# Stored data for newform 600.2.d.h, downloaded from the LMFDB on 19 April 2024.
{"label": "600.2.d.h", "space_label": "600.2.d", "level": 600, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525403583578712, "dim": 8, "is_polredabs": true, "nf_label": "8.0.214798336.3", "trace_hash": 102360778706050009, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [1, 0, 156, 0, 134, 0, 28, 0, 1]], [11, [1600, 0, 1344, 0, 336, 0, 32, 0, 1]], [13, [9, -32, -22, 0, 1]], [37, [64, -128, -64, 0, 1]]], "qexp_display": "q+\\beta _{6}q^{2}+q^{3}+(-1-\\beta _{1}+\\beta _{3}+\\beta _{6}+\\cdots)q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 40, "char_orbit_label": "d", "char_is_real": true, "Nk2": 2400, "analytic_conductor": 4.791024121276823, "hecke_ring_index": 4, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [600, 2, [151, 301, 401, 577], [2, 1, 2, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [349], "field_disc": 214798336, "field_disc_factorization": [[2, 12], [229, 2]], "field_poly": [16, -16, 0, -4, 9, -2, 0, -2, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.992", "prec": 17}, {"__RealLiteral__": 0, "data": "0.100", "prec": 17}, {"__RealLiteral__": 0, "data": "247.807", "prec": 24}, {"__RealLiteral__": 0, "data": "3.686", "prec": 17}, {"__RealLiteral__": 0, "data": "13833.622", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c2", "trace_display": [2, 8, 0, 0], "traces": [0, 8, 2, 8, -4, 0, 2, 0, 8, 8, 0, 0, -4, 0, 6, 0, 8, 0, 2, 0, 0, 0, -20, 0, 8, 0, -2, 8, -24, 0, 0, 8, 12, 0, -12, 0, -4, 0, -14, 0, 0, 0, 6, 8, 12, 0, 20, 0, 8, 0, 0, 0, -24, -8, 2, 0, 8, 0, 20, 0, 0, 0, -26, 0, 32, 0, -20, -24, -36, 0, 0, -40, 8, 0, -8, 0, -20, 24, -2, 16, 0, 8, 16, 32, -24, 0, -18, 0, 8, 0, 0, 0, -28, 8, 4, 0, 12, 0, 40, 0, 0, 0, -12, 0, -20, 0, -32, 32, -4, 0, 0, 0, 40, 0, -14, 0, 20, 0, -52, -72, 0, 24, 46, 0, -28, 0, 6, 0, 16, 8, 0, 0, 12, -48, -6, 0, 16, 0, 20, 0, 0, 0, -16, 0, 8, 0, 44, 0, -40, 0, 0, -24, 52, 0, -44, 0, -24, 48, -28, -8, 0, -48, 2, -24, 60, 0, 4, 0, 8, -16, 0, 0, -56, 8, 20, 0, -24, 0, 64, 0, 0, 0, -38, 0, 8, 0, -26, -16, -16, 0, 0, 56, 32, 0, 70, 0, 8, -64, -20, -8, 0, -24, 64, 16, -36, 0, -44, 0, 40, 32, 0, 0, -44, -40, -32, 0, 8, 0, 78, 0, 0, 0, -8, 0, -44, 0, -32, -48, -20, 0, 0, 24, 16, 0, -2, 0, 88, 16, -4, 72, 0, 40, 22, 8, 4, 0, 16, 0, 76, 32, 0, 0, -24, 112, -60, 0, 16, 0, -18, 0, 0, 0, -56, 0, 8, 0, 54, 0, -64, 0, 0, 0, 72, 0, -20, 0, -28, -96, -40, 8, 0, 48, 4, -56, 52, 0, -4, 0, 12, -24, 0, 0, -8, -112, 40, 0, -88, 0, 44, 0, 0, 0, -54, 0, 32, 0, -12, 8, -36, 0, 0, -80, -20, 0, 114, 0, -72, 64, -32, 64, 0, 32, 84, -48, -4, 0, -58, 0, 48, -32, 0, 0, -8, 0, 48, 0, 40, 0, -44, 0, 0, 0, -14, 0, -88, 0, 76, -64, 20, 0, 0, 0, 24, 0, -52, 0, 88, -72, 12, -88, 0, -80, 30, 24, 60, 0, 46, 0, 64, 0, 0, 0, -28, -48, -64, 0, -32, 0, 6, 0, 0, 0, 44, 0, 16, 0, 106, 8, 0, 0, 0, 0, -56, 0, -20, 0, 12, 144, -38, -48, 0, -16, -6, 56, 12, 0, 68, 0, 16, 24, 0, 0, -56, 176, 20, 0, -52, 0, 12, 0, 0, 0, -6, 0, 40, 0, -16, 40, -4, 0, 0, 136, 8, 0, 98, 0, -12, -152, 44, 88, 0, 0, -36, -48, -40, 0, -70, 0, 8, -48, 0, 0, 24, -24, 32, 0, 52, 0, -42, 0, 0, 0, -44, 0, -64, 0, -80, 144, -24, 0, 0, 48, 40, 0, -28, 0, 44, -8, 8, 80, 0, 0, -54, -48, -28, 0, 2, 0, -64, -24, 0, 0, 60, 144, -150, 0, 16, 0, 4, 0, 0, 0, 16, 0, 8, 0, 24, -16, 88, 0, 0, -32, 8, 0, -32, 0, -56, -48, -40, 8, 0, 0, 20, 40, 4, 0, -16, 0, -24, -72, 0, 0, 80, -136, 64, 0, -144, 0, -44, 0, 0, 0, 52, 0, -8, 0, -38, -16, 32, 0, 0, -104, 8, 0, 34, 0, -56, 160, -26, -40, 0, -16, -20, -16, -16, 0, -26, 0, 16, 48, 0, 0, -36, 56, 40, 0, 32, 0, -46, 0, 0, 0, 70, 0, -80, 0, -60, 80, 8, 0, 0, -64, -80, 0, -20, 0, 32, -8, -36, -112, 0, 24, 2, -24, -140, 0, 64, 0, -92, 16, 0, 0, -36, -112, -26, 0, 96, 0, -44, 0, 0, 0, 12, 0, 40, 0, 38, 32, 48, 0, 0, 8, -88, 0, -8, 0, -44, 160, 40, -40, 0, -112, -32, -80, 100, 0, 60, 0, 8, -128, 0, 0, -8, 112, 78, 0, -16, 0, -52, 0, 0, 0, 8, 0, -16, 0, -8, -112, -4, 0, 0, 120, -44, 0, -26, 0, -56, -120, -32, 8, 0, -48, -76, 128, -20, 0, -142, 0, -136, 144, 0, 0, 44, 24, 100, 0, 16, 0, 24, 0, 0, 0, -2, 0, -24, 0, 44, -16, 88, 0, 0, 16, -48, 0, -4, 0, -32, 72, -16, 152, 0, -48, 12, 40, -4, 0, 22, 0, -20, 8, 0, 0, 4, 160, -46, 0, -40, 0, 16, 0, 0, 0, 48, 0, 76, 0, 22, 32, -32, 0, 0, -32, 32, 0, -92, 0, -24, -192, 138, 112, 0, 96, -60, -104, 20, 0, 192, 0, 16, -24, 0, 0, 40, -72, -18, 0, -44, 0, -88, 0, 0, 0, 120, 0, 176, 0, -56, 120, 136, 0, 0, 16, 8, 0, 78, 0, -4, 48, 54, -112, 0, 0, -40, -16, -64, 0, 22, 0, -64, -64, 0, 0, 4, 0, -16, 0, 72, 0, 22, 0, 0, 0, -20, 0, 32, 0, -76, -160, -28, 0, 0, -96, -136, 0, -40, 0, 108, 8, 120, 24, 0, -56, -160, 48, -36, 0, 4, 0, 40, -56, 0, 0, 52, -96, 42, 0, 216, 0, -4, 0, 0, 0, -20, 0, 12, 0, -34, -24, -48, 0, 0, 216, -40, 0, -76, 0, -8, 32, 2, -112, 0, 208, 40, -24, 44, 0, -96, 0, -88, 208, 0, 0, 56, 176, 44, 0, 0, 0, -32, 0, 0, 0, 32, 0, 32, 0, -54, 64, 156, 0, 0, 80, 32, 0, 60, 0, 20, 8, -12, 72, 0, 8, -32, -128, -36, 0, -12, 0, -120, -64, 0, 0, 148, -80, -20, 0, -20, 0, -170, 0, 0, 0, 114, 0, -176, 0, -60, -96, -72, 0, 0, 64, -40, 0, -32, 0, 44, 64, 124, 128, 0, 64, 48, 32, -52, 0, 84, 0, -48, -48, 0, 0, -4, -64, 38, 0, 24, 0, -58, 0, 0, 0, 152, 0, 48, 0, 152, -32, 104, 0, 0, -200, -164, 0, 64, 0, -8, -160, 118, 0, 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, 40, 6, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 6, "minimal_twist": "600.2.k.d", "char_is_minimal": false, "conrey_index": 349, "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, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, -1, 0, 1, 0, -1, 0, -1], [1, 0, 0, 1, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 1, 0], [-1, -1, 0, 1, 0, 0, 1, 0], [1, 1, -2, -1, 1, 0, -1, 0], [1, 1, 2, 1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -2, -1, 1, -1, 1, 2], [0, -1, 1, 2, 0, 0, 1, -2], [0, 0, 0, 0, 0, 0, 1, 0], [0, -1, -1, 0, -2, -3, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, -1, 0, -1], [-3, -1, 0, 1, 1, -1, 1, 0], [0, -2, -2, 0, -1, 0, -1, -1], [1, 0, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -2, -4, 0, -2], [1, 0, 0, 0, 0, 0, 0, 0], [-3, 1, -2, -1, 2, 0, 1, 2], [0, 0, -2, -2, -1, -4, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [3, 2, -1, 1, -1, 0, -2, 0], [0, -2, 0, 0, 0, -4, 2, 0], [0, 1, 1, 0, 0, 0, 1, 0], [-1, 1, 2, 3, -1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 1, 0, 0, 1, 0], [0, 0, 2, -2, 0, 0, -2, -2], [-3, -1, 3, 1, -3, 3, 1, 0], [1, 1, -2, -1, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 2, 2, -1, 0, 3, 1], [1, 1, 2, 1, -1, 1, 0, 0], [1, 0, 4, -2, -1, 0, -3, -3], [2, 0, 2, 2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 1, 0, -1, -3, 3, -1, 0], [0, 0, 2, 2, 2, 2, 0, 0], [1, 1, -2, -1, 1, -1, 1, 2], [0, 0, -6, -2, 4, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 2, 0, 0, 1, -2], [-4, 0, 4, 0, -1, 3, 0, 0], [2, 3, -3, 0, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 0, 1, 0, -5, -2, -1], [0, -1, -1, 0, -2, -3, 1, -2], [1, -1, 2, -3, -1, 1, -1, 0], [0, 4, 0, -4, -2, -2, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -2, -1, 1, 5, -3, 2], [-3, 3, -1, -3, -1, -5, 1, 2], [0, -1, 0, 1, 0, -1, 0, -1], [2, -2, 4, 2, 0, 4, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 0, 1, 1, -1, 1, 0], [-1, 2, -4, -4, 3, 0, -3, -1], [-4, 2, -2, 0, 2, -2, 0, 4], [0, -2, -2, 0, -1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-6, -1, 3, 2, -2, 0, 1, 0], [1, 0, 0, 1, 0, 1, 0, 1], [0, 0, 2, 2, 4, 2, -2, 2], [0, 0, 2, 0, 0, 4, -2, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -6, -2, 3, 7, -2, 4], [4, 1, 5, 2, -4, 0, -3, -2], [0, 0, 1, 0, -2, -4, 0, -2], [2, 0, 6, -2, -2, 0, -4, -4], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, -1, -2, 1, 3, 5, 1, 4], [2, -2, 6, 0, -2, 0, 0, -2], [-3, 1, -2, -1, 2, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 2, -1, 1, 7, -2, -4], [0, 0, -2, -2, -1, -4, -1, 1], [2, 4, 0, -2, 2, 0, 0, 2], [-4, -4, 0, 0, 2, 0, 6, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 1, -2, 0, 5, 1, 2], [-4, 0, -6, -4, 0, 2, 2, 2], [3, 2, -1, 1, -1, 0, -2, 0], [2, 2, 0, 2, 2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, -4, 2, 0], [0, -2, -4, -2, 0, 1, -4, 2], [4, -4, 2, 4, -4, -8, 2, -4], [0, 1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}