# Stored data for newform 63.2.h.b, downloaded from the LMFDB on 08 May 2024. {"label": "63.2.h.b", "space_label": "63.2.h", "level": 63, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504080697262143, "dim": 10, "is_polredabs": true, "nf_label": "10.0.991381711347.1", "trace_hash": 1829284012571076087, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [3, 3, -9, -5, 2, 1]]], "qexp_display": "q+(-\\beta _{1}+\\beta _{5})q^{2}-\\beta _{8}q^{3}+(1-\\beta _{4}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "h", "char_is_real": false, "Nk2": 252, "analytic_conductor": 0.5030575327340664, "hecke_ring_index": 3, "level_radical": 21, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [63, 3, [29, 10], [2, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [25, 58], "field_disc": -991381711347, "field_disc_factorization": [[-1, 1], [3, 9], [47, 2], [151, 2]], "field_poly": [9, -9, 36, -3, 90, -36, 40, -8, 9, -2, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.367", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "352.188", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "24839.550", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "1.2.3.c3", "trace_display": [-4, -1, 4, -4], "traces": [0, 10, -4, -1, 8, 4, -2, -4, -6, 11, -7, 4, -20, -8, -20, -19, -4, 12, 4, 1, 5, 13, -1, 3, 6, -1, 11, -7, -2, 7, 16, 6, 4, 14, 3, 5, 34, 0, 20, 2, -3, 5, -4, -7, -10, -16, 3, -54, -5, -8, 19, -9, -10, -21, 1, 4, 18, -4, -10, -60, 10, 28, -12, -59, -50, 22, 19, 4, 27, 15, 40, -6, -36, 15, -36, -14, 5, 11, -20, 8, 20, 23, -5, 9, 35, -6, -8, 2, -18, 28, 28, -4, 27, -6, 6, 28, 59, -12, 59, 35, 13, 8, -33, 5, 9, 25, 6, -8, -59, -21, -40, -30, -5, 28, -44, 18, -25, -7, 60, -15, -18, 23, -28, -14, -18, -60, 2, 48, 18, 70, -4, 52, -32, -46, -130, 50, -12, 0, -81, 15, -104, -60, -6, 7, -26, -8, -15, 29, 30, -39, -16, -19, 24, 33, -2, 24, 22, -38, 70, 51, -29, 60, 49, -5, 19, -31, -6, 19, 27, 27, 18, -28, 13, -64, 34, -14, 26, 9, 11, 35, -14, -44, 4, 5, 30, 24, 69, -6, 60, -17, 20, 34, 65, -10, 24, 44, -28, -50, -14, -24, -3, -43, -65, -13, -33, -70, 13, 81, 20, 28, -37, -2, -15, -78, 56, 62, 3, -9, 66, 3, 44, -30, 96, 28, 26, 25, -31, 18, 7, -37, -48, -17, -15, -39, -26, 0, -120, -68, 18, 9, -14, -25, -35, -61, -28, -44, -4, -32, -36, -48, 24, -56, -46, -108, 54, 33, -8, 8, -73, 96, -40, -34, 56, -2, -9, 57, -41, -1, 122, 9, -41, -8, -21, 64, -9, 11, 0, 19, -6, -15, 69, -31, 69, 22, 84, 41, 20, -14, 35, 31, 23, -48, 18, 2, -56, -9, -60, 47, -3, -42, 50, 25, 52, -5, -16, 37, 51, 52, 49, 34, -42, -102, 9, -10, 98, -107, 58, 72, -9, 94, -41, 26, -78, 54, -20, 29, -28, -27, 9, -3, 7, 2, 18, 84, -55, 49, -22, -20, 24, 41, -39, 30, 19, -61, 12, -18, -104, -94, 37, 10, -16, 32, 31, -8, -33, 36, 29, 48, -11, -4, -6, 12, 116, -38, -11, -12, -5, 45, -78, -23, -144, -9, -45, 23, -48, -81, -48, -32, 35, 54, -88, 15, -100, 57, -120, 47, 22, 73, -93, 15, -59, -36, 21, -67, -142, 8, -2, 48, -84, 112, -59, -45, 79, 12, 13, -25, -17, -30, 6, 32, 88, -57, 1, 27, -30, -54, -62, -87, 38, 84, 68, -31, 86, 3, 9, 60, 153, 35, -34, -13, -74, 9, 58, 16, 42, -10, -48, 90, 39, -114, 18, 29, 54, -144, -72, -20, -13, 93, 29, -90, 77, 23, -13, 94, 87, 17, 12, 70, 7, -33, 36, 83, -40, 31, 41, -33, 21, -51, 31, 113, -24, -49, 114, -64, -58, 2, -39, 9, 9, 101, 23, 24, -50, 81, 67, -24, 4, -5, 42, -40, 50, -61, 29, 21, 23, -34, 96, -66, -57, -2, 90, 47, 62, -96, 51, 98, -18, -111, 36, -19, -57, -120, 56, -13, -11, 47, 8, -33, -60, 37, 48, -15, -41, 10, -31, -46, 44, -9, 7, -20, -66, -138, -86, 50, 46, -218, -30, -35, -33, -56, -29, -10, -31, 104, -24, 39, -82, -20, 57, -58, -17, -104, 39, -77, -13, -96, 102, 49, -33, -112, 61, 33, 82, 16, -30, 70, 26, -140, -150, 76, -59, -160, -22, 113, 11, 138, -88, -56, -85, 181, 2, 165, 117, -30, -75, -13, 46, 22, -38, -15, 66, 74, 42, -15, 43, -45, -33, -60, 150, 0, -105, 24, -115, -34, -113, -73, 146, -58, -116, -38, -16, 57, 60, 34, 110, -11, -21, -54, 5, -83, 24, -24, -12, -10, -2, -1, 76, -16, 38, -12, 161, -106, -6, -4, 78, -36, -9, 76, 68, 72, 129, 111, -98, 14, 81, 58, 222, 50, -3, -27, -20, -9, 35, -15, -6, -11, -68, -39, 126, -66, 1, 214, -26, -21, 75, 2, -174, 81, -28, 53, -64, 7, -143, -17, -13, 88, 21, -42, -23, 12, 39, 171, -6, -6, 40, 90, 37, 31, -80, -18, 33, 14, -2, 4, 16, 18, -30, 48, -142, 99, -163, 78, -149, 90, 7, 165, -4, 130, 183, -48, -111, 67, -57, -75, -78, 7, 34, -66, -89, 9, 13, -134, -120, -134, -334, -88, -67, -55, 24, -97, 87, 9, 19, 36, -84, 44, -27, -44, 89, 18, 300, -34, -57, -9, 12, 90, -14, 57, -36, -82, 51, 121, 42, -46, -28, -112, 194, -16, -186, -72, 72, 9, -153, 27, 140, -60, -159, 81, 77, -43, 10, -2, -260, -73, -148, -60, 24, -144, -99, 17, 61, 30, -75, 65, -76, -38, -74, 28, 44, -136, -11, -79, -96, -5, -63, 45, 9, 19, 35, -21, 32, 125, -45, 144, -14, -3, -33, -15, -81, 51, 121, 56, -8, 122, 6, -62, 24, -106, 268, 109, -8, 116, 9, -84, -63, -41, 114, 240, 123, 23, -21, 41, 22, -24, 69, 154, 5, 51, -18, 28, -138, 56, 4, -65, 2, -87, -93, 112, -30, -22, 168, -144, -216, 32, -26, -49, 42, -131, 52, 89, 4, -76, 81, 42, 56, -16, 218, 92, 9, -22, 16, -20, 57, -117, 252, -21, -48, -77, 258, -14, -4, 12, 223, 44, -42, 42, 54, -43, 90, -66, -94, 152, 32, 12, 87, -46, 51, -72, -126, 48, -169, 51, -26, 47, 54, -17, -46, -16, -153, 97, -68, -39, 43, -168, -130, -142, -113, 20, -180, 41, 15, -118, -20, 39, -25, 30, -31, -5, 61, 74, 3, 130, -138, 180, 171, 6, 84, -174, 58, -80, 105, 212, 82, 192, 48, 94, 100, -22, -121, -66, -71, 75, 81, -46, -93, -116, 75, 77, -71, 9, 62, -208, -30, -28, 109, -67, -15, -2, 27, -150, 0, 54, -29, 39, 53, 31, 32, -186, 7, -56, -73, 6, -137, 54, -51, -50, 66, -12, -10, -105, -65, -70, 0, -254, 87, -144, 78, -161, -82, -60, -54], "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, 63, 8, 1, 3, 0]], "char_orbit_index": 8, "prim_orbit_index": 8, "minimal_twist": "63.2.g.b", "char_is_minimal": true, "conrey_index": 25, "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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [1, 0, 0, 0, -1, 0, 0, 1, 0, 0], [0, 1, 1, 0, 1, 0, 0, 0, 0, 0], [-1, 1, 0, 1, 1, -1, 1, -1, 1, -1], [-1, 1, 0, 0, 0, -1, 0, 0, 0, 1], [-1, 0, 0, -1, 0, 0, 0, 0, 0, 1], [2, -1, 0, 1, -1, 1, 0, 1, -1, 0], [0, -1, -1, -1, -1, 0, -1, 0, 0, 0], [1, 0, -1, 0, 1, 0, -1, 0, 1, -1], [-2, 0, -1, -1, 0, -1, -1, 0, 0, 1], [-2, 0, 0, 0, 0, 0, 2, -1, 1, 0], [-2, 1, 1, 0, 0, -1, -1, -2, 0, -1], [0, -1, 0, 0, -1, 1, -2, 1, -1, -1], [-1, 1, 1, 1, 2, -1, 0, -2, 1, -1], [0, -1, -1, 0, 0, 0, 3, 1, 1, 0], [1, -2, 0, -1, -1, 2, 0, -1, 0, 0], [0, 0, 1, 0, -1, 1, 0, -1, 0, 1], [0, 0, -1, 2, 0, 0, 2, 1, 1, 0], [1, 0, 2, -1, 0, -1, -1, 0, 0, 1], [0, 0, -1, 0, 1, 0, 0, 1, 0, 0], [0, -1, -3, -2, -1, 0, 1, 2, 2, 0], [0, 2, 1, 0, 0, -1, 0, 1, 0, 0], [2, 0, 1, 0, -1, 3, -2, 2, -3, 0], [2, 0, 1, 0, -1, -1, -2, 1, -2, 1], [-1, -1, 0, 1, 1, -2, 0, -2, 0, 0], [0, 2, 0, 1, 1, 1, 0, 1, -2, 0], [0, 1, 2, 1, 0, 0, 1, -2, -2, 0], [0, 2, -1, 0, 1, 0, 2, 1, 1, 1], [0, 1, 1, 1, 2, -1, 0, -2, 1, -1], [1, 1, -2, 1, -1, -1, 0, 1, -2, -1], [3, 0, -1, 0, 1, 2, -2, 0, 0, -1], [0, -4, -1, -1, 0, 0, 2, 1, 1, 0], [-1, 0, 1, 0, 3, 0, 1, -3, 1, 1], [3, 2, 2, 0, 1, 0, -1, 1, 1, 1], [0, 0, 0, 0, 0, -2, 0, 0, 0, -2], [5, 0, 3, 0, -3, 2, -5, 0, -3, 1], [-2, 1, 0, -1, -1, -1, 3, -1, 1, 0], [0, -1, 2, -1, 0, 0, -1, -2, -2, 0], [2, 0, 1, 0, -1, 1, -2, 2, -3, 1], [-2, -2, -2, -1, -1, 3, 5, 2, 2, 1], [0, -1, -4, -1, -3, 0, 0, 1, 1, 0], [-3, 0, 1, 0, -1, -2, 3, -1, 0, 0], [-1, -1, -3, 1, 1, 1, 0, 1, 3, 0], [0, -2, 1, 1, 3, 0, 1, 2, 2, 0], [-5, 0, 1, 1, -1, 0, 0, 1, 1, -1], [0, -2, 1, 0, 0, 3, 1, -1, 0, -1], [2, -4, -3, 0, 0, 2, -2, 3, 0, 0], [4, 0, 1, 0, -1, 1, -4, -2, 1, -1], [0, 2, 1, 0, -1, -1, -3, -2, -2, 0], [-1, 0, -1, 0, 1, 2, 1, 0, 1, -1], [0, -1, -2, 0, -2, 0, -3, 0, 0, 0], [-4, 3, -2, 1, 1, -2, 7, 0, 1, -1], [-1, 2, 1, -1, 0, -2, 0, 0, 1, 1], [4, -1, -1, 0, 0, -1, -4, -1, 0, -1], [-5, 1, 0, -1, 1, -4, 6, -1, 2, 0], [0, 1, 1, 1, -1, 0, -2, -2, -2, 0], [-7, 0, 1, -1, 2, 0, 0, -2, 1, 1], [1, -1, 2, -1, 1, -3, -3, -5, 1, 0], [1, 2, 1, -1, 2, -2, 0, -2, 1, 1], [-1, 0, -2, -1, -1, 0, 0, 1, -2, 1], [-6, 2, 2, 0, 1, 0, -1, 1, -2, 1], [-5, 0, -1, 0, 1, 0, 0, -1, -1, 0], [2, 0, -1, -1, 0, 0, 0, 0, -1, 1], [5, 0, 1, 1, 0, 1, -5, 0, -1, -1], [-2, 5, 1, -1, -1, -5, 0, 1, 1, 1], [0, -1, -2, 0, 1, 0, 6, 3, 3, 0], [2, 5, -2, -2, 0, -1, -4, 1, 0, 1], [5, 1, 0, 1, -3, -2, -1, 1, -1, -2], [0, 0, 2, 3, 1, 0, 0, -1, 2, -3], [-1, -2, -1, -2, -2, 1, -4, 2, -1, 1], [0, 0, 1, 3, 0, 0, 4, -1, -1, 0], [-8, 0, -4, 0, 4, 0, 8, 2, 2, 2], [1, -3, -4, 2, -1, -1, -1, 3, 1, -2], [4, 0, 1, 0, -1, 6, -4, 1, -2, 0], [-1, -1, 1, 1, -3, 0, 5, -1, -1, 1], [-1, -1, 2, 1, 1, 0, -2, 1, -2, 2], [2, -3, 1, 0, -1, 3, 0, 1, 1, 0], [0, 3, 1, -1, 1, 0, 2, 0, 0, 0], [1, 0, 5, 2, 2, 2, 2, -3, -1, 1], [-1, 0, 0, 0, 0, 1, 1, -3, 3, -2], [0, 2, 0, -4, 2, 0, -1, 2, 2, 0], [8, -5, -1, 1, -3, 1, -4, 2, -1, -2], [-1, 0, -1, 0, 1, 1, 1, 1, 0, 1], [0, 2, 5, 3, 4, 0, -3, -1, -1, 0], [-1, -4, 0, 1, -3, 1, 6, 1, -2, 0], [-5, 0, 1, 0, -1, -1, 5, -1, 0, 2], [8, 0, 0, 0, 0, 3, -8, 1, -1, -2], [5, 0, 1, -2, -2, -2, -5, 0, -2, -1], [0, 0, -4, -2, -1, 1, 0, 1, 2, -1], [0, -4, -2, -2, -2, 0, 7, 0, 0, 0], [0, -2, 1, 0, 0, 3, 1, -1, -1, -1], [-1, 2, -2, -4, -2, -2, 0, 2, -2, 4], [2, 0, 0, -1, 2, 0, 0, -2, 0, 1], [9, -5, -2, 0, -3, 3, -2, 2, -2, 2], [0, 1, 6, 1, 2, 0, -4, -4, -4, 0], [3, 0, -2, 0, 1, -1, 6, 1, 5, -3], [5, -1, -3, 1, 1, 1, 0, 1, 0, -3], [1, 0, 0, 0, 0, 1, -1, -1, 1, 4]]}