# Stored data for newform 441.2.h.e, downloaded from the LMFDB on 23 April 2024. {"label": "441.2.h.e", "space_label": "441.2.h", "level": 441, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014879579374009, "dim": 6, "is_polredabs": true, "nf_label": "6.0.19683.1", "trace_hash": 880103403168442028, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [3, 0, -3, 1]], [5, [9, 0, 9, -6, 9, -3, 1]]], "qexp_display": "q+(1-\\zeta_{18}^{3}-\\zeta_{18}^{4})q^{2}+(-\\zeta_{18}^{2}+\\cdots)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": 3, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 18, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 3, [344, 199], [2, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [214, 373], "field_disc": -19683, "field_disc_factorization": [[-1, 1], [3, 9]], "field_poly": [1, 0, 0, -1, 0, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.845", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "125.436", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5022.108", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c3", "trace_display": [6, 0, 3, 0], "traces": [0, 6, 6, 0, 6, 3, 9, 0, 12, 0, 0, -6, 9, -3, 0, -9, 6, 6, -18, -3, -6, 0, -9, -12, -9, 6, -3, -27, 0, -9, -9, 6, 0, 9, 9, 0, -27, 3, 6, 36, -9, 0, 0, 3, -15, -9, 0, -6, 0, 0, 6, 0, -21, -6, -27, 0, 0, -9, 9, 6, -9, -12, 60, 0, 24, 30, 18, -24, 6, 9, 0, 18, -9, -21, 30, -18, 15, 0, 54, -42, -15, 0, -9, -18, 0, -9, -6, 45, -27, 12, -27, 0, -3, 54, 36, -24, 27, -3, 0, 18, 15, -21, 9, 6, -60, 0, -18, -3, -27, -15, 18, 27, 0, -36, -27, 9, 36, 54, -54, 0, -18, 15, 24, -9, 60, 24, 0, -24, 6, -9, 72, -15, 36, 0, -42, -27, 0, -15, -45, 15, 0, 45, 18, -24, -27, 36, -48, 0, 30, 6, -27, 3, 12, -18, 0, 3, 45, 6, -60, -27, -9, 0, -27, -6, -9, 9, 9, -9, 0, -36, -9, -27, -6, -78, 54, 0, -24, -45, 9, 21, -9, 42, 0, 27, -45, 6, 9, -18, 30, 0, -18, 6, 0, 30, 15, 54, 0, 90, 54, 6, 39, -27, -36, 0, 27, 0, 24, -45, -57, 3, 0, 3, -33, 27, 9, -3, -54, 0, -24, -36, 36, 24, 0, 15, 0, -27, -36, -21, -27, 15, -18, 0, 45, -21, 117, 0, -84, -27, 0, -9, -9, -30, -3, 0, 42, 0, 0, 15, -42, 36, -36, 36, 0, 54, 102, -36, -102, 48, 9, 0, 48, 27, -27, 3, 63, -9, 0, -63, -24, -21, 0, 24, -3, 0, -36, 21, -72, -6, 60, -81, 0, -54, -9, -30, -36, 0, -45, 0, -54, 33, 36, 63, -57, 9, 0, 18, -21, 0, 27, 96, -36, 0, 21, -9, 24, -15, -27, -12, 0, 27, 27, 96, 27, 6, 96, 0, -42, -48, -63, -18, 30, 36, 0, -12, 0, 42, -15, 0, 9, 0, 0, 84, 18, 0, 63, -21, 0, -15, -72, 36, 9, -6, -45, 0, 15, -9, -180, 30, 72, 24, 0, 0, -9, 24, 9, 36, 39, 0, 18, 6, 54, 36, -12, -45, 0, 12, -18, 15, -21, 0, 54, 0, -18, -15, -36, -27, -72, -126, 0, -6, -6, 72, -36, -33, -18, 0, 66, 27, 60, 21, 45, 9, 0, -63, 90, -30, 99, -57, 24, 0, 33, -12, -36, 51, -39, 27, 0, 6, 45, 24, -18, 63, 33, 0, 27, 27, 0, -45, 27, -36, 0, 39, 21, -63, -45, 6, 27, 0, -3, -63, 9, -15, -27, -102, 0, 54, -15, 42, -90, -66, 36, 0, 18, -12, -63, -36, -3, 63, 0, 0, -72, 0, -54, -108, -9, 0, 0, -114, 87, -54, -27, 18, 0, 12, 72, -9, 18, -69, 135, 0, 27, 45, -18, -12, -63, -3, 0, -9, -63, -75, 0, -51, -12, 0, -30, 48, 81, 21, -6, -27, 0, 27, 18, 27, 60, -27, 6, 0, -27, -6, -102, -36, 162, 72, 0, -36, 36, -36, 210, -24, -54, 0, -150, 0, 18, 3, 9, 9, 0, -90, -54, -39, 108, 33, -78, 0, 36, 33, 63, -21, -18, 90, 0, 18, -90, 18, 24, 0, 27, 0, 54, -33, 33, -54, 9, 24, 0, -24, -78, -54, 36, 108, -9, 0, 39, 81, 105, 3, -18, -42, 0, -9, -27, 60, -36, -36, -192, 0, -126, -102, -36, -78, -87, -72, 0, -84, 27, -48, 24, 27, 9, 0, 126, 54, -42, -63, -27, 54, 0, 24, 0, 27, 3, 57, 0, 0, 69, 27, 36, 84, -54, -66, 0, 27, 84, -42, 9, 51, 27, 0, 0, 57, 9, 3, 42, -27, 0, -72, 45, -66, -6, 108, 126, 0, 9, 15, -138, 45, 186, 66, 0, 12, -12, 18, -162, -66, -108, 0, -126, 0, 45, -42, 36, -57, 0, 18, 0, -21, 108, 9, 60, 0, -6, 24, -18, -36, 0, 54, 0, 9, 9, -30, 30, 45, -36, 0, -9, -36, 117, -54, -27, 3, 0, -42, 39, 0, -72, -6, 54, 0, 36, 18, -63, -96, -54, 54, 0, 108, 3, 84, 27, 24, -204, 0, 36, -60, 135, -18, 60, -45, 0, 36, 0, -24, -6, 9, 0, 0, 9, 12, 54, 27, 117, 69, 0, -18, 21, -18, -45, -33, 45, 0, 45, 0, -12, 36, -36, -39, 0, 81, 9, 3, -18, 33, 60, 0, 36, 15, 0, 93, -12, 54, 0, 18, 72, 36, -24, -54, -54, 0, 36, -33, -24, 135, -342, -120, 0, 84, -6, -36, -18, 30, -36, 0, 24, -54, -72, -3, 9, 60, 0, -36, 84, -3, -9, -21, 111, 0, 36, 9, 0, 9, 9, 81, 0, -42, -198, 114, 36, -153, -27, 0, 135, 6, -30, 9, 33, 72, 0, 18, 0, -90, -99, 102, -9, 0, -30, 81, -36, -24, 0, 24, 0, -27, 63, -30, 54, -24, 60, 0, 0, -30, 126, 192, 21, 45, 0, 18, 36, 15, -9, 27, 42, 0, -135, -126, 48, -27, -90, 27, 0, -66, 30, 72, 21, 36, 27, 0, -51, -108, 18, 138, -27, 33, 0, -9, -54, -12, -198, -93, 6, 0, -117, 6, 0, -27, -138, -45, 0, 33, 81, -42, 6, 81, -90, 0, -189, -6, -246, 18, 54, -198, 0, 30, -84, -9, 72, 12, -108, 0, -126, -54, -39, 21, 144, -18, 0, -81, -54, 18, -108, 9, -18, 0, -126, 21, -189, -51, -12, 9, 0, -27, -9, 54, -168, 18, 123, 0, -81, -24, 18, 9, 27, 99, 0, 21, 12, -27, 54, -150, -90, 0, 60, 36, -54, 0, 99, -12, 0, -63, 9, 186, 9, -54, -84, 0, 18, -48, -36, 6, -39, -72, 0, 108, -27, -27, -81, -54, -72, 0, -36, 144, 30, 36, -3, 6, 0, 66, -33, -9, 72, -78, 162, 0, 75, 45, 42, 102, -27, 54, 0, 54, 126, 96, 27, 72, 18, 0, 69, 39, -27, -105, 162, -45, 0, 3, -45, 6, -24, 0, -90], "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.a", "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], [1, 0, 0, -1, -1, 0], [0, 0, -1, 0, 0, -1], [1, 0, 0, -1, -2, 0], [0, 1, -1, 1, 1, -1], [2, -1, -2, 2, 1, -2], [0, 0, 0, 0, 0, 0], [2, 0, 0, 1, -2, 0], [0, 0, -2, 3, 2, -1], [0, 0, -2, 1, 1, -1], [-2, 2, 1, -1, 0, 1], [3, -3, -2, 3, 1, -3], [-1, 1, 4, -4, 0, 2], [0, 0, 0, 0, 0, 0], [-2, 1, -2, 1, 0, 0], [1, 0, 0, 0, -3, 0], [0, 2, -1, 0, 0, 0], [-3, 0, -3, 3, 3, -3], [-1, 1, -1, 1, 0, -2], [0, -2, -1, 1, 1, -1], [0, 0, 0, 0, 0, 0], [-3, 3, 2, -2, 0, 4], [0, -4, -2, -1, -1, 1], [1, -5, -1, 1, -1, -4], [2, -2, -2, 2, 0, -1], [-1, 1, 6, -6, 0, 7], [-6, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -3, 4, -5, -5, 5], [-3, 3, -2, 3, 2, -1], [1, 0, 0, -6, -3, 0], [0, 0, 0, -3, -3, 0], [1, 1, 1, -2, -3, 3], [0, 3, -1, -1, -1, 1], [0, 0, 0, 0, 0, 0], [-3, -3, -2, 3, 5, -4], [1, -1, 3, -3, 0, -3], [2, -2, -3, 3, 0, -2], [6, 0, 2, -6, -3, 5], [0, -3, 2, 2, 2, -2], [0, 0, -1, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, -1], [-5, 5, 4, -4, 0, 7], [-3, 3, 0, 3, 0, 0], [0, 0, -1, 5, 5, -5], [-1, 0, 0, -5, -2, 0], [3, -6, -1, 3, 0, -4], [0, 0, 0, 0, 0, 0], [2, -2, -3, 3, 0, -5], [-1, 2, -3, 2, -1, -1], [-7, 7, 5, -5, 0, 10], [0, -2, -2, 3, 3, -3], [-6, 3, 0, 3, 3, 3], [0, 0, 0, -1, -2, 0], [0, 0, 0, 0, 0, 0], [0, -3, -2, 3, 1, 0], [0, 3, 9, -6, -6, 6], [1, 0, 0, 5, 5, 0], [-2, 1, 1, 1, 3, 0], [-2, 0, 0, -3, -3, 0], [10, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 3, 0], [5, 0, 0, -6, -1, 0], [0, 6, 4, -6, -7, 5], [-4, 0, 0, 3, 0, 0], [0, 2, 2, -3, -3, 3], [-1, 5, 2, 5, 6, -3], [0, 0, 0, 0, 0, 0], [3, 0, 0, -3, 3, 0], [3, -9, 0, 6, 9, -3], [0, -7, 1, 4, 4, -4], [10, -10, 0, 0, 0, -1], [-3, 0, -1, 3, 3, -4], [5, -5, -3, 3, 0, -3], [0, 0, 0, 0, 0, 0], [5, 8, 7, -13, -8, 7], [-7, 0, 0, 3, 0, 0], [0, -5, 2, 1, 1, -1], [0, 0, 3, 0, -3, 6], [-3, 3, 0, 0, 0, 0], [0, -6, -1, -4, -4, 4], [0, 0, 0, 0, 0, 0], [-3, 3, -4, 4, 0, -2], [0, -2, 0, -1, -1, 1], [9, -3, 7, -3, -1, -1], [-9, 9, 7, -7, 0, 8], [4, -4, -7, 7, 0, -3], [-6, 3, 0, 0, -3, 3], [0, 0, 0, 0, 0, 0], [0, -1, -2, 8, 8, -8], [9, 0, -7, 9, 6, -4], [6, 0, 0, 1, 2, 0], [-4, 0, 0, 0, -1, 0], [6, -3, -3, 6, 3, -3], [0, -1, 8, -7, -7, 7], [0, 0, 0, 0, 0, 0], [3, 0, 0, 0, -3, -3], [5, -5, -4, 4, 0, -8]]}