# Stored data for newform 637.2.g.c, downloaded from the LMFDB on 19 April 2024.
{"label": "637.2.g.c", "space_label": "637.2.g", "level": 637, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007611605156477, "dim": 4, "is_polredabs": true, "nf_label": "4.0.225.1", "trace_hash": 1323326626812349850, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 3, 8, 3, 1]], [3, [1, -3, 1]], [5, [1, -3, 8, -3, 1]]], "qexp_display": "q+(-1-\\beta _{1}-\\beta _{3})q^{2}+(1-\\beta _{2})q^{3}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 91, "char_orbit_label": "g", "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": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [637, 3, [248, 197], [2, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [7, 13], "conrey_indexes": [263, 373], "field_disc": 225, "field_disc_factorization": [[3, 2], [5, 2]], "field_poly": [1, 1, 2, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "4.052", "prec": 17}, {"__RealLiteral__": 0, "data": "0.613", "prec": 17}, {"__RealLiteral__": 0, "data": "61.191", "prec": 20}, {"__RealLiteral__": 0, "data": "20.071", "prec": 20}, {"__RealLiteral__": 0, "data": "1558.026", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-3, 6, 3, 0], "traces": [0, 4, -3, 6, -3, 3, -7, 0, 12, 2, -14, -6, -12, 10, 0, 7, -13, 6, -9, -6, 12, 0, -3, 0, 38, 3, -21, 0, 0, -3, -36, 4, -15, 6, 2, 0, -24, -8, -3, 15, 19, 6, 0, -5, -18, 9, 10, 0, -27, 0, -3, -1, 6, -12, -5, 3, 0, 6, 34, 0, 33, 24, -9, 0, 8, -6, -12, -24, -21, 10, 0, 6, 66, -4, -12, -3, -18, 0, -49, -8, -54, 4, -8, 0, 0, 1, -30, -17, 42, 21, -52, 0, -60, -9, 10, 3, -30, 31, 0, 42, 36, 6, 18, -4, 30, 0, -13, 9, -15, -8, -24, -12, 0, 6, -12, 20, -42, 5, 10, 0, 51, 10, -18, 4, 78, 24, 0, 35, 9, -30, -35, -15, -27, 0, 33, 5, -22, 3, 30, -11, 0, -5, 34, -15, -29, 17, -6, 0, 24, -6, -12, 16, 42, -27, 0, -18, 24, 23, 24, -13, 30, 0, 12, 12, -6, 12, 15, 24, 0, -2, 9, 42, 150, 36, 96, 0, -3, -5, 19, -36, 51, -12, 0, 36, 40, -24, -31, -39, -15, 0, -24, 90, 42, -24, 54, -14, 0, 9, -24, -22, -21, -66, -27, 0, -24, -4, 42, 30, -91, 54, 0, 4, 6, 34, 11, -60, 40, 0, 3, -6, 27, -12, -28, 7, 0, -21, -1, -6, -27, 14, -30, 0, -59, -3, -63, 5, -15, -12, 0, -72, -136, 29, 15, -24, -18, 0, -12, -15, -48, -30, -23, 6, 0, 30, -120, 9, 9, -9, -85, 0, 84, -39, 80, 36, 78, -26, 0, 19, 63, -15, -30, 10, -18, 0, -14, -27, -120, 10, 6, -43, 0, 36, 30, 0, -168, 12, -21, 0, -30, -24, 48, 54, 12, -18, 0, 5, -24, 30, -3, 0, 54, 0, 9, 54, -3, 18, 46, 6, 0, -21, 31, -9, 95, 10, 42, 0, -12, -48, -27, -33, 21, 11, 0, -39, 42, 21, 6, 3, -2, 0, -66, -54, 45, -4, -82, -33, 0, -6, -66, -1, -48, -51, -24, 0, -105, 60, -27, -66, -93, 28, 0, 0, 0, -102, 30, 68, 12, 0, 27, 33, 77, -22, 24, -30, 0, -12, -42, -48, 30, -12, 28, 0, 132, -42, 42, 46, -20, 6, 0, 19, 27, 60, -65, -6, 1, 0, 18, -70, -138, -12, -90, -80, 0, -40, -82, 12, -9, 48, 126, 0, -3, -15, 87, 28, -72, -12, 0, 12, -33, 49, -6, 7, -51, 0, 50, -15, 30, 6, -18, -6, 0, -48, 18, -15, -16, 78, 96, 0, -12, 15, 85, -18, -15, 2, 0, 48, -66, 30, -14, 23, 39, 0, 5, 6, 96, 38, -96, 6, 0, -48, -24, -24, 42, 9, -2, 0, 78, -4, 48, -20, -60, 27, 0, 0, 114, -62, 14, 36, 48, 0, 15, 42, -20, -60, 56, -27, 0, 9, 69, -6, 75, -56, -132, 0, 60, 108, 53, -13, 72, -12, 0, -27, 6, -41, -21, 24, -19, 0, 45, -23, -33, 41, 4, 51, 0, 27, 30, -3, 75, 12, 26, 0, -36, 30, 34, 21, 330, -15, 0, 54, -38, 6, 152, -38, -75, 0, -27, 144, -42, 6, 27, -15, 0, -12, 36, 22, -192, -54, 140, 0, 30, -37, -15, -48, 15, 6, 0, -12, 12, 12, -18, -33, 90, 0, -30, -56, -102, -18, -57, -35, 0, -21, -52, -60, -30, -2, 30, 0, 118, -12, -66, 11, 36, 130, 0, 30, 94, -34, 24, -36, -186, 0, 131, 33, -12, -18, -22, -51, 0, -51, 15, 41, -52, 63, -15, 0, -18, -63, -20, -21, -39, 7, 0, -102, 42, -15, -78, 92, 0, 0, -84, 0, 12, 98, -12, -6, 0, -18, 118, -8, 66, 20, 4, 0, -189, 8, -120, 36, -114, -48, 0, 5, -24, -9, 154, -60, 84, 0, 84, 78, 2, 57, 24, -14, 0, -170, 42, -108, -108, -15, 6, 0, 36, 3, 17, 40, -48, -2, 0, 12, 63, 60, 33, 2, -120, 0, -36, -100, 51, 48, 174, -36, 0, -2, 27, -15, 69, 45, -9, 0, 33, 1, -39, 6, -9, -7, 0, -24, -100, -84, -80, -5, -27, 0, 188, 12, -141, -38, -114, -7, 0, 36, -35, 12, 78, 15, 69, 0, -30, 54, -96, -4, 13, 60, 0, -6, 27, -138, -124, 48, -192, 0, 39, 66, 54, 66, 50, 96, 0, -118, 14, 150, -72, -31, 6, 0, -60, -54, -4, -108, 48, 15, 0, -63, -97, 3, 54, -90, 54, 0, -57, -32, 30, 4, 85, 18, 0, -56, -42, 30, 39, 102, -290, 0, -60, 23, -48, 0, 36, -10, 0, 34, 18, 6, -135, -51, 123, 0, 22, -24, 231, 66, 30, -25, 0, 84, 210, 32, 96, 54, 28, 0, 66, 60, -6, -54, -123, 6, 0, -20, 0, -27, -85, 6, 162, 0, 18, -70, 198, 36, 76, -90, 0, -15, -12, -6, 58, -60, -102, 0, 12, -30, -36, 50, -72, -18, 0, -30, -120, 10, 90, 15, 20, 0, 29, -41, 27, -30, 58, -15, 0, -9, 6, 104, -39, -69, 50, 0, -63, -60, -21, 0, -372, 24, 0, 24, 17, 3, -84, -8, 165, 0, -14, 12, -15, 27, 3, 24, 0, 12, 127, -60, 36, 38, 30, 0, 48, -24, 42, -22, -84, -24, 0, 116, -147, 15, -28, 78, -76, 0, -36, -96, 123, -15, -12, -27, 0, 70, -62, 138, 18, -112, 12, 0, -22, -24, 11, -96, 21, 138, 0, 30, -42, -90, -36, 42, -114, 0, 30, -120, 180, 24, -17, 42, 0, 12, -15, -47, -60, 72, 84, 0, -12, 4, -38, 21, 165, 144, 0, 60, -60, 72, 103, -40, 30, 0, -75, -9, -48, -28, -18, -77, 0, 18, -29, 65, 99, -42, 57, 0, 59, -36, 24, -3, 111, -18, 0, -156, -150, -21, -131, -180, 123, 0, 144, -21, -78, -108, 24, -69, 0, 41, 76, 39, 12, -41, -39, 0, 36, 90, -102, -78, 30, -66, 0, 63, 90, 98, 84, 0, 112], "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, 7, 1, 3, 0]], "char_orbit_index": 7, "prim_orbit_index": 7, "minimal_twist": "91.2.f.a", "char_is_minimal": false, "conrey_index": 263, "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], [-1, -1, 0, -1], [1, 0, -1, 0], [0, 3, 3, 0], [0, -1, -1, -1], [-2, -3, 0, -2], [0, 0, 0, 0], [1, 0, -4, 0], [-1, 0, -3, 0], [-2, 0, 3, 0], [-3, 0, -3, 0], [0, 6, 6, 3], [1, 0, 0, -3], [0, 0, 0, 0], [0, -3, -3, -2], [-5, -3, 0, -5], [0, 4, 4, -5], [-2, -5, 0, -2], [-3, 0, -3, 0], [3, 6, 0, 3], [0, 0, 0, 0], [0, -3, 0, 0], [-2, 4, 0, -2], [5, 0, -9, 0], [3, -3, 0, 3], [-4, -1, 3, -1], [-1, 0, -2, 0], [0, 0, 0, 0], [0, 5, 5, -1], [-5, 0, 8, 0], [5, -6, 0, 5], [0, 3, 3, 6], [0, 0, -3, 0], [-1, 0, -3, 0], [0, 0, 0, 0], [0, 6, 6, 9], [-4, 0, 0, -4], [0, -3, 0, 0], [1, -3, -4, -3], [0, -9, -9, -5], [0, 2, 2, -4], [0, 0, 0, 0], [2, -9, 0, 2], [0, 0, 0, 9], [0, -5, -5, -2], [0, -6, -6, -2], [0, 2, 2, -1], [-8, -11, 0, -8], [0, 0, 0, 0], [0, 3, 3, 0], [0, 3, 3, -1], [0, 12, 3, 0], [-7, 2, 0, -7], [-1, -3, 0, -1], [0, -3, -3, 0], [0, 0, 0, 0], [0, 0, -3, 0], [4, 0, -9, 0], [0, 2, 2, -1], [9, 15, 0, 9], [6, 0, 0, 0], [0, 7, 7, 1], [0, 0, 0, 0], [-1, 0, -6, 0], [-3, -4, -1, -4], [-3, -6, 0, -3], [-3, 0, 6, 0], [-12, 3, 0, -12], [2, 6, 0, 2], [0, 0, 0, 0], [-2, 10, 0, -2], [11, 0, -11, 0], [-2, 0, 0, -2], [0, 4, 4, 4], [0, -3, 0, 0], [0, 0, 0, 9], [0, 0, 0, 0], [-8, -3, 9, -2], [0, 0, 0, 4], [-8, 0, 11, 0], [4, 0, 6, 0], [-2, 0, 0, 0], [3, 0, 6, 0], [0, 0, 0, 0], [-1, 3, 0, -1], [0, 16, 16, 7], [0, 9, 9, 4], [9, 0, -3, 0], [13, -5, 0, 13], [-7, 0, 12, 0], [0, 0, 0, 0], [-12, 0, 6, 0], [-1, -7, 0, -1], [1, 0, -3, 0], [0, -3, -3, 0], [0, 12, 12, 9], [14, 3, 0, 14], [0, 0, 0, 0], [12, 0, 3, 0], [9, 0, 0, 0]]}