# Stored data for newform 285.2.i.e, downloaded from the LMFDB on 12 May 2025.
{"Nk2": 1140, "analytic_conductor": 2.275736457606491, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 19, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 3, "char_parity": 1, "char_values": [285, 3, [191, 172, 211], [3, 3, 2]], "cm_discs": [], "conrey_index": 106, "dim": 4, "field_disc": 225, "field_disc_factorization": [[3, 2], [5, 2]], "field_poly": [1, 1, 2, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, 1, 2, -1, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014948298850589, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "285.2.i.e", "level": 285, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [3, 5, 19], "level_radical": 285, "minimal_twist": "285.2.i.e", "nf_label": "4.0.225.1", "prim_orbit_index": 3, "qexp_display": "q+\\beta _{1}q^{2}+(-1-\\beta _{3})q^{3}+(\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "285.2.i", "trace_display": [1, -2, 2, 12], "trace_hash": 968023520115613012, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.891", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "56.861", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1406.000", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.015", "prec": 17}, "traces": [0, 4, 1, -2, 1, 2, 1, 12, 0, -2, -1, 8, -2, -2, -2, 2, 3, -2, -2, -4, 2, -6, 2, -4, 0, -2, 8, 4, 8, 6, 2, -24, -9, -4, -9, 6, 1, -8, -13, 4, 0, -2, -2, -10, 2, -4, 16, -8, 3, 28, -2, -2, 6, 2, 1, 4, -20, -4, -4, 4, -1, -16, -11, -6, 8, -4, 2, 2, -22, 8, 2, -14, 0, 16, 8, 4, -4, 24, -4, 0, -3, -2, 16, 16, -16, 2, 20, -12, 0, -16, -1, -16, 12, 12, 2, 4, 18, 4, -23, -4, 1, 6, 18, -32, 10, 6, 2, 8, 1, 14, -2, 4, -6, 44, -4, -8, -8, -2, -2, -26, 0, -28, -36, -2, -1, -4, 4, 26, 25, -10, 4, -4, -4, 18, 12, 2, 20, -14, -8, -12, 16, 16, 12, -4, -6, 12, 2, -14, -12, 6, 1, -40, -30, 4, -4, -12, 6, -40, 0, -4, -18, -32, 1, 0, 28, 4, 29, -24, 10, 14, -18, 8, 20, -12, 2, -6, 6, 4, 4, 44, -1, 18, 24, 32, 20, -4, -11, -4, 9, 12, 4, 60, -4, -14, -2, 2, 37, 28, -4, -8, 0, -4, -44, 28, 11, 2, 12, -4, 24, -8, -4, -16, -1, -14, -33, 10, 0, -52, -7, 16, 4, 44, 8, 14, -32, -2, 1, 16, -13, 36, 8, -12, -10, 18, -4, -16, 4, 0, -22, 4, 6, -2, -7, -2, -2, 14, -32, 8, -20, -8, -1, -36, 8, -8, 36, -4, -7, 16, -40, -64, -6, 6, -8, -4, 0, 4, -34, 32, 4, -32, -1, -20, -27, 32, -74, -4, 12, 44, -2, 12, -10, 2, -1, 2, -4, -8, 16, 24, -9, -8, -2, 4, 36, -68, -23, -4, 40, 8, -18, -24, 1, 0, -25, -12, -39, -32, -9, 18, 16, 16, 11, -32, -20, -14, 20, -12, 0, 26, -1, 12, 4, -4, 48, -64, -2, -2, 20, 14, -30, -34, 4, 8, -21, 4, 26, 4, -6, 4, -17, -22, -11, -48, 17, 120, -30, 4, -34, 16, -8, -108, 4, -2, -18, 88, 4, 14, 18, -26, 26, -56, 0, 22, 38, 14, 28, -16, 18, 10, 48, 4, -8, 6, 2, 44, -18, 2, 10, 16, -2, 120, 13, -52, 30, -32, 25, 12, 2, 20, 4, 26, 4, 88, -120, -4, 17, 0, 2, 6, 72, -42, -6, -54, -6, 2, -28, 2, -32, -16, 20, 8, 32, 28, -28, 12, -8, 8, -14, 24, -26, 104, -8, -8, 33, -8, 0, 4, -24, -28, 37, 8, 40, 12, 3, 30, 2, -6, 14, 16, -4, 8, 0, -14, -4, 0, 24, -32, 28, 6, 4, 12, 1, -4, 21, 20, 4, -32, 30, 108, 19, -2, -12, 74, -4, -124, -12, -12, 11, -72, -12, -4, 1, -40, 0, -20, 0, 8, -96, 2, 46, 10, 9, 24, 98, 64, -7, -4, -2, -108, -20, 0, 23, 30, -14, -52, -8, -8, -33, -32, 29, 16, -1, 48, -96, -52, 10, 12, 32, 14, -8, -30, 9, 68, 48, -4, -44, -16, -10, -16, 24, -12, 20, -48, 2, -36, -24, 12, -13, -8, 6, -2, 1, -8, -32, -56, -2, 4, 10, -22, 36, 56, 2, 58, 15, -36, 38, -14, -12, 4, -23, -16, -4, -24, -40, 0, 26, -4, 11, 16, 22, -40, 6, -4, -8, -32, 9, 22, 24, -6, -10, -24, -17, 0, 12, -30, 28, -4, -4, -72, 32, -14, 8, -52, 4, 4, -20, 2, 13, -24, -74, 54, -4, -14, 24, -10, 2, 26, -24, 16, -8, -38, 0, 24, 20, 2, 5, -14, 22, 104, 36, -56, -18, -18, 11, -44, -34, -4, -40, 14, 12, -24, -2, -4, -38, -68, -12, -2, -124, -8, -40, 44, 2, -48, 0, -16, -54, 52, -1, -74, -8, 28, -25, 52, -33, -24, 56, -20, 36, 8, 0, 8, -4, 26, -20, -32, 14, 4, 48, -32, 36, -20, -2, 66, -8, -22, 100, 42, -16, 32, 37, 14, 6, -32, 64, 36, -12, -2, -6, 60, 1, 12, -20, -8, -22, 96, 17, -28, -60, -18, 60, 2, 8, -64, -92, -12, -53, -24, 20, 58, -27, 18, 8, 24, 8, -52, 16, 8, 42, 68, -2, -30, 24, 0, 20, 4, 44, -8, -4, -2, 18, 24, -3, -176, 22, 4, 1, 6, -7, -78, 40, 4, 4, 50, -2, 116, -40, 14, -28, 4, 16, 8, -24, 26, -4, -28, 10, -6, 66, -8, -44, 164, -1, -28, 6, 72, 12, -20, 8, -2, 20, 16, -30, 40, -18, 42, 0, 2, 61, -8, 14, 14, 4, -32, -24, -20, 20, 12, 0, 32, -64, 86, 12, -28, -8, 6, -69, 40, 16, 68, -3, -4, 0, 172, 0, 4, -28, -2, 44, -84, 8, 56, -9, -16, 42, 32, 4, -64, -48, -32, -50, -68, 2, -16, -44, -20, 16, 0, 54, 70, -92, -16, 14, -30, 37, 28, 80, 8, 4, -56, -24, -4, -29, -22, 6, -134, 1, -48, -8, -24, 46, -18, -10, 30, -46, -4, 34, -14, -1, -84, 6, 2, -9, 48, 2, -92, -8, 4, -140, 42, -8, 20, 10, 24, -8, 56, -9, 12, -80, 16, -28, 0, -2, -8, 0, -8, -16, -12, -18, -24, -9, 34, -6, -28, 46, 0, 26, 8, -30, 64, -20, 68, 2, -4, 84, 32, 36, 22, 70, -24, -62, -26, -2, -4, 32, 0, -40, 36, -25, 8, 4, 6, 12, -100, -12, 32, 22, 16, -1, -32, -9, 0, 40, 18, -32, 8, -32, 4, -46, 16, 32, -40, -22, 152, 58, 16, -13, 4, 10, -40, 16, 28, -9, 56, -40, -112, -6, 6, 40, -32, 0, -72, 17, -52, 70, -58, -1, 30, -44, -24, 140, 18, 4, 40, -16, -4, 51, 14, -24, 20, 0, 8, -4, 34, 1, -46, -42, -2, -108, 28, 20, -32, 74, -28, -30, 28, -30, 14, 22, 68, 42, -80, -2, 8, 49, -4, -4, -16, 42, 100, -43, -8, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [-1, 0, 0, -1], [0, 1, 1, -1], [1, 0, 0, 1], [0, -1, -1, 0], [4, 0, 2, 0], [-1, 0, -2, 0], [0, 0, 0, 1], [0, 1, 1, 0], [2, 0, 0, 0], [-1, 0, -1, 0], [0, -2, -2, 2], [-2, 2, 0, -2], [0, 0, 0, -1], [0, 3, 0, 0], [-3, 4, 0, -3], [0, 0, 1, 0], [-1, 2, 4, -3], [1, 0, 1, 0], [-4, 2, 0, -4], [0, 2, 0, 0], [0, -4, -4, 4], [1, -2, 0, 1], [0, 0, 0, 1], [2, 0, 0, 0], [1, 0, 0, 0], [0, 4, 4, -6], [0, 2, 2, -4], [0, 0, -1, 0], [-5, 0, 2, 0], [0, -1, -1, 5], [-2, 0, 0, -2], [0, 1, 1, 4], [4, -2, 0, 4], [1, -1, 0, 1], [-4, 0, -4, 0], [-4, -3, -1, -2], [2, 0, 2, 0], [-1, 2, 0, -1], [2, -6, 0, 2], [0, -2, -2, 2], [-2, -6, 0, -2], [0, 2, 2, -2], [-1, 0, 0, 0], [4, 0, 0, 0], [0, -2, -2, 5], [0, -3, -3, 0], [13, 0, 12, 0], [0, 0, 1, 0], [0, -4, -4, 3], [4, -2, 0, 4], [0, 0, 0, -1], [0, 1, 0, 0], [2, 0, 0, 2], [-8, 0, -6, 0], [-2, 2, -2, 1], [-2, 0, -2, 0], [2, 0, 0, 2], [-1, 1, 0, -1], [0, 4, 4, 6], [-2, -7, 0, -2], [0, -2, -2, 4], [1, 0, -2, 0], [-2, 0, -2, 0], [0, -2, -2, 0], [0, -2, -2, 0], [-7, 0, -3, 0], [4, 0, 4, 0], [0, 2, 2, -2], [-6, -2, 0, -6], [0, 2, 2, -1], [10, -4, 0, 10], [4, 0, 0, 4], [1, 0, 0, 0], [-5, 2, -1, -6], [8, 0, 4, 0], [-2, 0, 0, -2], [0, 0, 0, 0], [0, 3, 3, 0], [-1, 0, 0, -1], [0, -4, -4, -6], [-1, 0, -10, 0], [-6, 0, -4, 0], [0, 4, 4, -3], [0, -8, -8, -6], [-4, 0, -2, 0], [-2, 0, -4, 0], [0, -4, -4, 10], [0, -1, 0, 0], [0, -8, -8, 12], [8, -4, 0, 8], [5, 2, 0, 5], [2, 0, 3, 0], [2, -2, 2, -1], [5, 0, 1, 0], [2, 0, 0, 2], [-12, 1, 0, -12], [0, 0, 0, 2], [1, -1, 0, 1]]}