# Stored data for newform 270.2.a.a, downloaded from the LMFDB on 23 April 2024. {"label": "270.2.a.a", "space_label": "270.2.a", "level": 270, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554702, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1826914269468194469, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [-3, 1]], [13, [1, 1]]], "qexp_display": "q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1080, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 2.1559608545745705, "hecke_ring_index": 1, "level_radical": 30, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.021", "prec": 17}, "analytic_rank_proved": true, "char_values": [270, 1, [191, 217], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "0.994", "prec": 17}, {"__RealLiteral__": 0, "data": "0.083", "prec": 17}, {"__RealLiteral__": 0, "data": "1.923", "prec": 17}, {"__RealLiteral__": 0, "data": "0.262", "prec": 17}, {"__RealLiteral__": 0, "data": "4.644", "prec": 17}], "related_objects": ["EllipticCurve/Q/270/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [5, 1]], "trace_display": [-1, 0, -1, 2], "traces": [0, 1, -1, 0, 1, -1, 0, 2, -1, 0, 1, 3, 0, -1, -2, 0, 1, 3, 0, 8, -1, 0, -3, -3, 0, 1, 1, 0, 2, 9, 0, -7, -1, 0, -3, -2, 0, 2, -8, 0, 1, 12, 0, -7, 3, 0, 3, 3, 0, -3, -1, 0, -1, -12, 0, -3, -2, 0, -9, -12, 0, -10, 7, 0, 1, 1, 0, -4, 3, 0, 2, 0, 0, 2, -2, 0, 8, 6, 0, -1, -1, 0, -12, -18, 0, -3, 7, 0, -3, 0, 0, -2, -3, 0, -3, -8, 0, 14, 3, 0, 1, 3, 0, 14, 1, 0, 12, -6, 0, -4, 3, 0, 2, 15, 0, 3, 9, 0, 12, 6, 0, -2, 10, 0, -7, -1, 0, 2, -1, 0, -1, -3, 0, 16, 4, 0, -3, 6, 0, 14, -2, 0, 0, -3, 0, -9, -2, 0, 2, -15, 0, -1, -8, 0, -6, 7, 0, 17, 1, 0, 1, -6, 0, -19, 12, 0, 18, -12, 0, -12, 3, 0, -7, -6, 0, 2, 3, 0, 0, 12, 0, 8, 2, 0, 3, -2, 0, 9, 3, 0, 8, -18, 0, 14, -14, 0, -3, -12, 0, 5, -1, 0, -3, 18, 0, -12, -14, 0, -1, 24, 0, -10, -12, 0, 6, 7, 0, -14, 4, 0, -3, -3, 0, -4, -2, 0, -15, -12, 0, -16, -3, 0, -9, 18, 0, -3, -12, 0, -6, -18, 0, 5, 2, 0, -10, 3, 0, -8, 7, 0, 1, 15, 0, -9, -2, 0, 1, 15, 0, 4, 1, 0, 3, 12, 0, 12, -16, 0, -4, -21, 0, -16, 3, 0, -6, 3, 0, -22, -14, 0, 2, -6, 0, -16, 0, 0, 3, 24, 0, -8, 9, 0, 2, 30, 0, 12, -2, 0, 15, 3, 0, -14, 1, 0, 8, 10, 0, 29, 6, 0, -7, -12, 0, -4, -17, 0, -1, -24, 0, 27, -1, 0, 6, 24, 0, -1, 19, 0, -12, 6, 0, -10, -18, 0, 12, 4, 0, -16, 12, 0, -3, -21, 0, -20, 7, 0, 6, 12, 0, 26, -2, 0, -3, -3, 0, 0, 0, 0, -12, 24, 0, 45, -8, 0, -2, -2, 0, -10, -3, 0, 2, -24, 0, 29, -9, 0, -3, -9, 0, 8, -8, 0, 18, -3, 0, -6, -14, 0, 14, -27, 0, -9, 3, 0, 12, 1, 0, 35, -5, 0, 1, 12, 0, 7, 3, 0, -18, 6, 0, -25, 12, 0, 14, -24, 0, 18, 1, 0, -24, -3, 0, 8, 10, 0, 12, 3, 0, -20, -6, 0, -7, 0, 0, 14, 14, 0, -4, -24, 0, 8, 3, 0, 3, 0, 0, 0, 4, 0, 2, 6, 0, 36, 15, 0, 12, 2, 0, -28, 16, 0, 3, -30, 0, -22, 9, 0, -18, 0, 0, -8, 3, 0, 12, -21, 0, 8, 6, 0, 18, 0, 0, -2, -5, 0, -2, -14, 0, -4, 10, 0, -3, 36, 0, 27, 8, 0, -7, 0, 0, -4, -1, 0, -15, 21, 0, -3, 9, 0, 2, 21, 0, 4, -1, 0, -15, -14, 0, 9, -4, 0, -1, 0, 0, -25, -3, 0, -12, -21, 0, -14, -12, 0, 16, -12, 0, 6, 4, 0, 21, -9, 0, -22, 16, 0, -3, 4, 0, -19, 6, 0, -3, 72, 0, -2, 22, 0, 14, 0, 0, 7, -2, 0, 6, -18, 0, -15, 16, 0, 0, -24, 0, 26, -3, 0, -24, -3, 0, -16, 8, 0, -9, -36, 0, -36, -2, 0, -30, 6, 0, -56, -12, 0, 2, -21, 0, -6, -15, 0, -3, -6, 0, 29, 14, 0, -1, 2, 0, -22, -8, 0, -10, -3, 0, -25, -29, 0, -6, 21, 0, -10, 7, 0, 12, 0, 0, 1, 4, 0, 17, 6, 0, 8, 1, 0, 24, -2, 0, 3, -27, 0, 1, 42, 0, 41, -6, 0, -24, 12, 0, -36, 1, 0, -19, -48, 0, 3, 12, 0, -6, 0, 0, 14, 10, 0, 18, -16, 0, -27, -12, 0, -4, -30, 0, 26, 16, 0, -12, 36, 0, 28, 3, 0, 21, -24, 0, -6, 20, 0, -7, 12, 0, -10, -6, 0, -12, -14, 0, 36, -26, 0, 2, 33, 0, 16, 3, 0, 3, 6, 0, -4, 0, 0, 0, 21, 0, 3, 12, 0, -24, -18, 0, 28, -45, 0, 8, 9, 0, 44, 2, 0, 2, -21, 0, 14, 10, 0, 3, -12, 0, -16, -2, 0, 24, -33, 0, 15, -29, 0, 9, -12, 0, -13, 3, 0, 9, 1, 0, -7, -8, 0, 8, 42, 0, -8, -18, 0, 3, 12, 0, -1, 6, 0, 14, -6, 0, -7, -14, 0, 27, 96, 0, 0, 9, 0, -3, -17, 0, -31, -12, 0, -1, 30, 0, 10, -35, 0, 5, 0, 0, 9, -1, 0, -12, 6, 0, 6, -7, 0, -3, 0, 0, -10, 18, 0, -6, 19, 0, -56, 25, 0, -12, 30, 0, 44, -14, 0, 24, 42, 0, 20, -18, 0, -1, -9, 0, 12, 24, 0, 3, 6, 0, 52, -8, 0, -10, 12, 0, -4, -12, 0, -3, -6, 0, -1, 20, 0, 6, 30, 0, 50, 7, 0, 0, -33, 0, 6, -14, 0, -14, -3, 0, 4, 4, 0, 24, -2, 0, 53, -8, 0, -3, -18, 0, -28, -3, 0, 0, 15, 0, 4, 0, 0, -4, 24, 0, -12, -2, 0, -6, -63, 0, -36, -36, 0, -15, -8, 0, 53, -12, 0, -2, 24, 0, -54, 28, 0, -16, -6, 0, 11, -3, 0, 30, 0, 0, 2, 22, 0, -9, 0, 0, -24, 18, 0, 0, -9, 0, -22, 8, 0, -3, -3, 0, -36, -12, 0, 21, -42, 0, -2, -8, 0, -6, 57, 0, 18, -18, 0, 0, 12, 0, 18, 2, 0, 5, -14, 0, -58, 2, 0, 14, -33, 0, 28, 4, 0, -10, -33, 0, 0, 3, 0, -36, 45, 0, 12, -27, 0, -8, 21, 0, -7, 7, 0, 0, -5, 0, 17, 4, 0, 1], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "270.2.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-1], [0], [1], [-1], [0], [2], [-1], [0], [1], [3], [0], [-1], [-2], [0], [1], [3], [0], [8], [-1], [0], [-3], [-3], [0], [1], [1], [0], [2], [9], [0], [-7], [-1], [0], [-3], [-2], [0], [2], [-8], [0], [1], [12], [0], [-7], [3], [0], [3], [3], [0], [-3], [-1], [0], [-1], [-12], [0], [-3], [-2], [0], [-9], [-12], [0], [-10], [7], [0], [1], [1], [0], [-4], [3], [0], [2], [0], [0], [2], [-2], [0], [8], [6], [0], [-1], [-1], [0], [-12], [-18], [0], [-3], [7], [0], [-3], [0], [0], [-2], [-3], [0], [-3], [-8], [0], [14], [3], [0], [1]]}