# Stored data for newform 1170.2.e.f, downloaded from the LMFDB on 16 April 2024. {"label": "1170.2.e.f", "space_label": "1170.2.e", "level": 1170, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22518273048315026, "dim": 6, "is_polredabs": true, "nf_label": "6.0.3534400.1", "trace_hash": 661522862791568953, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [400, 0, 305, 0, 34, 0, 1]], [11, [2, 1]]], "qexp_display": "q+\\beta _{5}q^{2}-q^{4}+(-\\beta _{1}-\\beta _{2}+\\beta _{3}-\\beta _{4}+\\cdots)q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "e", "char_is_real": true, "Nk2": 4680, "analytic_conductor": 9.342497036489805, "hecke_ring_index": 1, "level_radical": 390, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [1170, 2, [911, 937, 1081], [2, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 13], "conrey_indexes": [469], "field_disc": -3534400, "field_disc_factorization": [[-1, 1], [2, 6], [5, 2], [47, 2]], "field_poly": [40, -12, 1, 16, -3, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "5.265", "prec": 17}, {"__RealLiteral__": 0, "data": "1.349", "prec": 17}, {"__RealLiteral__": 0, "data": "142.666", "prec": 24}, {"__RealLiteral__": 0, "data": "108.436", "prec": 24}, {"__RealLiteral__": 0, "data": "5766.272", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 6, 0, 0, -6, 0, 0, 0, 0, 0, -4, -12, 0, 0, -4, 0, 6, 0, 0, -4, 0, 0, 0, 0, 0, -16, -6, 0, 0, -4, 0, 24, 0, 0, -8, 6, 0, 0, 0, 0, 4, -4, 0, 0, 12, 0, 12, 0, 0, -26, 16, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 20, 0, 0, -6, -4, 0, 0, 0, 0, 12, 16, 0, 0, -16, 0, 4, 0, 0, -56, 0, 0, 0, 0, 0, 28, 24, 0, 0, -4, 0, -4, 0, 0, 20, 4, 0, 0, 0, 0, 16, 28, 0, 0, 6, 0, 12, 0, 0, -48, 8, 0, 0, 0, 0, 40, 4, 0, 0, -112, 0, -42, 0, 0, -24, -12, 0, 0, 0, 0, 0, 20, 0, 0, -24, 0, 8, 0, 0, -20, -6, 0, 0, 0, 0, 4, 36, 0, 0, 0, 0, 16, 0, 0, 8, 28, 0, 0, 0, 0, -4, 56, 0, 0, 4, 0, -32, 0, 0, -6, 10, 0, 0, 0, 0, 64, -12, 0, 0, -20, 0, -12, 0, 0, -12, 30, 0, 0, 0, 0, 52, -32, 0, 0, -52, 0, 26, 0, 0, -16, -16, 0, 0, 0, 0, 32, -4, 0, 0, 8, 0, 60, 0, 0, 0, -32, 0, 0, 0, 0, 0, -8, 0, 0, -4, 0, 24, 0, 0, -56, -28, 0, 0, 0, 0, 22, -4, 0, 0, 40, 0, 36, 0, 0, -20, 44, 0, 0, 0, 0, 10, 72, 0, 0, 36, 0, 6, 0, 0, -28, 4, 0, 0, 0, 0, 40, -80, 0, 0, -44, 0, -32, 0, 0, -60, 32, 0, 0, 0, 0, -12, -92, 0, 0, -16, 0, 12, 0, 0, -102, 52, 0, 0, 0, 0, -4, 16, 0, 0, 12, 0, -56, 0, 0, -4, 32, 0, 0, 0, 0, 16, -72, 0, 0, 44, 0, 56, 0, 0, 8, 0, 0, 0, 0, 0, 16, 16, 0, 0, -52, 0, 44, 0, 0, 0, 16, 0, 0, 0, 0, -28, -48, 0, 0, -24, 0, -84, 0, 0, -80, -22, 0, 0, 0, 0, -18, 4, 0, 0, 56, 0, 70, 0, 0, 4, 24, 0, 0, 0, 0, -16, 56, 0, 0, 16, 0, -20, 0, 0, 4, -4, 0, 0, 0, 0, -12, 12, 0, 0, -28, 0, 56, 0, 0, -80, -4, 0, 0, 0, 0, -16, -52, 0, 0, -28, 0, -80, 0, 0, 28, 84, 0, 0, 0, 0, 28, -6, 0, 0, -36, 0, -32, 0, 0, -12, 118, 0, 0, 0, 0, 42, 32, 0, 0, 32, 0, 48, 0, 0, -40, -8, 0, 0, 0, 0, 4, -52, 0, 0, 4, 0, 8, 0, 0, 40, 12, 0, 0, 0, 0, -40, -64, 0, 0, -4, 0, -8, 0, 0, 32, 12, 0, 0, 0, 0, 52, 112, 0, 0, -120, 0, -16, 0, 0, 42, -148, 0, 0, 0, 0, 90, 12, 0, 0, 4, 0, 24, 0, 0, -60, 12, 0, 0, 0, 0, 80, -24, 0, 0, 16, 0, 24, 0, 0, -56, 64, 0, 0, 0, 0, 0, 184, 0, 0, -20, 0, -20, 0, 0, 2, -28, 0, 0, 0, 0, 32, 24, 0, 0, 52, 0, 120, 0, 0, -8, -42, 0, 0, 0, 0, -32, 184, 0, 0, -12, 0, 20, 0, 0, 24, 6, 0, 0, 0, 0, 16, -24, 0, 0, -88, 0, 12, 0, 0, -32, -52, 0, 0, 0, 0, -4, -104, 0, 0, -36, 0, 48, 0, 0, 0, -52, 0, 0, 0, 0, 46, 0, 0, 0, 40, 0, 24, 0, 0, -16, 0, 0, 0, 0, 0, 68, 20, 0, 0, -64, 0, -8, 0, 0, 156, -28, 0, 0, 0, 0, -32, -112, 0, 0, -88, 0, -96, 0, 0, 4, 56, 0, 0, 0, 0, 4, 124, 0, 0, -56, 0, -168, 0, 0, -8, 16, 0, 0, 0, 0, -72, -4, 0, 0, 80, 0, 32, 0, 0, 32, -120, 0, 0, 0, 0, -28, -40, 0, 0, 64, 0, 6, 0, 0, -48, -10, 0, 0, 0, 0, -8, 20, 0, 0, 12, 0, -60, 0, 0, 104, -40, 0, 0, 0, 0, -64, 68, 0, 0, 12, 0, 84, 0, 0, 80, -76, 0, 0, 0, 0, 8, 20, 0, 0, -80, 0, -216, 0, 0, 12, 52, 0, 0, 0, 0, 0, -28, 0, 0, 116, 0, 12, 0, 0, 36, -30, 0, 0, 0, 0, 0, 36, 0, 0, 48, 0, 16, 0, 0, 4, -74, 0, 0, 0, 0, -52, -92, 0, 0, 32, 0, -28, 0, 0, -100, -24, 0, 0, 0, 0, -88, 52, 0, 0, 200, 0, -32, 0, 0, -26, -20, 0, 0, 0, 0, -12, 16, 0, 0, -92, 0, 16, 0, 0, -80, 16, 0, 0, 0, 0, -108, -24, 0, 0, 72, 0, 92, 0, 0, 32, 124, 0, 0, 0, 0, -32, -128, 0, 0, 4, 0, 80, 0, 0, 140, -4, 0, 0, 0, 0, -128, -8, 0, 0, 80, 0, 10, 0, 0, -60, 0, 0, 0, 0, 0, -32, -32, 0, 0, -48, 0, 0, 0, 0, 232, 32, 0, 0, 0, 0, -88, 64, 0, 0, 112, 0, -24, 0, 0, -24, -124, 0, 0, 0, 0, 0, 80, 0, 0, 8, 0, -8, 0, 0, 72, 52, 0, 0, 0, 0, -40, 4, 0, 0, 0, 0, 56, 0, 0, -24, 84, 0, 0, 0, 0, -6, -160, 0, 0, 20, 0, 56, 0, 0, -112, 28, 0, 0, 0, 0, 76, 56, 0, 0, -52, 0, 132, 0, 0, 144, -56, 0, 0, 0, 0, -22, 24, 0, 0, 4, 0, -48, 0, 0, 36, 76, 0, 0, 0, 0, -20, -40, 0, 0, 8, 0, 22, 0, 0, -36, -88, 0, 0, 0, 0, 60, -132, 0, 0, 48, 0, 20, 0, 0, 8, -44, 0, 0, 0, 0, -158, -168, 0, 0, 120, 0, 40, 0, 0, 48, 76, 0, 0, 0, 0, -10, 8, 0, 0, -72, 0, 4, 0, 0, -20, 28, 0, 0, 0, 0, -120, -36, 0, 0, -140, 0, -120, 0, 0, -6, 28, 0, 0, 0, 0, 20, 16, 0, 0, -40, 0, 28, 0, 0, -16, -4, 0, 0, 0, 0, -8, -48, 0, 0, 144, 0, -116, 0, 0, 8, -8, 0, 0, 0, 0, -40, 32, 0, 0, 80, 0, 4, 0, 0, 84, -28, 0, 0, 0, 0, -34, 44, 0, 0, -32, 0, 8, 0, 0, 32, 152, 0, 0, 0, 0, -16, -224, 0, 0, 64, 0, 60, 0, 0, 112, -32, 0, 0, 0, 0, 10, 120, 0, 0, 12, 0, -56, 0, 0, 88, -270, 0, 0, 0, 0, 12, -184, 0, 0, 92, 0, -152, 0, 0, 4, 0, 0, 0, 0, 0, -8, 16, 0, 0, 8, 0, 24, 0, 0, -12, -34, 0, 0, 0, 0, -8, 40, 0, 0, 60, 0, 102, 0, 0, 184, -52, 0, 0, 0, 0, -100, -24, 0, 0, -192, 0, -60, 0, 0, 64, 0, 0, 0, 0, 0, 4, 112, 0, 0, -16, 0, -116, 0, 0, 200, 172, 0, 0, 0, 0, 10, -12, 0, 0, 96, 0, 92, 0, 0, 56, -44, 0, 0, 0, 0, 28, -104, 0, 0, -12, 0, 4, 0, 0, -136, -32, 0, 0, 0, 0, 54, 4, 0, 0, 96, 0, -56, 0, 0, -28, 52, 0, 0, 0, 0, -16, 48, 0, 0, 72, 0, -80, 0, 0, -16, -32, 0, 0, 0, 0, 56, -44, 0, 0, -44, 0, -52, 0, 0, -56, -80, 0, 0, 0, 0, -28, 112, 0, 0, 26, 0, -8, 0, 0, 136, 0, 0, 0, 0, 0, -36, 88, 0, 0, 100, 0, -100, 0, 0, 28, -16, 0, 0, 0, 0, -16, 28, 0, 0, -16, 0, -20, 0, 0, 224, -118, 0, 0, 0, 0, 4, 52, 0, 0, 104, 0, -132, 0, 0, -44, -52, 0, 0, 0, 0, -20, 216, 0, 0, -24, 0, 0, 0, 0, -4, -16, 0, 0, 0, 0, 24, -8, 0, 0, -200, 0, -136, 0, 0, 140, 94, 0, 0, 0, 0, 28, -136, 0, 0, 48, 0, -32, 0, 0, 98, -28, 0, 0, 0, 0, 24, 24, 0, 0, -132, 0, 36, 0, 0, 84, -188, 0, 0, 0, 0, -10, 0, 0, 0, -128, 0, 80, 0, 0, 72, 22, 0, 0, 0, 0, -60, -88, 0, 0, 36, 0, -216, 0, 0, 208, 144, 0, 0, 0, 0, 18, 132, 0, 0, -4, 0, -64, 0, 0, 36, 0, 0, 0, 0, 0, 8, -56, 0, 0, 56, 0, -40, 0, 0, -70, 20, 0, 0, 0, 0, 76, 4, 0, 0, 196, 0, -4, 0, 0, 232, -24, 0, 0, 0, 0, 38, 16, 0, 0, 24, 0, -208, 0, 0, 48, -52, 0, 0, 0, 0, 16, -80, 0, 0, -56, 0, -4, 0, 0, 196, 0, 0, 0, 0, 0, -28, -16, 0, 0, 32, 0, -144, 0, 0, 20, 78, 0, 0, 0, 0, -140, 208, 0, 0, 28, 0, -4, 0, 0, 72, 4, 0, 0, 0, 0, -36, -40, 0, 0, 40, 0, 36, 0, 0, -4, -124, 0, 0, 0, 0, 12, -64, 0, 0, -12, 0, -144, 0, 0, -200, 44, 0, 0, 0, 0, 40, 28, 0, 0, 136, 0, 4, 0, 0, -56, -140, 0, 0, 0, 0, 4, -124, 0, 0, -40, 0, 80, 0, 0, -28, 4, 0, 0, 0, 0, -96, -20, 0, 0, 288, 0, 160, 0, 0, 12, -8, 0, 0, 0, 0, 16, 276, 0, 0, 52, 0, -72, 0, 0, 64, -116, 0, 0, 0, 0, -164, 28, 0, 0, 188, 0, -148, 0, 0, 80, 10, 0, 0, 0, 0, -60, -304, 0, 0, 8, 0, -28, 0, 0, 0, -84, 0, 0, 0, 0, -4, -52, 0, 0, 24, 0, 36, 0, 0, -32, -92, 0, 0, 0, 0, -28, -32, 0, 0, 6, 0, 8, 0, 0, -88, 112, 0, 0, 0, 0, 44, 36, 0, 0, -72, 0, 82, 0, 0, 32, -20, 0, 0, 0, 0, 4, 184, 0, 0, 28, 0, 12, 0, 0, -84, -118, 0, 0, 0, 0, -56, -8, 0, 0, -32, 0, -184, 0, 0, 0, 150, 0, 0, 0, 0, -42, 20, 0, 0, -32, 0, 188, 0, 0, -80, 28, 0, 0, 0, 0, 184, -32, 0, 0, 36, 0, 28, 0, 0, -48, -90, 0, 0, 0, 0, -88, -392, 0, 0, -64, 0, 40, 0, 0, 8, 8, 0, 0, 0, 0, -104, -88, 0, 0, 184, 0, -112, 0, 0, 28, -72, 0, 0, 0, 0, -4, -60, 0, 0, 52, 0, -96, 0, 0, -144, -10, 0, 0, 0, 0, -36, -4, 0, 0, -192, 0, 92, 0, 0, -8, 96, 0, 0, 0, 0, 104, 4, 0, 0, -88, 0, -40, 0, 0, 40, -12, 0, 0, 0, 0, -96, 64, 0, 0, 0, 0, 24, 0, 0, -92, 176, 0, 0, 0, 0, 40, -144, 0, 0, 64, 0, -16, 0, 0, -90, 34, 0, 0, 0, 0, -108, 4, 0, 0, 12, 0, 192, 0, 0, 8, 204, 0, 0, 0, 0, -20, 56, 0, 0, -16, 0, -32, 0, 0, -24, -12, 0, 0, 0, 0, 52, -136, 0, 0, -132, 0, 208, 0, 0, 56, 36, 0, 0, 0, 0, -52, 12, 0, 0, -112, 0, 80, 0, 0, 48, 88, 0, 0, 0, 0, -190, 120, 0, 0, -152, 0, 32, 0, 0, 16, -128, 0, 0, 0, 0, 84, -180, 0, 0, 172, 0, -42, 0, 0, 192, 148, 0, 0, 0, 0, 128, -100, 0, 0, -292, 0, 208, 0, 0, -20, -164, 0, 0, 0, 0, -90, -32, 0, 0, -12, 0, 132, 0, 0, 40, 72, 0, 0, 0, 0, 108, -4, 0, 0, -132, 0, 224, 0, 0, -24, 72, 0, 0, 0, 0, 8, 24, 0, 0, 132, 0, 60, 0, 0, -192, -12], "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, 5, 2, 1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "130.2.b.a", "char_is_minimal": true, "conrey_index": 469, "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], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, -1, -1, 1, -1, 1], [0, 0, 0, 0, 0, 0], [0, 1, 1, 0, -1, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [-1, 0, -1, -1, 0, 0], [-2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, -2, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 2, -1, -1, 0], [0, 0, 0, 0, 0, 0], [-2, 2, -2, -2, 0, 0], [0, 1, 1, -1, 1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2], [0, 0, 0, -2, 2, -2], [0, 0, 0, 0, 0, 0], [-3, 0, -1, 0, 1, -2], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, -1, 0, 1, 0], [-2, 2, -2, -2, 0, 0], [0, 0, 0, 0, 0, 0], [4, -2, -2, 0, -2, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, -3, 1, 2, -1, 0], [2, -4, -1, 0, -1, -2], [0, 0, 0, 0, 0, 0], [0, 1, 1, -2, 1, 2], [0, 2, 2, -2, 0, -2], [0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0], [-2, 0, -4, -2, -2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 3, -3, -4], [2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 2, 0], [0, 1, 1, 0, -1, -4], [0, 0, 0, 0, 0, 0], [-5, -2, -4, -1, -3, 0], [2, 2, 0, -1, 0, -3], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, -2, 2, -2], [0, 0, 0, 0, 0, 0], [0, 2, 2, -2, 2, -2], [0, 2, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0], [0, 2, 2, -2, 0, -2], [2, -2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, -4, -2, -2, 0], [0, 0, 0, -2, 2, 4], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 2, 4], [0, -2, -2, 1, 1, 0], [0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 4, 2], [4, -1, 3, 2, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -6], [-2, 0, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0], [2, -2, 2, 2, 0, 0], [0, -2, -2, 0, 2, 0], [0, 0, 0, 0, 0, 0], [-8, -2, 2, 2, 0, 0], [0, -1, -1, 1, -1, 1], [0, 0, 0, 0, 0, 0], [0, 2, 2, -4, 2, -2], [0, 2, 2, -2, 0, 4], [0, 0, 0, 0, 0, 0], [6, -6, -2, -1, -2, -2], [4, -3, -3, 0, -3, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2], [-2, 2, -2, -2, 0, 0], [0, 0, 0, 0, 0, 0], [0, -2, 0, 1, -1, 0], [0, 0, 0, 2, -2, 2], [0, 0, 0, 0, 0, 0], [4, -2, 0, 1, -1, 0], [0, 2, 0, 0, -4, -10], [0, 0, 0, 0, 0, 0], [0, -2, -2, 6, -4, 10], [0, 1, 1, -4, 3, -5], [0, 0, 0, 0, 0, 0], [3, 0, 1, 0, -1, 2]]}