# Stored data for newform 637.2.h.i, downloaded from the LMFDB on 24 April 2024. {"label": "637.2.h.i", "space_label": "637.2.h", "level": 637, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029278088856189, "dim": 8, "is_polredabs": true, "trace_hash": 806389527980417081, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, -3, -6, 1, 1]], [3, [36, -96, 202, -156, 103, -23, 10, -1, 1]], [5, [81, 9, 109, 114, 160, 86, 37, 7, 1]]], "qexp_display": "q+\\beta _{3}q^{2}+\\beta _{5}q^{3}+(1-\\beta _{2}-\\beta _{3})q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 91, "char_orbit_label": "h", "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [637, 3, [248, 197], [2, 2]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [7, 13], "conrey_indexes": [165, 471], "field_disc": 59066497296, "field_disc_factorization": [[2, 4], [3, 4], [43, 2], [157, 2]], "field_poly": [1, 3, 15, -16, 38, 0, 7, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.085", "prec": 17}, {"__RealLiteral__": 0, "data": "7.397", "prec": 17}, {"__RealLiteral__": 0, "data": "4.835", "prec": 17}, {"__RealLiteral__": 0, "data": "200.941", "prec": 24}, {"__RealLiteral__": 0, "data": "203.291", "prec": 24}, {"__RealLiteral__": 0, "data": "9256.918", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 1, -7, 0], "traces": [0, 8, -2, 1, 10, -7, -5, 0, -12, -7, -11, 1, 12, -4, 0, -3, 38, 8, 3, 1, -2, 0, -5, -4, -3, -5, 15, 52, 0, -1, 4, -4, -66, -19, -6, 0, 34, -20, -23, -1, -17, -22, 0, -3, 12, 22, 48, 2, 11, 0, -43, -7, 31, -2, -10, -3, 0, -34, 11, 16, 11, 8, -5, 0, 28, -11, 6, 6, 66, -18, 0, 14, -5, -8, 40, 14, 32, 0, -1, 26, 7, -24, -14, 0, 0, -5, -12, -26, -3, 2, -52, 0, 24, -14, 33, 42, -58, 3, 0, 46, -18, -9, -7, 22, 18, 0, -5, 46, 14, -28, 4, -26, 0, 24, -48, -20, 20, 22, -62, 0, 29, 25, -12, 20, -37, 36, 0, -17, -106, -4, -79, -39, 19, 0, -53, -47, -92, -74, 26, 15, 0, -5, 18, -1, -19, -18, 4, 0, -60, 13, -76, 8, -95, 11, 0, 26, 72, 11, -2, 106, 14, 0, -40, -32, 18, 64, 90, -20, 0, -16, -35, 11, 3, -24, 24, 0, 11, 55, 18, -6, -138, -4, 0, -40, 36, 0, -2, -7, -7, 0, 24, 21, 63, 30, -56, 60, 0, 65, 20, 16, -61, 39, 31, 0, 58, 116, -19, 24, -45, -34, 0, 18, -37, 22, 2, -18, -124, 0, -17, -24, 11, 12, 30, 19, 0, 39, -69, 84, 182, 10, -56, 0, -11, 13, 36, 37, 154, -64, 0, -4, -42, -2, -5, -52, 34, 0, 16, -90, 20, -25, 118, -10, 0, -18, 0, -21, 90, -38, 9, 0, -76, -21, 30, -48, 13, 18, 0, 39, 37, -82, -49, -60, 122, 0, -14, 14, 20, -24, -70, 37, 0, -48, -31, 10, 60, 58, -1, 0, -50, -56, -80, -98, 78, -10, 0, 15, 88, -45, 9, 46, 2, 0, 21, -21, 121, -8, -9, -78, 0, -45, 110, -27, -117, 22, 54, 0, 90, 30, -6, -26, 91, -5, 0, 49, 52, -6, -76, -98, -36, 0, 14, -3, -118, -6, -71, -41, 0, -26, 109, -13, -14, -14, 62, 0, -23, -10, -21, -8, 66, 30, 0, -100, -58, -63, -39, 46, 96, 0, 59, -23, -78, -35, -132, 62, 0, 24, -40, 26, -96, -80, 10, 0, -52, -53, -7, 39, 78, -34, 0, -55, 154, 148, 45, -7, -17, 0, 18, 8, 39, 14, -22, 60, 0, 60, -55, 50, -58, 0, 58, 0, 89, -190, 59, 22, -10, -88, 0, -26, -71, -38, 108, 57, -11, 0, 28, -45, -31, 22, -48, 30, 0, -108, 85, 50, 80, -25, -4, 0, -20, 46, -27, 13, 290, -56, 0, 14, -47, 2, 24, 62, 29, 0, 29, 26, -18, -11, -34, -86, 0, 16, 84, 20, -7, -150, -130, 0, -250, 172, -12, 104, -90, 41, 0, 92, -3, 15, 81, -4, -112, 0, 63, 168, -168, -4, 28, -59, 0, -17, -38, 27, -31, 4, -68, 0, 74, -50, 1, 26, -78, 132, 0, 1, -64, 33, 150, -56, -27, 0, 45, -1, 346, 166, -44, -29, 0, 13, 26, 16, -13, 28, 30, 0, -76, 81, 148, 25, -1, -5, 0, 110, -79, -18, -8, 76, -49, 0, -25, -30, -76, -24, 102, 77, 0, 10, 8, -47, -182, -27, 128, 0, 58, -71, -50, 50, -170, 146, 0, -48, -204, 22, -76, -25, 2, 0, 194, -22, -33, -45, 21, -7, 0, -1, -80, -156, 46, -21, 108, 0, -46, -48, -9, 7, 72, 42, 0, -106, 51, -84, -56, -16, -102, 0, 59, 106, -82, -199, -56, -15, 0, 9, -31, -58, -188, 15, -31, 0, -104, -43, 60, -17, -106, -55, 0, -146, 27, -90, -40, -36, -98, 0, -52, 12, 50, 57, 40, -28, 0, 20, 41, -74, 128, 32, -52, 0, 115, -70, 16, 14, -29, -8, 0, -99, -30, -210, -41, 68, -284, 0, 24, 28, 33, -46, -22, -16, 0, -2, -117, 10, -2, 55, 86, 0, -6, 34, 22, -48, -16, -94, 0, 20, -126, 26, 39, 115, 248, 0, 4, 56, 13, -120, -57, -40, 0, -32, 66, -13, -125, 27, 93, 0, -35, 73, -2, -156, -43, 81, 0, -40, 26, 140, 36, 46, 9, 0, -24, -40, -66, 8, 123, -83, 0, 148, 25, -8, 63, 82, 27, 0, 14, 11, 124, 148, 18, -36, 0, 60, 111, 15, 22, 60, 196, 0, 119, 12, 28, 63, -60, 92, 0, 158, -140, -1, 204, -19, -180, 0, 104, 39, 40, 6, -24, 91, 0, -55, 98, -70, -46, -39, 58, 0, 41, -52, -105, 120, 20, -74, 0, 64, 67, 30, 10, 25, 34, 0, -46, -26, 80, 54, 0, 28, 0, -64, -92, 176, -46, -61, -53, 0, -30, -48, -68, 22, 80, 21, 0, -152, -69, 4, 104, -9, 138, 0, -106, -94, -46, -103, -170, 22, 0, -12, -32, 93, 42, -24, -180, 0, -52, -38, 93, 84, -76, -122, 0, -123, 30, 280, 57, 44, -258, 0, 56, -60, 30, 76, 18, 24, 0, -122, 18, -55, -31, -37, -54, 0, 85, 222, 182, -2, 55, -57, 0, 71, 76, 130, -93, -118, 146, 0, -81, -38, -109, 92, -114, -124, 0, 84, 14, -37, 0, -38, -41, 0, -34, -6, -218, 138, 59, 40, 0, -64, -31, 54, -36, 144, -26, 0, 164, 34, -148, -44, -42, -74, 0, -16, 31, 71, -62, 92, 54, 0, -68, -130, -91, -170, -8, 47, 0, 114, 122, 31, 59, -90, 16, 0, -118, 70, 26, 46, 266, 138, 0, 206, 196, -25, -40, 60, 34, 0, -82, -16, -12, -64, -75, 146, 0, -40, -46, -102, 0, -2, 42, 0, -68, 232, -141, -21, -4, -100, 0, 20, 130, -54, 86, 2, 278, 0, 9, -98, -16, -90, -28, 15, 0, 10, -41, -174, 86, -24, -21, 0, -7, 82, -26, -83, 158, 78, 0, 232, -53, 154, -67, -100, 237, 0, -152, -65, 114, 132, -88, 39, 0, 29, 122, -25, -196, -150, -1, 0, -180, -22, -37, -55, 91, -66, 0, -45, -54, -72, -120, -24, -32], "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, 8, 1, 3, 0]], "char_orbit_index": 8, "prim_orbit_index": 8, "minimal_twist": "91.2.f.c", "char_is_minimal": false, "conrey_index": 165, "id": null, "nf_label": 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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [1, 0, -1, -1, 0, 0, 0, 0], [0, 1, 0, 0, 2, 0, 0, 0], [0, -1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 3, 0, 0, 1, 0], [-2, 0, -1, 0, -2, -1, 1, 1], [0, 1, 0, 0, 3, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0], [0, 2, 0, 0, -3, -2, 0, -1], [0, -1, -1, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 1, -1, -2, 2, 0], [4, 0, -1, -4, 0, 0, -1, 0], [1, 0, -1, -1, 0, 0, -1, 0], [1, 2, 0, 2, 1, -1, 1, 0], [0, -3, -1, -3, 0, 2, -2, 1], [0, 3, 0, 0, 1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, 0, 0, 0], [0, 0, -1, 1, 0, 0, -1, 0], [0, -4, 0, 0, 0, 1, 0, 2], [-2, -3, 1, -3, -2, 0, 0, -1], [2, 4, 0, 3, 0, -1, 1, -1], [7, 0, 0, -1, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 1, -1, 1], [1, 0, -1, 0, 1, 0, 0, 1], [-1, 0, 1, 0, -1, 0, 0, -1], [-7, 0, 2, 4, 0, 0, -1, 0], [-5, 0, -1, 0, -5, -1, 1, 1], [0, 0, 1, 4, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 0, 9, 2, -2, 0], [-2, 0, 0, 1, 0, 0, -1, 0], [-5, 4, 3, 4, -5, -1, 1, -3], [-2, -1, -2, -2, -4, -2, -1, 1], [0, 0, 0, 0, 4, -1, 0, 1], [-6, -2, -1, -2, -6, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0], [0, 2, 0, 0, -3, -2, 0, -1], [3, 0, 2, -2, 0, 0, -3, 0], [6, 0, -1, 1, 0, 0, 1, 0], [0, -3, 0, 0, -1, 1, 0, 0], [0, 5, 0, 0, -1, 2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-11, -2, 3, -2, -11, 1, -1, -3], [0, 2, 0, 0, 2, -1, 0, -2], [8, -4, -1, 0, 7, -1, 0, 2], [-1, 2, 2, 2, -1, -4, 4, -2], [0, 0, 1, 5, 0, 0, 0, 0], [-1, 1, 0, 1, -1, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, -3, -4, 0, 0, -1, 0], [3, 2, 0, 2, 3, -1, 1, 0], [1, 0, -1, -2, 0, 0, 2, 0], [4, 2, 0, 2, 4, 3, -3, 0], [2, -2, -1, -2, 2, 2, -2, 1], [-2, -4, 0, -4, -2, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, -10, 0, 0, 0, 0], [-2, 1, 1, -2, 0, -2, 1, 1], [1, -1, 0, -1, 1, -1, 1, 0], [0, 6, 0, 0, -1, -4, 0, -1], [7, 0, -2, -4, 0, 0, 1, 0], [0, 0, 0, 0, 4, -2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -4, -2, 0, -2], [0, 3, 0, 3, 0, 2, -2, 0], [-2, -2, -3, -2, -2, 2, -2, 3], [4, 0, -1, -4, 0, 0, 0, 0], [1, 0, 1, -2, 0, 0, 1, 0], [5, -11, -2, -11, 5, -1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 2, 5, -3, -1, 2, -1], [0, -1, 0, 0, -6, 3, 0, -1], [0, 2, 0, 0, -1, 1, 0, -2], [0, 1, 0, 0, 8, 7, 0, 0], [-4, -1, 2, -1, -4, -1, 1, -2], [1, 0, 1, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 2, 1, 0, 1], [0, 0, 0, 0, 3, 0, 0, 1], [-3, 0, -2, -1, 0, 0, -2, 0], [0, -4, 0, 0, 0, 1, 0, 2], [0, 0, -1, 1, 0, 0, 2, 0], [-7, 0, 2, -4, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 1, 7, 0, 0, 3, 0], [-2, 0, 1, 1, 0, 0, 2, 0], [0, 1, 0, 0, -8, 0, 0, -3], [5, 0, -1, 2, 0, 0, 3, 0], [0, -6, 0, 0, 13, 0, 0, 1], [0, 2, 0, 0, 1, 5, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [7, 0, 0, -1, 0, 0, -6, 0], [-7, -13, 0, -13, -7, 3, -3, 0]]}