# Stored data for newform 920.2.a.j, downloaded from the LMFDB on 27 March 2023. {"level_primes": [2, 5, 23], "is_polredabs": true, "sato_tate_group": "1.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 1104020203729066329, "level_radical": 230, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 10, "analytic_conductor": 7.346236985957796, "inner_twist_count": 1, "field_disc_factorization": [[1249, 1], [11173, 1]], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "920.2.a.j", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "920.2.a.j", "field_poly_is_cyclotomic": false, "dim": 5, "trace_zratio": {"__RealLiteral__": 0, "data": "0.007", "prec": 17}, "traces": [0, 5, 0, 0, 0, -5, 0, -2, 0, 13, 0, -1, 0, 4, 0, 0, 0, 4, 0, 7, 0, 6, 0, -5, 0, 5, 0, 3, 0, 4, 0, 19, 0, 17, 0, 2, 0, 15, 0, 19, 0, 25, 0, 0, 0, -13, 0, -11, 0, 25, 0, 19, 0, 3, 0, 1, 0, 48, 0, -1, 0, -5, 0, -41, 0, -4, 0, 9, 0, 0, 0, 1, 0, -1, 0, 0, 0, 18, 0, -2, 0, 57, 0, -45, 0, -4, 0, -9, 0, 6, 0, 11, 0, -39, 0, -7, 0, 25, 0, -65, 0, -11, 0, -9, 0, -6, 0, -45, 0, -13, 0, -2, 0, 9, 0, 5, 0, 34, 0, -19, 0, 16, 0, -26, 0, -5, 0, 23, 0, 0, 0, 19, 0, -15, 0, -3, 0, 13, 0, 18, 0, -15, 0, -46, 0, -4, 0, -21, 0, 9, 0, 46, 0, -58, 0, -19, 0, 21, 0, -20, 0, 2, 0, -8, 0, -17, 0, -28, 0, 43, 0, 66, 0, -7, 0, -2, 0, -18, 0, -13, 0, -49, 0, -23, 0, -15, 0, 61, 0, -29, 0, 0, 0, -43, 0, -19, 0, -24, 0, -36, 0, -70, 0, -25, 0, -25, 0, -13, 0, 24, 0, 21, 0, -66, 0, 0, 0, 28, 0, -15, 0, -14, 0, 18, 0, 13, 0, -54, 0, -10, 0, 27, 0, 3, 0, 11, 0, -22, 0, -48, 0, 38, 0, -46, 0, -25, 0, 3, 0, 2, 0, 19, 0, 1, 0, -19, 0, -5, 0, 29, 0, -61, 0, 4, 0, -3, 0, -44, 0, -6, 0, 54, 0, -119, 0, -1, 0, 13, 0, 73, 0, 38, 0, -25, 0, -48, 0, -51, 0, 23, 0, 37, 0, -25, 0, 1, 0, 41, 0, -4, 0, 0, 0, -10, 0, 5, 0, 1, 0, 43, 0, 63, 0, -2, 0, 41, 0, 29, 0, 44, 0, -54, 0, 18, 0, 4, 0, -68, 0, 86, 0, 28, 0, 45, 0, -9, 0, 33, 0, -66, 0, -74, 0, 23, 0, 0, 0, 21, 0, -74, 0, 156, 0, -33, 0, -1, 0, 3, 0, -46, 0, 36, 0, -28, 0, 1, 0, 73, 0, 56, 0, 47, 0, 32, 0, 0, 0, -33, 0, 37, 0, -79, 0, 5, 0, -18, 0, 0, 0, -3, 0, -4, 0, 39, 0, 2, 0, -20, 0, -37, 0, 56, 0, 54, 0, -57, 0, 6, 0, 27, 0, 60, 0, -13, 0, 45, 0, 153, 0, -2, 0, 75, 0, -82, 0, 4, 0, 56, 0, -121, 0, -34, 0, 4, 0, 9, 0, -7, 0, 76, 0, -93, 0, 50, 0, -6, 0, 130, 0, 68, 0, -31, 0, -82, 0, -11, 0, -33, 0, 171, 0, -21, 0, 94, 0, 39, 0, -37, 0, -99, 0, 8, 0, 0, 0, 7, 0, 55, 0, 8, 0, -16, 0, -6, 0, -25, 0, 7, 0, -17, 0, -2, 0, 89, 0, 65, 0, -5, 0, -2, 0, 32, 0, -50, 0, 11, 0, 178, 0, 43, 0, 82, 0, 97, 0, 9, 0, 74, 0, 5, 0, 8, 0, -56, 0, 6, 0, -83, 0, 5, 0, 87, 0, 29, 0, 45, 0, -29, 0, 40, 0, 1, 0, 102, 0, 13, 0, -48, 0, -165, 0, -30, 0, 24, 0, 2, 0, -23, 0, 0, 0, -136, 0, 5, 0, -9, 0, -123, 0, 106, 0, 59, 0, -56, 0, -5, 0, 63, 0, -147, 0, -17, 0, -116, 0, -34, 0, -30, 0, -59, 0, 36, 0, 86, 0, 19, 0, 44, 0, 45, 0, 17, 0, 95, 0, -16, 0, -56, 0, 50, 0, -129, 0, 48, 0, 26, 0, 64, 0, 73, 0, -3, 0, 104, 0, 5, 0, -21, 0, -31, 0, 6, 0, -46, 0, -23, 0, 46, 0, -96, 0, -132, 0, -17, 0, 0, 0, -51, 0, -8, 0, 23, 0, 36, 0, -19, 0, -56, 0, -62, 0, -55, 0, 9, 0, 15, 0, -4, 0, -28, 0, 55, 0, 1, 0, 3, 0, -43, 0, -14, 0, -96, 0, -38, 0, -13, 0, -6, 0, 146, 0, -10, 0, 169, 0, -18, 0, 44, 0, -69, 0, 35, 0, 34, 0, 15, 0, -149, 0, 3, 0, -136, 0, -19, 0, 46, 0, -79, 0, 122, 0, -72, 0, 94, 0, 4, 0, 18, 0, 220, 0, 0, 0, -39, 0, 21, 0, -62, 0, 14, 0, 119, 0, -53, 0, -9, 0, -123, 0, -29, 0, -36, 0, -102, 0, -46, 0, 21, 0, -17, 0, -1, 0, 39, 0, 58, 0, -110, 0, 20, 0, 55, 0, 32, 0, 19, 0, 48, 0, -26, 0, -43, 0, 75, 0, -21, 0, -23, 0, -41, 0, -169, 0, -6, 0, 20, 0, -57, 0, -52, 0, -62, 0, 72, 0, -2, 0, 107, 0, -32, 0, -6, 0, 68, 0, 8, 0, 0, 0, -219, 0, 82, 0, -61, 0, 17, 0, -25, 0, 37, 0, -23, 0, 138, 0, 28, 0, -154, 0, -92, 0, -47, 0, 24, 0, -43, 0, -9, 0, -104, 0, -15, 0, 37, 0, -66, 0, -45, 0, 26, 0, 47, 0, 25, 0, 7, 0, -220, 0, 108, 0, -84, 0, -93, 0, 2, 0, 109, 0, -114, 0, -70, 0, 31, 0, 18, 0, -103, 0, -128, 0, -340, 0, -12, 0, 13, 0, -19, 0, -44, 0, -113, 0, 0, 0, 49, 0, 95, 0, 37, 0, 64, 0, 0, 0, 23, 0, -174, 0, -24, 0, -79, 0, 53, 0, 15, 0, 33, 0, 20, 0, -99, 0, 89, 0, -61, 0, -9, 0, 108, 0, 17, 0, -25, 0, 29, 0, -134, 0, -121, 0, -192, 0, 127, 0, 0, 0, -68, 0, 101, 0, 62, 0, -129, 0, 43, 0, 3, 0, 27, 0, -17, 0, 137, 0, 19, 0, 68, 0, 0, 0, 14, 0, -48, 0, 24, 0, 122, 0, 0, 0, 86, 0, -187, 0, 36, 0, 4, 0, -118, 0], "hecke_ring_index_factorization": [], "nf_label": "5.5.13955077.1", "field_poly": [16, 32, -1, -14, 0, 1], "atkin_lehner_string": "-++", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[2, -1], [5, 1], [23, 1]], "char_values": [920, 1, [231, 461, 737, 281], [1, 1, 1, 1]], "Nk2": 3680, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "a", "weight": 2, "trace_display": [0, 0, -5, -2], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+\\beta _{1}q^{3}-q^{5}+(-\\beta _{3}-\\beta _{4})q^{7}+(2+\\cdots)q^{9}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 13955077, "level_is_prime_power": false, "relative_dim": 5, "hecke_cutters": [[3, [16, 32, -1, -14, 0, 1]]], "space_label": "920.2.a", "level": 920, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 7, "hecke_orbit_code": 40532396679889816, "fricke_eigenval": -1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.057", "prec": 17}, {"__RealLiteral__": 0, "data": "4.816", "prec": 17}, {"__RealLiteral__": 0, "data": "0.176", "prec": 17}, {"__RealLiteral__": 0, "data": "62.444", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1202.194", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0, 0, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, -1, -1], [0, 0, 0, 0, 0], [2, 0, 1, 0, 1], [0, 0, 0, 0, 0], [0, 1, -1, 0, 0], [0, 0, 0, 0, 0], [1, 0, 1, 0, -1], [0, 0, 0, 0, 0], [0, -1, 0, 0, 0], [0, 0, 0, 0, 0], [1, 1, -1, 1, 0], [0, 0, 0, 0, 0], [1, 2, 0, 0, 1], [0, 0, 0, 0, 0], [1, -1, -1, 0, 1], [0, 0, 0, 0, 0], [-1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [1, 3, 0, 2, -1], [0, 0, 0, 0, 0], [1, 0, -1, 1, 0], [0, 0, 0, 0, 0], [4, -2, 1, -1, -1], [0, 0, 0, 0, 0], [3, -2, 0, -2, 1], [0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 0], [3, 0, 0, -1, 0], [0, 0, 0, 0, 0], [3, 1, 2, 2, 1], [0, 0, 0, 0, 0], [5, -1, 0, 1, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-2, 0, -1, 0, -1], [0, 0, 0, 0, 0], [-2, 0, -1, -2, 0], [0, 0, 0, 0, 0], [6, -1, -1, 1, -2], [0, 0, 0, 0, 0], [3, -2, 2, -2, 1], [0, 0, 0, 0, 0], [1, -2, 2, -1, -2], [0, 0, 0, 0, 0], [0, -1, 1, 0, 0], [0, 0, 0, 0, 0], [9, 3, 1, 0, 1], [0, 0, 0, 0, 0], [-1, 0, 0, -1, 2], [0, 0, 0, 0, 0], [0, -1, -1, 0, -2], [0, 0, 0, 0, 0], [-8, 1, -3, 1, 1], [0, 0, 0, 0, 0], [-1, 0, -1, 0, 1], [0, 0, 0, 0, 0], [1, -2, 0, 1, 2], [0, 0, 0, 0, 0], [0, -1, 0, 0, 0], [0, 0, 0, 0, 0], [1, -3, 0, 1, -2], [0, 0, 0, 0, 0], [0, 0, -1, -2, 0], [0, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0], [3, 1, 1, -2, 1], [0, 0, 0, 0, 0], [0, 0, -2, 0, 0], [0, 0, 0, 0, 0], [10, -3, 5, 0, 1], [0, 0, 0, 0, 0], [-9, 0, 0, 1, 0], [0, 0, 0, 0, 0], [-1, -1, 1, -1, 0], [0, 0, 0, 0, 0], [-2, -2, 1, -2, 0], [0, 0, 0, 0, 0], [2, -2, 0, -2, -2], [0, 0, 0, 0, 0], [4, -5, -1, 0, -4], [0, 0, 0, 0, 0], [-7, 5, -2, 2, -1], [0, 0, 0, 0, 0], [-1, -2, 0, 0, -1], [0, 0, 0, 0, 0], [6, 1, -1, 2, -2], [0, 0, 0, 0, 0], [-11, 4, -4, 0, -3], [0, 0, 0, 0, 0]]}