# Stored data for newform 288.2.v.a, downloaded from the LMFDB on 25 April 2024.
{"label": "288.2.v.a", "space_label": "288.2.v", "level": 288, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1443142566176, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 784210606544134534, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [98, -28, 6, -4, 1]]], "qexp_display": "q+(\\zeta_{8}+\\zeta_{8}^{3})q^{2}-2q^{4}+(1+\\zeta_{8}+2\\zeta_{8}^{2}+\\cdots)q^{5}+\\cdots", "char_order": 8, "char_parity": 1, "char_degree": 4, "char_conductor": 32, "char_orbit_label": "v", "char_is_real": false, "Nk2": 1152, "analytic_conductor": 2.299691578212875, "hecke_ring_index": 1, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 8, "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": "0.131", "prec": 17}, "analytic_rank_proved": true, "char_values": [288, 8, [127, 37, 65], [8, 1, 8]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [37, 109, 181, 253], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "3.911", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "43.365", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "770.111", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c8", "trace_display": [0, 0, 4, 4], "traces": [0, 4, 0, 0, -8, 4, 0, 4, 0, 0, 4, 8, 0, 4, 0, 0, 16, 0, 0, -8, -8, 0, 4, -12, 0, 4, 4, 0, -8, 4, 0, -16, 0, 0, -16, -4, 0, 4, 4, 0, -8, 12, 0, 16, -16, 0, 16, 0, 0, 0, -20, 0, -8, -4, 0, -20, 0, 0, 4, 16, 0, 4, 0, 0, -32, 8, 0, -8, 0, 0, -8, 12, 0, 28, -4, 0, 16, 4, 0, 0, 16, 0, 16, -16, 0, 8, 28, 0, -8, -12, 0, 4, 24, 0, 32, -64, 0, -40, 0, 0, -8, -20, 0, 4, -8, 0, -20, 8, 0, -20, 24, 0, 16, 0, 0, -20, -8, 0, -20, 0, 0, 28, -4, 0, 32, -4, 0, -16, 0, 0, 0, 40, 0, -20, -4, 0, 32, 12, 0, 16, 8, 0, 16, 0, 0, 0, 0, 0, -8, 20, 0, 28, -8, 0, 16, -16, 0, 4, 0, 0, 16, -24, 0, 16, -24, 0, -20, -36, 0, 4, -16, 0, -32, -4, 0, 0, 32, 0, -32, 32, 0, 28, 0, 0, -32, 12, 0, 8, 0, 0, 0, 48, 0, -40, 0, 0, 0, -44, 0, 4, 40, 0, 4, 12, 0, 52, 48, 0, 16, 0, 0, 16, 8, 0, 4, 20, 0, -16, -44, 0, 40, 8, 0, -16, 0, 0, 32, -32, 0, -68, -64, 0, -8, -12, 0, 32, -32, 0, -16, 0, 0, 0, -4, 0, -8, 40, 0, -20, 0, 0, -8, 16, 0, -68, 0, 0, 64, -24, 0, 4, -16, 0, -44, 12, 0, -44, 24, 0, 16, -28, 0, 0, 0, 0, -32, -16, 0, 4, -20, 0, 16, 36, 0, -8, -24, 0, 8, 24, 0, 36, 56, 0, -56, 4, 0, 52, 8, 0, -20, -12, 0, 28, 48, 0, -32, 0, 0, -8, -8, 0, -16, -12, 0, 4, -4, 0, 0, -44, 0, 32, -32, 0, 0, 8, 0, 24, -52, 0, -32, 24, 0, -8, 32, 0, -32, 0, 0, 0, -44, 0, -16, -32, 0, 48, -56, 0, -20, -32, 0, 28, -40, 0, 16, -24, 0, -44, 24, 0, 28, 60, 0, 28, 4, 0, -8, 84, 0, 0, -48, 0, -8, -20, 0, -44, -32, 0, -64, -4, 0, 16, 128, 0, 0, 0, 0, -40, 0, 0, 80, 76, 0, 32, 0, 0, 52, 48, 0, -68, -96, 0, 16, 0, 0, -16, 40, 0, 16, 4, 0, 52, 32, 0, -8, 20, 0, -16, 16, 0, 56, -8, 0, 28, 52, 0, 40, -40, 0, 4, -16, 0, 88, 0, 0, 0, 0, 0, 40, -60, 0, -68, -48, 0, -16, 40, 0, 76, 0, 0, -32, -24, 0, 4, 0, 0, 4, 8, 0, 4, 92, 0, 40, -28, 0, 0, 16, 0, -32, -40, 0, -20, 104, 0, 40, 36, 0, -60, 0, 0, -64, -48, 0, 8, 48, 0, -56, 32, 0, -44, 8, 0, 60, -64, 0, 8, -16, 0, -64, 0, 0, 16, 8, 0, 28, -12, 0, -44, 40, 0, 32, 28, 0, 56, 0, 0, 0, -100, 0, 8, -8, 0, 0, -36, 0, 40, -80, 0, 16, 0, 0, 0, -48, 0, 40, 12, 0, -20, 8, 0, -68, 20, 0, -44, 0, 0, -64, 56, 0, -56, -24, 0, -44, 44, 0, 24, 4, 0, -32, -52, 0, 0, -16, 0, 16, -40, 0, 80, -28, 0, -32, -36, 0, -8, 0, 0, 0, 56, 0, 8, 0, 0, 0, -12, 0, 4, 0, 0, 52, 8, 0, 32, -16, 0, 16, 0, 0, -16, -40, 0, -8, 84, 0, -20, 32, 0, -56, -20, 0, -64, 16, 0, 8, -16, 0, 76, -44, 0, -32, -12, 0, -56, 32, 0, -32, 0, 0, 0, -48, 0, -8, -8, 0, 28, 0, 0, 52, -160, 0, 0, 0, 0, -32, 72, 0, -8, 48, 0, 32, -36, 0, 28, -20, 0, -32, 68, 0, 0, 48, 0, 32, 32, 0, -68, -20, 0, 40, -64, 0, -20, 72, 0, -88, 16, 0, 56, 96, 0, -8, -20, 0, -40, 32, 0, -16, 32, 0, 4, 0, 0, 64, 0, 0, -32, 8, 0, 28, -124, 0, 32, 44, 0, 0, -20, 0, -16, -64, 0, 0, -4, 0, 4, 24, 0, 64, 48, 0, -20, -64, 0, 16, 0, 0, 0, 28, 0, -56, -8, 0, 28, 0, 0, 112, 56, 0, -68, 0, 0, 64, -56, 0, 16, -24, 0, -8, -36, 0, -140, -92, 0, -16, 4, 0, 0, 0, 0, 16, 132, 0, -68, 68, 0, 0, 108, 0, 4, -96, 0, 0, 32, 0, 56, 0, 0, 80, 28, 0, -16, 0, 0, -92, -36, 0, 28, 48, 0, 0, 0, 0, 16, 88, 0, 72, 48, 0, 4, -92, 0, -8, 28, 0, 64, -80, 0, -16, 84, 0, 24, -16, 0, -8, 60, 0, -104, -24, 0, -8, 0, 0, 0, 48, 0, -104, 44, 0, 76, -96, 0, -32, -56, 0, 100, 0, 0, -32, 0, 0, 100, 0, 0, -44, -84, 0, 4, -52, 0, -32, -32, 0, 0, -16, 0, -16, 4, 0, 100, 0, 0, -8, -84, 0, 64, -40, 0, 32, 48, 0, 56, -48, 0, 32, 24, 0, 4, 88, 0, -32, -16, 0, -68, 0, 0, -80, 0, 0, 136, -16, 0, -20, 36, 0, -16, -72, 0, 32, 56, 0, 80, 0, 0, 0, -16, 0, -40, -8, 0, -64, -100, 0, -32, 64, 0, -24, 0, 0, 0, 48, 0, 136, 36, 0, -68, 128, 0, -20, -4, 0, 4, -96, 0, 16, 72, 0, 60, 24, 0, 28, 48, 0, 76, -24, 0, -64, -28, 0, 0, 64, 0, 40, 56, 0, 28, 4, 0, 32, -36, 0, 48, 0, 0, 0, 24, 0, -60, 0, 0, 0, -112, 0, -92, 8, 0, -136, -64, 0, -20, 0, 0, 16, 0, 0, -44, -80, 0, 4, -12, 0, -140, -16, 0, 40, -76, 0, -64, 0, 0, 32, 188, 0, -44, 4, 0, 16], "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, 32, 7, 1, 8, 0]], "char_orbit_index": 22, "prim_orbit_index": 7, "minimal_twist": "32.2.g.a", "char_is_minimal": true, "conrey_index": 37, "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], [1, 0, 0, 0], [0, 1, 0, 1], [0, 0, 0, 0], [-2, 0, 0, 0], [1, 1, 2, -2], [0, 0, 0, 0], [1, 0, 1, 0], [0, -2, 0, -2], [0, 0, 0, 0], [1, -1, 3, 3], [2, -2, 1, 1], [0, 0, 0, 0], [1, 0, 0, -1], [0, 0, 0, 2], [0, 0, 0, 0], [4, 0, 0, 0], [0, 2, 0, 2], [0, 0, 0, 0], [-2, -3, 3, 2], [-2, -2, -4, 4], [0, 0, 0, 0], [1, 1, -3, 3], [-3, 0, 3, -4], [0, 0, 0, 0], [1, 5, 1, 0], [1, 1, 1, 1], [0, 0, 0, 0], [-2, 0, -2, 0], [1, -2, -2, 1], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 4, 0, 4], [0, 0, 0, 0], [-4, 0, 0, 0], [-1, 3, 3, -1], [0, 0, 0, 0], [1, 1, 0, 0], [1, -5, -5, 1], [0, 0, 0, 0], [-2, 2, -6, -6], [3, 0, -3, -4], [0, 0, 0, 0], [4, -4, -3, -3], [-4, 4, -2, -2], [0, 0, 0, 0], [4, -6, 4, 0], [0, -4, -6, -4], [0, 0, 0, 0], [0, 0, -5, 0], [-5, 0, 5, 2], [0, 0, 0, 0], [-2, 0, 0, 2], [-1, 1, 4, 4], [0, 0, 0, 0], [-5, 0, 5, -6], [0, 0, 0, -4], [0, 0, 0, 0], [1, 3, -3, -1], [4, 4, -1, 1], [0, 0, 0, 0], [1, 0, 0, 1], [0, -4, 0, -4], [0, 0, 0, 0], [-8, 0, 0, 0], [2, 3, 0, -3], [0, 0, 0, 0], [-2, 3, 3, -2], [0, -4, 0, -4], [0, 0, 0, 0], [-2, -4, 4, 2], [3, -4, 3, 0], [0, 0, 0, 0], [7, 0, -7, 0], [-1, 1, 1, 1], [0, 0, 0, 0], [4, 6, -6, -4], [1, -3, 3, -1], [0, 0, 0, 0], [0, 0, -6, 0], [4, 4, 8, -8], [0, 0, 0, 0], [4, 6, 4, 0], [-4, 1, -1, 4], [0, 0, 0, 0], [2, -2, 6, 6], [7, 7, -1, 1], [0, 0, 0, 0], [-2, -2, 6, -6], [-3, 8, -3, 0], [0, 0, 0, 0], [1, 1, 1, -1], [6, 0, -6, 8], [0, 0, 0, 0], [8, 6, 0, -6], [-16, -3, 0, 3], [0, 0, 0, 0], [-10, 6, 0, -6], [0, 5, 0, -5], [0, 0, 0, 0], [-2, -10, -2, 0]]}