# Stored data for newform 1440.2.q.m, downloaded from the LMFDB on 27 December 2024. {"Nk2": 5760, "analytic_conductor": 11.498457891064374, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 17, "char_orbit_label": "q", "char_order": 3, "char_parity": 1, "char_values": [1440, 3, [991, 901, 641, 577], [3, 3, 1, 3]], "cm_discs": [], "conrey_index": 481, "dim": 8, "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 24, "has_non_self_twist": 1, "hecke_cutters": [[7, [1, 0, 4, 0, 15, 0, 4, 0, 1]], [11, [16, 0, 112, 0, 780, 0, 28, 0, 1]]], "hecke_orbit": 13, "hecke_orbit_code": 54044295073629600, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 9, "hecke_ring_index_factorization": [[3, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0], [1, 1, 36, 6, -1, 6, 0], [1, 1, 4, 2, -1, 2, 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": "1440.2.q.m", "level": 1440, "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": false, "level_primes": [2, 3, 5], "level_radical": 30, "minimal_twist": "1440.2.q.m", "nf_label": "8.0.5308416.1", "prim_orbit_index": 3, "qexp_display": "q+(-\\beta_{7}+\\beta_{6})q^{3}+\\beta_1 q^{5}-\\beta_{7} q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1440.2.q", "trace_display": [0, 0, 4, 0], "trace_hash": 1541534428841841926, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.078", "prec": 17}, {"__RealLiteral__": 0, "data": "4.148", "prec": 17}, {"__RealLiteral__": 0, "data": "352.638", "prec": 24}, {"__RealLiteral__": 0, "data": "446.258", "prec": 24}, {"__RealLiteral__": 0, "data": "28535.982", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.516", "prec": 17}, "traces": [0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 8, 0, 0, 0, -12, 0, 0, 0, -4, 0, 0, 0, -12, 0, 0, 0, -24, 0, 0, 0, -8, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 48, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, -48, 0, 0, 0, -20, 0, 0, 0, 36, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 36, 0, 0, 0, 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -24, 0, 0, 0, -60, 0, 0, 0, -24, 0, 0, 0, -40, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 12, 0, 0, 0, 36, 0, 0, 0, -32, 0, 0, 0, -72, 0, 0, 0, 40, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 48, 0, 0, 0, 48, 0, 0, 0, 16, 0, 0, 0, -24, 0, 0, 0, -84, 0, 0, 0, 40, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 88, 0, 0, 0, 48, 0, 0, 0, -8, 0, 0, 0, -20, 0, 0, 0, -36, 0, 0, 0, 40, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 96, 0, 0, 0, -12, 0, 0, 0, -44, 0, 0, 0, -24, 0, 0, 0, -12, 0, 0, 0, -104, 0, 0, 0, -76, 0, 0, 0, 36, 0, 0, 0, -12, 0, 0, 0, 16, 0, 0, 0, 60, 0, 0, 0, 12, 0, 0, 0, -12, 0, 0, 0, -72, 0, 0, 0, 8, 0, 0, 0, -28, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 12, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 24, 0, 0, 0, 84, 0, 0, 0, 20, 0, 0, 0, -48, 0, 0, 0, -96, 0, 0, 0, 16, 0, 0, 0, -64, 0, 0, 0, -36, 0, 0, 0, 64, 0, 0, 0, -32, 0, 0, 0, 24, 0, 0, 0, -80, 0, 0, 0, -4, 0, 0, 0, -24, 0, 0, 0, 152, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 128, 0, 0, 0, 168, 0, 0, 0, 4, 0, 0, 0, -36, 0, 0, 0, 24, 0, 0, 0, 40, 0, 0, 0, -48, 0, 0, 0, -72, 0, 0, 0, 16, 0, 0, 0, 32, 0, 0, 0, 60, 0, 0, 0, -12, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 4, 0, 0, 0, 72, 0, 0, 0, -52, 0, 0, 0, 184, 0, 0, 0, 12, 0, 0, 0, 84, 0, 0, 0, -76, 0, 0, 0, -108, 0, 0, 0, 136, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 8, 0, 0, 0, 128, 0, 0, 0, 24, 0, 0, 0, -8, 0, 0, 0, -56, 0, 0, 0, -192, 0, 0, 0, -160, 0, 0, 0, -32, 0, 0, 0, -36, 0, 0, 0, -24, 0, 0, 0, -120, 0, 0, 0, 108, 0, 0, 0, 40, 0, 0, 0, 12, 0, 0, 0, 36, 0, 0, 0, 248, 0, 0, 0, -56, 0, 0, 0, -36, 0, 0, 0, -4, 0, 0, 0, 16, 0, 0, 0, 36, 0, 0, 0, 8, 0, 0, 0, -128, 0, 0, 0, 36, 0, 0, 0, -176, 0, 0, 0, -28, 0, 0, 0, 216, 0, 0, 0, -112, 0, 0, 0, -24, 0, 0, 0, 84, 0, 0, 0, -92, 0, 0, 0, -76, 0, 0, 0, -168, 0, 0, 0, -48, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, -32, 0, 0, 0, -36, 0, 0, 0, 76, 0, 0, 0, -20, 0, 0, 0, -168, 0, 0, 0, 136, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 136, 0, 0, 0, 48, 0, 0, 0, 40, 0, 0, 0, 64, 0, 0, 0, -60, 0, 0, 0, 232, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 240, 0, 0, 0, 24, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, -136, 0, 0, 0, -60, 0, 0, 0, 216, 0, 0, 0, 8, 0, 0, 0, 48, 0, 0, 0, 204, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 36, 0, 0, 0, -208, 0, 0, 0, 32, 0, 0, 0, -108, 0, 0, 0, 80, 0, 0, 0, 72, 0, 0, 0, -84, 0, 0, 0, -148, 0, 0, 0, 12, 0, 0, 0, -60, 0, 0, 0, -64, 0, 0, 0, -16, 0, 0, 0, 144, 0, 0, 0, -28, 0, 0, 0, 48, 0, 0, 0, 24, 0, 0, 0, 52, 0, 0, 0, -60, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -216, 0, 0, 0, -92, 0, 0, 0, -64, 0, 0, 0, 48, 0, 0, 0, 4, 0, 0, 0, 80, 0, 0, 0, -132, 0, 0, 0, -64, 0, 0, 0, -52, 0, 0, 0, -36, 0, 0, 0, 96, 0, 0, 0, 72, 0, 0, 0, 108, 0, 0, 0, 68, 0, 0, 0, -12, 0, 0, 0, 48, 0, 0, 0, 80, 0, 0, 0, -60, 0, 0, 0, -36, 0, 0, 0, 24, 0, 0, 0, 24, 0, 0, 0, -168, 0, 0, 0, -80, 0, 0, 0, -56, 0, 0, 0, 12, 0, 0, 0, -200, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 32, 0, 0, 0, -12, 0, 0, 0, 32, 0, 0, 0, -52, 0, 0, 0, -252, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 84, 0, 0, 0, -272, 0, 0, 0, -84, 0, 0, 0, 112, 0, 0, 0, 12, 0, 0, 0, 60, 0, 0, 0, 56, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -172, 0, 0, 0, 72, 0, 0, 0, 240, 0, 0, 0, -8, 0, 0, 0, -108, 0, 0, 0, -96, 0, 0, 0, 128, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 200, 0, 0, 0, 256, 0, 0, 0, -120, 0, 0, 0, 52, 0, 0, 0, -4, 0, 0, 0, 228, 0, 0, 0, 136, 0, 0, 0, 76, 0, 0, 0, 108, 0, 0, 0, 44, 0, 0, 0, -8, 0, 0, 0, -12, 0, 0, 0, 124, 0, 0, 0, 96, 0, 0, 0, 72, 0, 0, 0, 96, 0, 0, 0, 36, 0, 0, 0, 36, 0, 0, 0, -56, 0, 0, 0, -16, 0, 0, 0, -72, 0, 0, 0, -160, 0, 0, 0, -92, 0, 0, 0, 72, 0, 0, 0, -40, 0, 0, 0, 56, 0, 0, 0, 288, 0, 0, 0, -128, 0, 0, 0, 96, 0, 0, 0, 24, 0, 0, 0, 68, 0, 0, 0, 28, 0, 0, 0, -60, 0, 0, 0, 64, 0, 0, 0, 20, 0, 0, 0, -108, 0, 0, 0, -12, 0, 0, 0, -216, 0, 0, 0, -144, 0, 0, 0, 8, 0, 0, 0, -132, 0, 0, 0, -264, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, -128, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 84, 0, 0, 0, 96, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 16, 0, 0, 0, 72, 0, 0, 0, -36, 0, 0, 0, -264, 0, 0, 0, -88, 0, 0, 0, 36, 0, 0, 0, 56, 0, 0, 0, -88, 0, 0, 0, 204, 0, 0, 0, 20, 0, 0, 0, 172, 0, 0, 0, -180, 0, 0, 0, -48, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -120, 0, 0, 0, -24, 0, 0, 0, -80, 0, 0, 0, 36, 0, 0, 0, 96, 0, 0, 0, -256, 0, 0, 0, -52, 0, 0, 0, -36, 0, 0, 0, -136, 0, 0, 0, 104, 0, 0, 0, -132, 0, 0, 0, 76, 0, 0, 0, 8, 0, 0, 0, 120, 0, 0, 0, -24, 0, 0, 0, -72, 0, 0, 0, -72, 0, 0, 0, 128, 0, 0, 0, -72, 0, 0, 0, 144, 0, 0, 0, 48, 0, 0, 0, 12, 0, 0, 0, 228, 0, 0, 0, 136, 0, 0, 0, 76, 0, 0, 0, 72, 0, 0, 0, 8, 0, 0, 0, 128, 0, 0, 0, 144, 0, 0, 0, -72, 0, 0, 0, -20, 0, 0, 0, 144, 0, 0, 0, -344, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 24, 0, 0, 0, -132, 0, 0, 0, -108, 0, 0, 0, -36, 0, 0, 0, -24, 0, 0, 0, -24, 0, 0, 0, -116, 0, 0, 0, 216, 0, 0, 0, 116, 0, 0, 0, 168, 0, 0, 0, 60, 0, 0, 0, 248, 0, 0, 0, -16, 0, 0, 0, 48, 0, 0, 0, 336, 0, 0, 0, 4, 0, 0, 0, -288, 0, 0, 0, -28, 0, 0, 0, 120, 0, 0, 0, 108, 0, 0, 0, 28, 0, 0, 0, 64, 0, 0, 0, -72, 0, 0, 0, -328, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, -200, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 304, 0, 0, 0, 124, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, -320, 0, 0, 0, -120, 0, 0, 0, -80, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, -72, 0, 0, 0, -240, 0, 0, 0, -20, 0, 0, 0, 76, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 240, 0, 0, 0, -12, 0, 0, 0, 176, 0, 0, 0, 160, 0, 0, 0, 96, 0, 0, 0, -160, 0, 0, 0, -52, 0, 0, 0, -144, 0, 0, 0, -8, 0, 0, 0, -16, 0, 0, 0, -240, 0, 0, 0, 24, 0, 0, 0, 88, 0, 0, 0, -60, 0, 0, 0, -8, 0, 0, 0, 68, 0, 0, 0, -180, 0, 0, 0, 100, 0, 0, 0, -24, 0, 0, 0, -216, 0, 0, 0, -188, 0, 0, 0, 88, 0, 0, 0, 84, 0, 0, 0, -8, 0, 0, 0, 48, 0, 0, 0, 144, 0, 0, 0, 12, 0, 0, 0, -368, 0, 0, 0, 24, 0, 0, 0, 84, 0, 0, 0, 16, 0, 0, 0, 120, 0, 0, 0, 64, 0, 0, 0, 188, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 40, 0, 0, 0, -192, 0, 0, 0, 60, 0, 0, 0, 20, 0, 0, 0, 228, 0, 0, 0, -96, 0, 0, 0, 104, 0, 0, 0, -108, 0, 0, 0, -144, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, -56, 0, 0, 0, -312, 0, 0, 0, -48, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, -192, 0, 0, 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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, -1], [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, 0, 0, 0, 0, 0, -1], [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, 0, 0, 1, 0, -1, 0, -2], [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, 0, 0, -1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, -2, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -4, -2, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, -5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 3, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 5, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -3, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 1, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, -2, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -5, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 3, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, -6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, -3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, -6, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, -2, 0, -3], [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, 0, 0, -3, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, -1, -1, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 2, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, 0, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 6, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0]]}