# Stored data for newform 720.2.q.l, downloaded from the LMFDB on 16 April 2024. {"label": "720.2.q.l", "space_label": "720.2.q", "level": 720, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49540695446258384, "dim": 8, "is_polredabs": true, "nf_label": "8.0.856615824.2", "trace_hash": 1782942467972429017, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [16, 28, 109, -113, 214, -29, 16, 1, 1]], [11, [190096, 8720, 18712, 32, 1348, 2, 43, -1, 1]]], "qexp_display": "q+\\beta _{4}q^{3}-\\beta _{1}q^{5}+(\\beta _{2}-\\beta _{4})q^{7}+(-\\beta _{1}+\\cdots)q^{9}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "q", "char_is_real": false, "Nk2": 2880, "analytic_conductor": 5.749228945532187, "hecke_ring_index": 9, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [720, 3, [271, 181, 641, 577], [3, 3, 2, 3]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [241, 481], "field_disc": 856615824, "field_disc_factorization": [[2, 4], [3, 6], [271, 2]], "field_poly": [4, 0, 32, 0, 36, 0, 11, 0, 1], "hecke_ring_index_factorization": [[3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "7.509", "prec": 17}, {"__RealLiteral__": 0, "data": "2.626", "prec": 17}, {"__RealLiteral__": 0, "data": "224.946", "prec": 24}, {"__RealLiteral__": 0, "data": "353.469", "prec": 24}, {"__RealLiteral__": 0, "data": "12393.740", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 0, -4, -1], "traces": [0, 8, 0, 0, 0, -4, 0, -1, 0, 0, 0, 1, 0, -4, 0, -3, 0, 10, 0, -2, 0, 0, 0, 7, 0, -4, 0, 18, 0, -7, 0, -2, 0, -3, 0, 2, 0, 12, 0, 6, 0, -12, 0, -11, 0, -3, 0, 7, 0, -3, 0, -39, 0, 24, 0, -2, 0, 27, 0, 11, 0, -19, 0, 33, 0, -4, 0, -10, 0, -9, 0, -24, 0, 18, 0, 3, 0, -32, 0, -24, 0, -12, 0, 23, 0, -5, 0, -24, 0, 42, 0, -28, 0, 18, 0, 1, 0, -1, 0, 84, 0, -18, 0, -26, 0, 15, 0, 0, 0, -26, 0, 48, 0, -18, 0, 7, 0, -24, 0, 28, 0, -41, 0, -69, 0, 8, 0, 78, 0, 9, 0, 18, 0, -2, 0, 0, 0, -19, 0, -21, 0, 24, 0, -80, 0, 14, 0, -60, 0, 1, 0, -16, 0, -9, 0, -2, 0, 26, 0, -48, 0, 58, 0, 52, 0, -9, 0, 21, 0, -12, 0, 81, 0, -2, 0, -1, 0, 6, 0, -52, 0, 94, 0, 12, 0, -6, 0, -19, 0, 9, 0, 32, 0, -19, 0, -24, 0, 32, 0, 32, 0, -51, 0, -19, 0, -12, 0, -12, 0, -7, 0, 26, 0, -18, 0, 22, 0, -92, 0, -57, 0, 4, 0, -13, 0, 3, 0, -21, 0, -37, 0, -102, 0, -18, 0, -14, 0, 78, 0, 30, 0, -56, 0, 90, 0, -3, 0, -80, 0, -72, 0, -54, 0, 68, 0, 36, 0, -27, 0, -48, 0, 51, 0, 30, 0, -12, 0, 39, 0, -14, 0, 48, 0, -12, 0, 1, 0, -32, 0, 54, 0, 11, 0, 35, 0, 30, 0, 30, 0, 34, 0, 27, 0, 8, 0, 11, 0, -9, 0, 22, 0, -32, 0, 12, 0, 38, 0, 28, 0, 12, 0, -22, 0, 13, 0, -15, 0, -36, 0, -44, 0, 24, 0, 2, 0, 8, 0, -21, 0, 79, 0, 90, 0, 30, 0, -10, 0, -13, 0, -24, 0, -52, 0, 106, 0, -6, 0, -13, 0, 3, 0, -54, 0, 19, 0, 12, 0, -48, 0, -120, 0, 186, 0, -51, 0, -9, 0, -94, 0, 69, 0, -6, 0, 8, 0, 0, 0, 56, 0, 58, 0, -81, 0, 42, 0, -32, 0, -12, 0, 21, 0, 38, 0, -102, 0, 48, 0, -4, 0, 36, 0, -3, 0, 28, 0, 15, 0, -24, 0, 5, 0, -69, 0, -100, 0, -46, 0, 72, 0, 6, 0, -24, 0, -63, 0, -5, 0, -37, 0, -144, 0, 92, 0, -14, 0, 9, 0, -4, 0, -50, 0, 51, 0, -30, 0, -21, 0, 99, 0, -66, 0, -138, 0, -18, 0, 14, 0, 47, 0, 72, 0, 9, 0, -66, 0, 30, 0, 98, 0, 62, 0, 150, 0, 23, 0, 1, 0, -48, 0, -32, 0, -36, 0, -27, 0, 2, 0, 256, 0, 60, 0, 27, 0, -20, 0, -39, 0, -12, 0, 29, 0, 39, 0, -30, 0, 36, 0, -99, 0, 35, 0, 12, 0, 72, 0, -26, 0, 56, 0, 6, 0, -124, 0, -62, 0, -15, 0, -70, 0, 49, 0, 33, 0, 0, 0, 0, 0, -60, 0, 114, 0, -10, 0, 9, 0, 13, 0, 20, 0, 99, 0, -86, 0, -30, 0, -24, 0, -20, 0, 40, 0, -129, 0, -68, 0, -18, 0, -138, 0, 85, 0, 37, 0, -108, 0, -14, 0, 46, 0, -54, 0, 5, 0, -102, 0, -36, 0, -96, 0, 86, 0, -108, 0, 48, 0, -56, 0, 66, 0, 30, 0, -49, 0, 63, 0, -41, 0, -21, 0, -69, 0, -44, 0, 120, 0, 39, 0, -33, 0, 17, 0, 63, 0, 15, 0, -4, 0, 147, 0, -120, 0, -68, 0, 0, 0, -39, 0, 108, 0, -60, 0, 24, 0, 6, 0, 39, 0, 246, 0, -242, 0, 36, 0, 4, 0, 18, 0, -69, 0, 48, 0, -126, 0, 36, 0, 4, 0, 10, 0, 42, 0, -80, 0, 18, 0, -18, 0, 20, 0, -106, 0, -45, 0, 102, 0, 38, 0, 27, 0, 36, 0, 14, 0, 96, 0, -21, 0, 75, 0, 15, 0, 22, 0, 168, 0, -63, 0, -66, 0, -35, 0, -114, 0, 50, 0, 40, 0, -24, 0, 4, 0, 112, 0, 15, 0, -7, 0, -25, 0, 108, 0, 65, 0, 66, 0, 57, 0, 46, 0, -126, 0, -132, 0, -9, 0, 1, 0, -63, 0, 51, 0, 6, 0, -3, 0, 32, 0, -140, 0, 12, 0, 45, 0, 97, 0, -15, 0, -88, 0, -61, 0, 6, 0, -204, 0, 4, 0, 120, 0, 93, 0, -42, 0, -81, 0, 26, 0, -22, 0, -48, 0, 72, 0, -40, 0, 42, 0, -60, 0, -88, 0, 27, 0, -57, 0, -29, 0, 213, 0, -138, 0, -130, 0, 30, 0, -26, 0, 5, 0, 90, 0, 11, 0, 37, 0, 12, 0, 30, 0, -106, 0, 162, 0, 57, 0, 21, 0, -72, 0, 14, 0, 37, 0, -72, 0, 24, 0, -14, 0, -3, 0, -36, 0, 28, 0, -87, 0, -78, 0, 11, 0, 75, 0, -78, 0, 4, 0, -129, 0, 138, 0, 86, 0, 84, 0, -1, 0, -10, 0, 36, 0, 18, 0, -88, 0, -33, 0, -140, 0, 3, 0, -69, 0, 86, 0, 26, 0, 12, 0, -104, 0, 228, 0, -90, 0, -47, 0, -42, 0, 78, 0, -32, 0, 40, 0, -9, 0, 228, 0, 152, 0, -42, 0, 72, 0, -6, 0, -132, 0, -40, 0, 165, 0, -30, 0, 38, 0, -148, 0, -129, 0, 41, 0, 9, 0, -72, 0, 52, 0, 60, 0, 0, 0, -186, 0, -64, 0, 48, 0, 8, 0, 0, 0, 42, 0, -19, 0, -39, 0, -105, 0, -40, 0, -264, 0, 18, 0, 25, 0, 156, 0, 69, 0, -3, 0, -16, 0, 195, 0, 20, 0, -76, 0, -12, 0, -16, 0, 24, 0, -36, 0], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 9, 3, 1, 3, 0]], "char_orbit_index": 17, "prim_orbit_index": 3, "minimal_twist": "360.2.q.e", "char_is_minimal": false, "conrey_index": 241, "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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, -1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 2, 1, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 2, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 0, -1, -2, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 2, -1, 3, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 4, 1, 2, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 1, -1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 1, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 0, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 3, 2, 1, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 0, 1, 3, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [4, -2, 1, 3, 1, 1, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 1, 0, 2, -1, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, 0, -1, -3, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -2, 1, 4, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -3, -2, -4, 1, -2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 5, 2, 2, 2, 1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [4, -2, 0, 0, -2, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 2, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 5, 3, 4, 1, 1, 3, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 6, 2, 1, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, 1, -2, 1, 0, 1, -3, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -1, -1, -1, -1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -4, -1, -3, 1, -2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, 1, -1, -1, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 1, -1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, -2, 0, 0, -3, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -10, -1, -4, 2, -3, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 2, -2, -2, -6, -2, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 5, 2, 2, 3, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [4, -8, -1, -2, -3, -2, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 0, -1, 0, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, -1, 0, -2, -1, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [4, 2, 0, 0, 1, 3, -4, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -2, 0, -3, -1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 6, -3, -1, 1, -1, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 2, -1, 2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 3, 0, -4, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [12, 2, -1, 2, 3, 2, 3, -2], [0, 0, 0, 0, 0, 0, 0, 0]]}