# Stored data for newform 441.2.s.a, downloaded from the LMFDB on 25 April 2024.
{"label": "441.2.s.a", "space_label": "441.2.s", "level": 441, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1236984136121, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 655624819631000140, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [3, 3, 1]]], "qexp_display": "q+(-1-\\zeta_{6})q^{2}+(2-\\zeta_{6})q^{3}+\\zeta_{6}q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "s", "char_is_real": false, "Nk2": 1764, "analytic_conductor": 3.521402729138465, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.178", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 6, [344, 199], [1, 5]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [362, 374], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.936", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.419", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "93.297", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c6", "trace_display": [-3, 3, 6, 0], "traces": [0, 2, -3, 3, 1, 6, -6, 0, 0, 3, -9, 0, 3, 3, 0, 9, 5, -3, -9, 9, 3, 0, -3, 0, 3, 8, -3, 0, 0, -9, -18, 6, -9, -3, 9, 0, 6, -7, -18, 6, 0, -3, 0, -1, 3, 9, 9, 0, 0, 0, -12, 0, 0, -15, -9, 0, 0, 9, 18, 0, 9, -24, -12, 0, -2, 9, 0, 4, -6, 9, 0, 0, 9, 9, 0, 12, 9, 0, -9, -8, 15, -9, 9, 15, 0, -9, 0, -9, 6, -3, -27, 0, -9, 6, 0, 27, -9, 3, 0, -9, 4, 6, 9, 0, -3, 0, 15, -15, 9, -19, -9, -21, 0, 3, -27, 0, -9, 9, 0, 0, 9, 16, 24, 0, 6, -6, 0, 40, 21, -3, -9, 18, 3, 0, 0, 0, -9, 0, 0, 15, 0, 0, -6, 3, -15, -27, -9, 0, 7, 0, -24, -34, 9, 9, 0, 18, 3, 0, 24, -30, -27, 0, 0, -11, -6, -9, 0, 9, 0, -10, 27, 0, 1, 6, 27, 0, -15, 0, 0, 27, 18, 0, 0, -48, -18, -21, -18, 9, 0, 0, -54, -30, -3, 2, -6, 18, 0, 0, 9, 15, 0, 12, -9, 0, -9, -9, 21, 27, 15, -9, 0, 5, 0, -6, 30, -3, 18, 0, 57, 18, 9, -9, 21, 9, 0, 12, -3, -42, 18, 0, 27, 0, -9, 9, -18, 0, 0, 0, 0, 3, 0, 0, -24, -27, 0, 0, 9, 18, 6, 45, 9, -24, 0, 18, -60, 0, -19, 6, 3, 0, 0, 0, -27, 0, 9, -45, 0, -9, -4, -15, -27, 21, 15, 0, 21, 0, -9, -2, -15, 0, 0, -33, 0, -6, 6, 27, -9, 0, 0, 8, 54, 3, 0, 9, 0, 0, 21, -18, 3, -9, 12, 0, 51, 9, 0, -72, 0, 0, 0, 21, -36, 24, 0, 36, 0, 0, -16, 0, 45, 9, -6, -15, 0, 0, 9, 12, 0, 0, -9, 0, 0, 8, -15, -42, -27, 12, 0, -19, 0, 6, -18, -6, -27, 0, 3, 27, -18, -6, -18, -21, 0, 9, 9, -42, 0, 0, 3, 0, -27, -39, 27, 8, 0, 24, 0, 27, 72, 0, 45, 9, 0, 0, 12, -74, -9, -9, 0, -18, 0, -40, 27, 60, 30, 18, 42, 0, 0, -6, 3, 0, -27, -27, 0, 27, 24, -24, 0, -15, -15, 0, 20, 0, -12, 12, 3, -27, 0, -21, -18, 12, 27, 21, -21, 0, -27, 45, -18, 30, 0, 33, 0, -11, -15, 0, 15, -12, 0, 0, -15, 0, 0, 27, -45, 0, 0, -27, -38, 27, -27, -54, 18, 0, 18, 54, 0, -9, -18, 3, 0, 0, -36, 9, 0, -51, 63, 0, 27, 26, 15, 27, -27, -15, 0, 1, 0, 18, -18, -3, 9, 0, 0, 0, 0, -3, 24, 36, 0, -45, -3, 54, -27, 0, -39, 0, 8, 9, 27, 23, 24, -33, 0, -45, -9, 0, -27, -27, 0, 0, -45, 50, -3, 0, 36, 48, 0, 18, -27, -30, 20, -66, 27, 0, 0, -27, -9, 0, 0, 0, 0, 0, -9, 45, 27, 33, 9, 0, -39, 0, -30, -8, 45, 0, 0, -9, 9, -45, -12, 54, 45, 0, 27, 13, -42, 0, 0, -57, 0, 19, -21, -72, -12, -27, -27, 0, 3, -63, 0, 21, -18, 0, 0, 18, 66, -36, 0, 9, 12, 0, 12, 12, -81, -32, 6, -60, 0, 0, -3, 69, 0, 6, -27, 0, -9, -15, -9, 27, -27, -21, 0, 18, 0, 24, -70, -39, 27, 0, -3, 30, 27, -42, 12, 51, 0, 24, -17, 48, -18, 0, -27, 0, 72, 0, -9, -47, 42, 0, 0, -9, 0, 0, 18, 54, 0, 0, 15, -58, -36, -27, 0, 42, 0, 16, -24, 0, 0, 120, -15, 0, 0, -18, 63, 0, 45, -21, 0, -9, 27, 3, 27, 0, -12, 0, 11, 0, 57, 54, 15, 27, 0, 21, 9, -72, -24, -9, -45, 0, 63, -27, 18, 9, 0, -24, 0, 29, 57, 0, 10, -18, -9, 0, -27, -63, 0, 15, 27, 0, 0, 15, -10, -15, 0, 6, 12, 0, 12, 45, -27, -9, 42, 9, 0, 0, -27, -63, 0, 0, 63, 0, 0, -10, -18, 24, 9, 18, 0, 9, 0, 6, 78, 9, -45, 0, -24, -39, 0, -36, -48, 21, 0, -54, -27, 6, -24, 0, 9, 0, -27, 12, 0, 7, 21, 27, 0, -21, 18, 0, 111, 90, 0, 0, 18, 74, 0, -36, 27, -102, 0, 20, 60, 27, 27, -90, -120, 0, 0, 27, -27, 0, -57, 27, 0, 9, -2, -51, 9, 24, 3, 0, -63, 0, 9, -12, 27, 27, 0, 0, -54, 66, -24, -39, 72, 0, 9, -24, 30, -90, 0, 45, 0, 0, -36, -18, -57, 9, 0, 0, -18, 0, 0, -3, 0, 0, 0, 21, 42, -33, 45, -9, -24, 0, -18, 12, 0, 16, -42, -12, 0, 0, 0, -63, 0, -3, -3, 0, -45, 27, 9, -18, -99, 39, 0, -2, 0, -33, 10, -30, 0, 0, -75, -6, 36, 63, 6, -45, 0, 0, -15, 54, -9, 0, 3, 0, -27, -75, 27, 18, -24, 24, 0, 24, 81, 0, -57, 0, 0, 0, 9, 46, 54, 0, -45, 108, 0, 8, -9, 0, -54, -30, 21, 0, 0, -27, 9, 0, 0, 81, 0, 0, -60, -18, 24, 45, -9, 0, -3, 0, 102, 38, -21, 9, 0, 9, -45, 45, -78, -144, -15, 0, -27, 29, -54, 42, 0, 6, 0, -28, -3, 63, 27, 30, -54, 0, 9, 72, 0, 27, 9, 0, 0, 72, 0, -18, 0, -27, 0, 0, 6, -90, -24, 9, -72, 0, 0, 0, 90, -90, 0, 27, -81, 0, -9, -19, -21, 0, 39, 6, 0, 25, 0, 27, -18, 57, 0, 0, -69, 24, -120, -72, 33, -9, 0, 57, 45, 78, -18, 0, -27, 0, 9, 9, 27, 47, -18, 0, 0, 45, 0, 0, -75, -63, 0], "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, 19, 1, 6, 0]], "char_orbit_index": 19, "prim_orbit_index": 19, "minimal_twist": "63.2.i.a", "char_is_minimal": false, "conrey_index": 362, "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], [1, 0], [-1, -1], [2, -1], [0, 1], [3, 0], [-3, 0], [0, 0], [-1, 2], [3, -3], [-3, -3], [1, -2], [1, 1], [1, 1], [0, 0], [6, -3], [5, -5], [-3, 3], [-6, 3], [6, -3], [0, 3], [0, 0], [-3, 3], [-3, 6], [0, 3], [4, 0], [0, -3], [3, -6], [0, 0], [-6, 3], [-9, 0], [4, -2], [-6, 3], [0, -3], [6, -3], [0, 0], [3, 0], [0, -7], [-9, 0], [3, 0], [-3, 6], [-3, 3], [0, 0], [0, -1], [2, -1], [9, -9], [9, -9], [0, 0], [5, -10], [0, 0], [-4, -4], [-3, 6], [-1, 2], [-5, -5], [-9, 9], [3, -6], [0, 0], [9, -9], [9, 0], [0, 0], [3, 3], [-8, -8], [-6, 0], [0, 0], [-1, 0], [3, 3], [-3, 6], [0, 4], [-3, 0], [0, 9], [0, 0], [2, -4], [3, 3], [3, 3], [-7, 14], [8, -4], [3, 3], [0, 0], [-3, -3], [-8, 8], [15, -15], [0, -9], [6, -3], [0, 15], [0, 0], [-9, 9], [-1, 2], [-9, 9], [3, 0], [0, -3], [-18, 9], [0, 0], [-6, 3], [6, -6], [0, 0], [18, -9], [-9, 9], [2, -1], [0, 0], [-3, -3], [0, 4]]}