# Stored data for newform 441.2.h.b, downloaded from the LMFDB on 25 April 2024. {"label": "441.2.h.b", "space_label": "441.2.h", "level": 441, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504080697262521, "dim": 6, "is_polredabs": true, "nf_label": "6.0.309123.1", "trace_hash": 234494707908866137, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, -4, 1, 1]], [5, [121, -22, 59, 32, 23, 5, 1]]], "qexp_display": "q+(\\beta _{2}+\\beta _{3})q^{2}+(-\\beta _{1}-\\beta _{2}+\\beta _{5})q^{3}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "h", "char_is_real": false, "Nk2": 1764, "analytic_conductor": 3.521402729138465, "hecke_ring_index": 1, "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": "0.016", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 3, [344, 199], [2, 2]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [214, 373], "field_disc": -309123, "field_disc_factorization": [[-1, 1], [3, 3], [107, 2]], "field_poly": [3, -12, 19, -15, 10, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.031", "prec": 17}, {"__RealLiteral__": 0, "data": "5.568", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "121.949", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5036.375", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, -2, -5, 0], "traces": [0, 6, -2, -2, 6, -5, -1, 0, -12, -4, 0, 2, -13, 3, 0, 11, 6, -12, 10, -3, -16, 0, 15, 0, 15, -6, -1, 7, 0, -1, 31, 6, -16, 13, -3, 0, -11, 3, 8, -4, 21, -22, 0, 3, -23, 1, -12, 18, 14, 0, -10, -12, 3, 18, -13, 12, 0, 11, 9, 18, -17, 12, 36, 0, -24, -10, -34, 0, 6, 39, 0, 18, 15, 3, -6, -4, -21, 0, 10, 30, 11, -40, 9, -12, 0, -9, -34, -11, 21, -2, -73, 0, -15, -18, -48, 32, 7, 3, 0, -46, -21, -13, 33, -30, -6, 0, -18, -7, 65, 21, -94, -9, 0, -4, -35, -27, -8, -8, 18, 0, 6, -9, -28, 31, 0, 24, 0, 24, 78, 29, 0, 19, 74, 0, 118, 5, 6, 21, 27, 3, 0, -39, -30, -2, -23, 0, -18, 0, -30, -6, -23, -9, 24, -48, 0, -21, -11, -18, -100, 51, 15, 0, -11, -6, -11, 17, -3, -11, 0, 36, -21, -17, 42, -22, 2, 0, -20, -33, 51, 1, 35, -78, 0, 23, 15, 66, -39, -66, 126, 0, -42, 38, -8, -42, 39, 16, 0, 2, 10, -6, 27, 1, 18, 0, 51, 48, -2, -9, 3, -23, 0, 3, 3, 21, 9, 11, -72, 0, 24, 84, 60, -24, -18, -15, 0, 13, 60, -15, 61, 21, -36, 0, 9, 27, -13, -48, 48, 11, 0, -33, -65, -6, 29, -2, -18, 0, -64, 3, -6, -12, 72, -8, 0, 6, 30, -12, -6, -28, -17, 0, -32, 23, 9, -1, -87, 3, 0, 53, -120, -39, 52, -42, -9, 0, 12, 1, -18, 6, 6, 15, 0, -26, 39, -30, -12, -20, -15, 0, 2, -15, 26, -21, -45, -25, 0, -42, 27, -32, -45, 0, 28, 0, 53, 31, -6, 17, -45, 72, 0, 19, -57, 36, 15, 42, 20, 0, 78, -72, -39, 30, 4, 16, 0, -12, -8, 6, 61, -60, 33, 0, 88, -60, 6, -36, 45, 1, 0, 33, -12, 64, -39, 24, 35, 0, -45, -9, 108, 94, -22, 36, 0, 8, -21, -68, -27, 12, -55, 0, -18, -38, -36, 36, 44, -37, 0, -60, 22, 39, 51, 68, 30, 0, 6, -39, -48, 9, -144, -2, 0, -6, 82, -24, 12, -9, -48, 0, -142, -101, -54, -51, 5, 15, 0, -55, 114, -4, -17, -21, -66, 0, 45, 36, -118, 3, 13, -29, 0, -30, -39, 96, -10, -9, -45, 0, -57, -9, -8, 3, 51, 48, 0, 39, -11, -33, -21, 18, 21, 0, 37, 5, -99, -87, -19, 102, 0, 26, 33, 30, 54, 66, -72, 0, -6, 36, 45, 12, -37, 15, 0, 0, 80, 24, -2, 62, -21, 0, -72, -42, 73, 18, -3, 56, 0, -48, -20, 87, -66, -21, 17, 0, 63, 17, -66, -140, 85, -21, 0, 15, -3, 53, -64, -3, 46, 0, -30, -12, 101, -3, 6, 67, 0, -17, 62, 3, -8, -53, -102, 0, 33, 54, -90, 56, 66, -36, 0, -36, -60, 24, 18, 32, -36, 0, 58, -52, 30, -77, 109, -69, 0, 10, 42, -45, -20, 75, 56, 0, -48, -15, 41, 3, -36, 0, 0, 22, -110, -78, 120, -40, 15, 0, -26, 27, 71, 86, 39, 78, 0, 0, 18, -20, 60, 16, -21, 0, 19, -27, -15, -61, -12, 6, 0, -33, -15, -104, -60, -108, 56, 0, -6, -22, 26, 42, 23, 22, 0, 132, 35, 0, -32, 29, -21, 0, 6, 30, 42, 5, -87, 76, 0, 0, -36, 13, 51, -27, 128, 0, 69, 3, -24, 108, -24, 12, 0, 59, 0, -10, -31, -27, 1, 0, 36, 9, 63, -69, -94, -103, 0, 24, 137, 30, 6, 24, -126, 0, -23, 27, 94, -67, -54, -90, 0, 84, -108, -14, -90, -36, -30, 0, -38, -24, -87, 30, 14, -15, 0, -110, 0, -13, 48, 3, 10, 0, -66, 36, -120, 84, -38, 18, 0, -3, -71, 54, 110, -3, 6, 0, 63, 12, 5, -34, -177, 7, 0, -18, -41, -124, 36, -42, -70, 0, 48, -6, 9, 0, -16, -102, 0, -32, 63, 36, -21, 180, -128, 0, -108, 12, 33, 198, -64, -93, 0, 108, 4, -30, 14, -51, 66, 0, -27, 36, 36, -65, 57, -51, 0, 6, 77, 30, 27, -51, 185, 0, 21, 52, -216, -20, 28, 57, 0, 65, -51, -27, -38, 39, -12, 0, 12, 119, 70, -3, 24, -2, 0, 54, 12, 18, 32, -48, 114, 0, -84, -33, 36, 83, 18, -88, 0, -156, -126, 90, -114, -6, -42, 0, -56, 18, 36, 9, 31, 24, 0, -68, 84, -25, 107, -57, 51, 0, 48, -11, 20, 9, -51, -17, 0, 26, -122, -54, -140, -47, 135, 0, 63, 6, 102, -39, 123, 70, 0, 18, 28, -98, 21, 66, 59, 0, 18, 21, 0, 0, 110, 48, 0, 113, 51, 22, -162, -84, -116, 0, 216, -158, 48, -216, 75, -133, 0, -126, -84, 39, -21, 13, -12, 0, -15, -78, -58, 33, 0, -23, 0, 78, 14, 122, -63, 60, 105, 0, 69, 92, 114, 162, -51, -39, 0, -37, -30, -92, -2, -15, 88, 0, 3, 18, -8, 21, 146, -17, 0, -59, -47, 0, -54, 141, 18, 0, -81, 54, -102, -62, 234, -30, 0, -114, 12, 81, 168, -88, -36, 0, -302, 38, 93, -63, -6, 60, 0, 27, 42, 18, 56, 87, 88, 0, 6, 125, -71, -87, 6, 47, 0, -27, 55, -66, -104, -26, -93, 0, 39, 48, 30, -79, 75, 9, 0, -75, 4, -49, -6, 14, 114, 0, 36, 36, 30, 0, -9, -72, 0, 25, -123, 98, -11, -54, -84, 0, 186, -128, -110, 6, 7, 72, 0, -116, 81, 3, 3, -32, -42, 0, 32, -72, 6, 56, -165, 50, 0, -6, 39, -45, 120, -24, -46, 0, -53, -35, 114, -90, -139, -102, 0, 78, 66, -24, -93, 12, 18, 0, 21, -21, 89, 27, -54, -1, 0, 51, 51, -78, 76, -144, 66], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "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.f.b", "char_is_minimal": false, "conrey_index": 214, "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], [1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, -1, -1, 0, 0, 1], [0, 1, 0, -2, 1, 0], [1, -1, 0, 1, 1, -1], [-2, 1, -1, -1, -2, 0], [0, 0, 0, 0, 0, 0], [-1, -1, 0, 2, -1, 0], [0, 2, 1, 1, 2, -1], [0, 3, 0, 0, 1, -3], [1, 2, 1, 2, 1, -1], [-1, -3, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [1, 1, 2, 2, -2, 0], [1, -1, -3, -1, -1, 0], [-1, 2, 0, -1, 5, 0], [4, -1, 0, -1, 4, -1], [-1, 1, 0, 1, -1, 0], [1, -3, 0, 1, 4, 1], [0, 0, 0, 0, 0, 0], [5, -2, 0, -2, 5, 0], [2, -1, 0, 2, -1, -3], [1, 4, 1, 0, 0, -2], [-3, -1, -3, -1, -3, 3], [0, 1, 1, 1, 0, -1], [-2, 2, 0, -4, 1, 2], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 1], [5, -2, 1, -3, 3, 3], [1, 1, 3, 1, 1, 0], [-3, 0, -1, -1, 0, 0], [-1, 2, -2, -5, 2, 3], [1, 1, 0, 1, 1, -3], [0, 0, 0, 0, 0, 0], [-2, 2, 3, 5, -5, -4], [0, 0, -3, 0, 0, 3], [2, -3, -2, -3, 2, 2], [-1, 0, 0, 0, 0, 1], [-2, 4, 0, -2, -5, 0], [-7, 0, 1, 0, -7, -1], [0, 0, 0, 0, 0, 0], [-1, 5, 0, -1, 1, -3], [-6, 5, 5, 5, -6, -5], [-2, -1, -6, -4, -2, 2], [1, 1, 0, 1, 4, -3], [0, 3, 0, -6, 3, 0], [7, -1, 2, 3, 6, 0], [0, 0, 0, 0, 0, 0], [-5, -4, -5, -4, -5, 5], [-5, 4, 4, -3, 3, 1], [1, -1, 0, -1, 1, 0], [2, -1, 0, 2, -7, -3], [-2, -3, 2, 4, -4, 3], [1, -1, -6, -4, -1, 0], [0, 0, 0, 0, 0, 0], [1, 2, -1, -3, 3, 0], [-1, 2, 0, -1, -2, 0], [2, 2, 3, -1, 2, 0], [-6, 6, 5, 4, -4, -2], [3, -2, -3, 1, -2, 0], [5, 2, 3, -1, 2, 0], [0, 0, 0, 0, 0, 0], [-4, 1, 3, 1, 1, 0], [-1, -1, -1, 1, -1, 0], [-5, -4, 2, 6, -6, 3], [3, -1, 6, 8, -1, 0], [4, -5, 0, 4, -5, -3], [7, -2, 1, 3, -3, 1], [0, 0, 0, 0, 0, 0], [4, -2, -3, 1, -2, 0], [2, -4, -4, -6, 3, 5], [5, -4, 0, 5, -4, -6], [-3, -3, -3, -3, -3, 3], [3, 4, 1, 0, 9, -4], [-6, 4, 3, 4, -6, -3], [0, 0, 0, 0, 0, 0], [0, 0, -1, -2, -1, 1], [4, -1, -6, -4, -1, 0], [0, -7, 0, 0, -6, 7], [-5, -3, -1, -2, 2, 0], [1, -6, -6, -6, 1, 6], [-1, 2, 0, -1, 5, 0], [0, 0, 0, 0, 0, 0], [-5, -2, -6, -2, -5, 6], [4, -9, 0, 4, 7, 1], [-2, 1, 0, 1, -1, -1], [5, -7, -6, -7, 5, 6], [1, 6, 5, 6, 1, -5], [-11, -6, -4, 4, -7, 3], [0, 0, 0, 0, 0, 0], [-2, 4, 0, -2, 7, 0], [-7, -1, -4, -3, -6, 2], [-3, -3, 6, 12, -3, 0], [4, 1, -1, -3, 1, 0], [2, 2, 4, 1, 2, -3], [2, -7, 0, 2, -4, 3], [0, 0, 0, 0, 0, 0], [-4, -2, 0, -2, 8, 1], [-7, 0, 0, 0, -7, 0]]}