 58, 68, -84, 0, 82, 8, -74, -14, -12, 6, 0, 64, 32, -36, -26, -70, 6, 0, -34, -24, 0, 34, 58, -24, 0, 26, -28, -64, -12, 1, 32, 0, 28, 20, -98, -140, -8, -4, 0, -72, 68, -56, -10, -24, 0, 0, 56, 44, -24, -48, 120, 34, 0, -8, -39, -30, -16, 6, 24, 0, 34, -25, -28, 22, 36, 36, 0, 76, -16, -2, -4, 88, 42, 0, 76, -8, -60, -8, 36, -148, 0, -8, 142, 100, 48, 32, -132, 0, 78, 48, 86, -32, -120, -40], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, -1, 1], [1, 0, 1], [-1, 1, 0], [-2, 2, 0], [0, 0, 0], [1, 0, 1], [3, -2, 0], [3, -1, 1], [1, -1, 1], [4, 0, 0], [-1, 0, 0], [0, 0, 0], [-3, 3, -1], [-1, 2, -1], [-1, -1, -1], [-6, 3, -2], [1, 1, 0], [0, 2, 0], [0, 0, 0], [-2, 2, 0], [4, -2, -1], [4, 0, 0], [-1, -2, 1], [0, -1, 0], [4, -4, 0], [0, 0, 0], [8, 0, 1], [8, -4, 2], [1, 1, -2], [3, -2, -1], [6, -2, 0], [-4, -2, -2], [0, 0, 0], [1, -4, 1], [-1, 3, 1], [3, 1, 1], [-1, 1, -1], [0, 2, 0], [0, -2, 2], [0, 0, 0], [4, -2, -3], [4, 0, 0], [-9, 5, -2], [-7, 3, -3], [3, -1, 4], [-8, 4, 0], [0, 0, 0], [-5, 0, -1], [-2, -2, 0], [-1, 0, -1], [2, 2, -3], [-12, 4, -4], [-3, 3, -1], [0, 0, 0], [-1, 1, 1], [1, 9, 1], [2, -2, -4], [-4, 4, 0], [2, 0, 0], [1, -1, -1], [0, 0, 0], [-5, -2, -1], [1, -1, 0], [-6, 6, -2], [-2, -6, 4], [-6, -4, -2], [5, -9, 5], [0, 0, 0], [-3, 3, -1], [1, -4, 1], [3, 1, 4], [10, 0, 4], [6, -2, -2], [2, 2, 2], [0, 0, 0], [2, -2, 0], [-6, 4, -1], [6, -4, 2], [3, -6, 4], [-4, 2, 0], [1, 9, -4], [0, 0, 0], [-3, -1, -1], [-9, 1, -5], [11, -7, 7], [4, 0, 0], [1, -5, 2], [13, -11, 3], [0, 0, 0], [-2, -6, 2], [-7, -1, 3], [1, 7, 3], [2, 0, 1], [4, -8, 4], [3, 1, 0], [0, 0, 0], [7, -7, 3], [1, -2, -3]]}