# Stored data for newform 72.2.n.b, downloaded from the LMFDB on 25 April 2024.
{"label": "72.2.n.b", "space_label": "72.2.n", "level": 72, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504493014122568, "dim": 16, "is_polredabs": true, "trace_hash": 561341930010211156, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [4096, 0, -11712, 0, 26129, 0, -18357, 0, 9318, 0, -2049, 0, 326, 0, -21, 0, 1]]], "qexp_display": "q+\\beta _{6}q^{2}+(-\\beta _{3}-\\beta _{10})q^{3}+(\\beta _{8}-\\beta _{13}+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 72, "char_orbit_label": "n", "char_is_real": false, "Nk2": 288, "analytic_conductor": 0.5749228945532188, "hecke_ring_index": 36, "level_radical": 6, "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": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [72, 6, [55, 37, 65], [6, 3, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [13, 61], "field_disc": 988177457384100000000, "field_disc_factorization": [[2, 8], [3, 8], [5, 8], [197, 4]], "field_poly": [256, -128, 64, 0, 32, -32, 0, -16, 4, -8, 0, -4, 2, 0, 1, -1, 1], "hecke_ring_index_factorization": [[2, 2], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "13.863", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1530.526", "prec": 27}, {"__RealLiteral__": 0, "data": "1841.563", "prec": 27}, {"__RealLiteral__": 0, "data": "307081.260", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c6", "trace_display": [1, 0, 0, 6], "traces": [0, 16, 1, 0, -1, 0, -7, 6, -2, 2, -16, 0, -16, 0, 16, -10, -9, -28, 4, 0, -8, 0, 1, -10, 7, 2, 28, 0, 4, 0, 22, -10, 11, 0, 1, 0, 27, 0, 23, 2, 6, -8, 8, 0, 18, 0, -20, 6, 39, 18, -23, 0, -8, 0, -29, -4, 10, 10, -14, 0, 6, 0, -52, 2, 26, -14, -72, 0, -39, 0, 0, 72, -77, -44, -38, 0, 5, 0, 10, -30, -96, 10, 38, 0, -28, 0, 7, 42, 31, 64, 64, 0, -30, 0, -12, 44, -26, 0, 66, 0, 18, 0, 41, -14, 38, -28, 10, 0, 37, 0, 30, 8, -4, 18, 11, 0, 72, 0, 42, -16, 82, -8, -30, 0, 22, 0, -50, 0, 71, -40, 38, 0, 33, 0, -90, -86, -26, 0, -70, 0, -14, 0, 18, -156, -26, -28, -39, 0, 4, 0, -34, 10, -74, 26, -16, 0, -114, 0, 46, -96, -36, 20, 101, 0, -51, 0, 30, -62, -38, 2, 52, 0, -14, 0, 96, 44, 33, 58, -4, 0, 40, 0, 22, 66, -50, -8, 22, 0, 156, 0, -32, 38, 67, -32, -47, 0, -33, 0, -81, 72, 55, -6, 20, 0, 2, 0, -72, 170, -48, 66, -38, 0, -48, 0, -5, 52, -46, 84, -22, 0, -58, 0, -38, 38, -40, -16, -108, 0, -66, 0, 70, 126, -38, -92, 40, 0, -37, 0, 10, 30, 52, 32, 92, 0, -48, 0, 109, 20, 74, -14, -40, 0, 84, 0, 40, -88, 31, -24, -14, 0, 96, 0, -60, -110, 51, 8, -28, 0, -9, 0, -82, 16, 1, -4, -75, 0, 20, 0, -70, -182, 76, -30, -96, 0, -60, 0, -48, -92, -109, -60, -66, 0, 49, 0, 57, -26, 8, -48, 148, 0, -61, 0, 18, -82, 81, -12, 16, 0, -24, 0, -38, -82, -62, 8, 64, 0, 76, 0, 54, -46, 20, -78, 40, 0, 90, 0, 46, -32, 71, 18, -12, 0, 32, 0, 152, 114, 96, 0, -27, 0, 64, 0, 14, -12, -13, 50, 28, 0, -24, 0, -56, 166, -26, -24, -55, 0, -30, 0, 30, 272, -22, -28, -22, 0, -2, 0, -36, -14, -80, -32, 68, 0, -32, 0, 27, 144, 18, 36, -14, 0, -24, 0, 52, 162, -1, -62, 54, 0, -122, 0, 4, -40, -9, 46, 60, 0, 9, 0, 58, -20, -53, 72, 57, 0, -104, 0, -100, -84, 49, 72, -82, 0, -62, 0, -20, -92, 8, 130, -3, 0, -24, 0, -56, -150, -8, -22, -54, 0, -39, 0, 20, -144, -33, 20, -28, 0, -16, 0, -27, -62, -204, 66, -188, 0, 0, 0, -28, -198, -80, 132, 85, 0, 6, 0, -91, -62, -43, -40, 56, 0, 100, 0, -30, -18, -24, 82, -85, 0, 16, 0, -36, 62, -13, 0, 38, 0, -48, 0, 12, 202, -64, -8, 23, 0, 60, 0, 26, -208, 78, -148, -42, 0, 43, 0, 16, 204, 168, 0, 44, 0, 72, 0, -29, 168, 94, 84, 90, 0, 100, 0, -68, 56, 34, 116, 18, 0, -39, 0, 34, 78, 38, -156, -24, 0, -16, 0, -22, 64, 78, -6, -12, 0, 176, 0, 52, 44, -33, 52, -14, 0, -18, 0, 0, 64, 53, -160, 40, 0, 30, 0, 138, -132, 10, -62, 44, 0, 35, 0, -40, 28, -24, -174, 72, 0, -36, 0, 148, -242, -192, 48, 116, 0, 42, 0, 86, -280, -9, 148, -4, 0, -28, 0, 14, 116, 78, -110, 112, 0, 51, 0, -8, -152, -12, -192, -69, 0, 12, 0, 100, -94, 79, 32, 28, 0, -212, 0, -38, 42, 49, -222, 42, 0, -75, 0, -21, -14, -46, 8, -162, 0, 20, 0, -260, 40, -80, 8, 71, 0, -140, 0, -38, 48, -26, 110, 2, 0, 132, 0, 0, 192, -112, -184, 27, 0, 60, 0, -55, 192, 11, -64, -56, 0, -74, 0, 134, 46, 158, -78, -156, 0, 48, 0, -92, 176, -52, 152, 34, 0, 6, 0, -102, 42, -116, 50, -158, 0, 74, 0, -144, 94, -16, 56, -70, 0, -43, 0, -82, -98, -39, 96, -50, 0, 120, 0, -58, -130, -78, -86, 52, 0, 0, 0, 62, 320, -63, 252, -99, 0, -111, 0, 84, -106, 116, 130, 50, 0, 26, 0, -116, -208, 120, 116, 120, 0, 32, 0, -20, 10, 92, -40, 44, 0, 84, 0, -6, -120, 140, 144, -181, 0, 84, 0, 38, -230, 74, 26, -244, 0, -102, 0, -36, -46, -12, 234, 36, 0, -56, 0, -19, 0, 148, -22, 80, 0, -204, 0, 240, 74, -186, 90, 24, 0, 109, 0, 73, 88, -113, 8, 72, 0, 4, 0, 100, 246, -54, 154, 8, 0, -76, 0, 102, 252, 48, -204, 14, 0, 40, 0, 176, -168, 170, -116, 270, 0, 153, 0, -112, 312, -6, 36, -112, 0, 102, 0, 114, 172, -135, 2, -62, 0, -304, 0, -90, -106, -90, -168, 58, 0, -30, 0, -68, -50, -112, -102, 5, 0, -150, 0, 40, -170, -80, -14, 122, 0, -68, 0, 186, -200, 12, -130, 55, 0, -36, 0, -12, -292, -74, -30, 162, 0, -6, 0, -72, -336, 191, -268, 161, 0, -148, 0, 6, -162, 40, 122, -160, 0, 54, 0, 6, -282, -100, -176, -39, 0, 40, 0, -65, -66, 88, -80, -172, 0, 196, 0, -30, 4, -76, -310, -111, 0, -177, 0, -39, 2, -36, 152, 114, 0, -86, 0, -76, 162, -79, -58, -31, 0, 116, 0, 85, -80, -10, 42, -134, 0, -42, 0, 244, 318, 304, -94, 194, 0, 141, 0, -61, 240, 122, -16, -36, 0, 126, 0, -122, 70, 78, 76, 78, 0, 116, 0, -61, 122, 64, 180, -6, 0, 138, 0, -34, 150, 84, -6, -220, 0, 214, 0, -100, 86, -112, 142, 66, 0, -139, 0, -124, -88, 84, 176, -206, 0, -216, 0, 354, -86, -100, 16, 18, 0, 84, 0, 192, -304, -56, 194, 114, 0, -6, 0, -6, -152, -148], "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, 8, 2, 1, 2, 0], [1, 1, 9, 3, 1, 3, 0], [1, 1, 72, 14, 1, 6, 0]], "char_orbit_index": 14, "prim_orbit_index": 14, "minimal_twist": "72.2.n.b", "char_is_minimal": true, "conrey_index": 13, "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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, -1], [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [-1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0], [0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0], [0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0], [-1, 1, 1, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, 1], [0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 1, -1, 0, 0, 0, 0], [2, 0, 0, 0, 2, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 1], [-1, 0, -1, 0, 1, 1, 0, -1, 2, 0, 1, 0, -1, -1, 0, -1], [0, -1, 1, 0, 2, 0, 1, 0, -2, 1, -2, -1, 0, 1, -1, 3], [-2, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, -1], [0, 1, 0, 0, -1, 1, 0, -1, 2, -1, 2, 0, 0, 0, 1, -2], [0, 2, -1, 0, 0, -2, -2, -2, 0, 1, 0, 1, 1, 0, 0, 0], [0, -1, -1, -2, 0, 0, -1, 0, 3, -1, 0, 1, 0, 0, 2, -2], [0, -1, 0, -1, 0, 0, 1, 0, 0, 1, -1, 1, 0, 1, 0, 1], [-1, 0, -1, 1, -1, 1, 0, 0, 1, 0, 0, 1, -1, 0, 1, -2], [1, 0, 2, 1, 1, -1, 0, 1, -2, 1, 0, -1, 2, 1, -2, 2], [-1, 0, 0, -1, -2, -1, -2, -1, 0, 0, 0, 0, -1, 0, 1, -2], [0, 2, 1, 1, 2, 0, 2, 0, -4, 2, -1, -2, 1, 2, -2, 3], [3, 0, 1, 0, 0, -1, -1, 0, 0, -1, 2, 0, 0, -2, -2, 0], [0, -2, -1, 1, 0, 2, 2, 2, 0, 0, -1, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 2, 2, 0, 0, -1, 0, 0, 0, 0, -1, 0], [0, 1, -1, 2, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0], [1, -2, 0, 2, 1, 2, 1, 1, -2, 1, 0, -1, 0, 1, -1, 3], [-3, 0, -2, -1, -3, -1, 0, 1, 2, -1, 0, 1, -2, -1, 2, -2], [0, 0, -1, -1, 0, 1, 0, -1, 0, -1, -2, 0, -1, -2, 1, -2], [0, 0, 0, 1, -1, -2, 0, 2, 0, 0, 1, 0, 0, 0, -2, 1], [0, 2, 0, -1, -1, 0, -2, 0, 2, -1, 0, 1, -1, -1, 1, -1], [0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, -1, -1, -1, 0, -1], [2, -1, 0, 1, -2, -1, -1, 3, 1, 0, 2, 1, 1, 0, 0, 0], [0, -2, 1, -1, 0, 2, 2, 2, 0, -1, 1, -1, -1, -2, 0, -1], [0, -1, 1, -2, -2, 0, 1, 0, -2, 1, -2, -1, 0, 3, -1, 3], [1, 2, 1, -1, 3, 1, 2, -1, 0, 1, -1, -1, 1, 0, 2, -1], [1, 0, 0, 0, 1, 1, 0, 3, 0, -1, 2, -1, 0, 1, 0, 1], [-3, 0, -2, -1, -3, 2, 0, -2, 6, -1, 2, 1, -2, -3, 2, -4], [1, -1, 0, 0, 2, 1, 1, 2, 0, 0, -2, -1, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1], [1, 1, -1, 3, 0, 1, 1, -1, 0, 1, 0, 1, 1, 3, -1, 3], [0, 2, 0, 0, 0, -3, -2, -3, 0, 1, -1, 1, 0, -2, 0, -2], [-1, -1, -1, -3, 0, -2, -2, 1, 0, 1, -2, 1, 1, -1, 1, -3], [0, 1, 0, 2, -1, 0, 1, 0, -4, 0, 0, 0, 0, 2, -4, 4], [4, 2, 1, 3, 2, -1, 0, 1, -4, 1, 0, 0, 1, 4, -3, 4], [2, 0, 0, 0, 2, 2, 0, -2, 2, 0, 1, 0, 0, -1, 0, -1], [-2, 0, 1, -1, -2, -1, 0, -1, -2, 1, -4, 0, 1, -2, -1, 0], [0, -2, 0, 2, 0, 0, 2, 0, 0, -1, 2, -1, 0, 2, 0, 2], [0, -1, 1, 0, 2, 0, 1, 0, -1, 1, 2, -1, 0, 0, 0, -2], [0, 0, -1, -1, 0, 0, 0, 0, 0, 1, -3, 1, 1, 2, 0, -1], [-1, 1, -1, -2, 3, -1, 0, -3, 3, 0, 0, 0, 0, -3, 2, -1], [1, 1, 1, -1, 0, 1, 1, -1, 0, -1, -1, 1, 1, 0, 2, -1], [0, 1, -1, 1, -1, 0, -1, 0, 2, 0, 2, 0, 1, -2, 2, -4], [2, -4, 1, -1, 0, -2, -4, 2, 0, 0, -1, 0, 1, 0, 2, -1], [-3, 0, -1, -3, -3, -1, 0, -4, 2, 0, 0, 1, -1, -1, 1, 1], [0, 0, 0, -1, 0, -2, 0, -2, 0, 0, 1, 0, 0, 1, 0, 2], [2, -2, 0, -1, 3, 0, 2, -2, 1, -1, -2, 1, -1, -2, 2, 0], [0, 1, 1, -2, 0, 0, -1, 0, 0, 0, -2, 0, -1, 1, 0, 2], [-3, 1, 1, 3, 0, 0, 0, -1, 0, -1, 2, -1, -1, 1, -3, 3], [0, -1, -1, 0, 1, -2, -1, 2, -2, 0, -1, 0, -1, 1, 0, 1], [0, 5, 0, 1, 0, 1, 1, -5, 0, 0, 2, -1, -1, -1, 0, 1], [0, -2, 0, 1, 1, 0, -2, 0, -2, 0, 0, 0, 0, 1, -2, 2], [-4, -2, 0, 1, 1, -1, 0, 0, -2, 1, 0, -1, 1, 1, -3, 1], [0, 0, 0, 2, 0, 4, 0, 4, 0, 1, 1, 1, 0, 2, 0, 0], [-6, 0, -1, 1, -6, 1, 0, 1, 0, -1, 2, 0, -1, 2, 1, 0], [0, 2, 1, 1, 0, 1, -2, 1, 0, 0, 2, 0, -1, 0, 0, 3], [0, 2, 0, 2, 0, 0, -1, 0, -1, 0, 2, 0, 0, -1, -1, -1], [6, 0, 1, -1, 0, 0, 0, 0, 0, -1, -1, 1, 1, 0, 2, -1], [-3, -3, 0, -2, 2, -2, 1, 2, 2, 0, 0, 1, 0, 1, 1, -1], [-2, -2, 0, 1, 0, -2, -2, 2, 0, 0, 1, 0, 0, 0, -2, 1], [0, 1, 1, 1, 5, 0, -1, 0, 2, 0, 2, 0, -1, -4, 2, -4], [0, 4, 0, 1, 0, 0, -4, 0, 0, -1, 3, -1, 0, 2, 0, -1], [2, 0, 1, 1, 2, -3, 0, 3, -4, -1, -2, -2, 1, 0, -1, 0], [0, 0, 0, -3, 0, -1, 0, -1, 0, 0, -1, 0, 0, -1, 0, 2], [-2, 1, -1, -3, -5, 1, 0, 2, 4, 0, -2, 2, -1, -4, 3, -4], [0, -3, -1, 0, 1, 0, -3, 0, 2, -2, 1, 2, -1, -1, 0, -1], [-4, -2, 2, 0, 0, 0, 0, 2, 0, -2, 2, 0, 0, -2, 0, 0], [-3, 2, 0, 1, -4, 4, 2, -4, -4, 1, -1, -1, 0, 2, -2, 3], [1, -3, -1, 3, 0, 0, 0, 3, 0, 1, 2, -1, -1, 1, 0, 3], [0, -2, -1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0], [-2, 3, -2, 1, 0, 1, 1, -1, 0, 0, 0, 1, 1, -1, -1, 1], [0, 0, 0, -1, 0, -2, 0, -2, 0, 1, -4, 1, 0, -3, 0, -2], [2, 0, 1, 1, 2, 0, 0, 1, -1, 1, 0, 0, 1, 1, -1, 1], [2, -1, 2, 1, -3, 2, -1, -2, -2, 1, 0, -1, 2, 1, -2, 2], [0, -4, -2, -1, -5, 0, 2, 0, 2, -1, -2, 1, 1, 1, 1, 1], [2, 0, -1, -1, 0, 0, 0, 0, 0, 1, -1, -1, -1, 0, 2, -1], [1, 2, -1, 0, -2, 1, 1, -2, -2, 3, -2, 0, 0, 4, -2, 2], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 3, 0, 2], [0, 4, 2, -1, 7, 0, 0, 0, -5, 3, -2, -3, 1, 4, -2, 4], [0, -2, 1, -1, 0, 1, 2, 1, 0, -2, 2, -2, -1, -2, 0, -5], [0, 0, 2, 2, 0, -1, 0, -4, -3, 0, 0, -2, 2, 1, -2, 1], [2, 0, -4, -2, 2, 0, 0, 0, 8, -2, 2, 2, -4, -4, 4, -6], [-2, -1, 0, 1, -4, 1, 3, -1, -2, 0, -2, 1, 3, 3, -2, 1], [0, 2, -1, -2, -1, 0, 2, 0, 6, -2, 1, 2, -1, -3, 4, -5], [3, -2, -1, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0, 2, 0], [0, 2, 2, -1, 0, 2, -2, 2, 0, -1, 2, -1, -2, -4, 0, -4], [-2, 5, -2, -3, 0, -3, -3, -5, 0, 2, -2, -1, -1, -1, 2, -3]]}