# Stored data for newform 357.2.a.h, downloaded from the LMFDB on 12 September 2025.
{"Nk2": 1428, "analytic_conductor": 2.8506593521597097, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [7, -1], [17, 1]], "atkin_lehner_string": "+-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [357, 1, [239, 52, 190], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 4, "field_disc": 7232, "field_disc_factorization": [[2, 6], [113, 1]], "field_poly": [4, 4, -5, -2, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [2, 8, -5, -2, 1]], [11, [-64, 80, -23, -2, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525197425148261, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "357.2.a.h", "level": 357, "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": true, "level_primes": [3, 7, 17], "level_radical": 357, "minimal_twist": "357.2.a.h", "nf_label": "4.4.7232.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{2}q^{2}-q^{3}+(1-\\beta _{2}-\\beta _{3})q^{4}+\\beta _{1}q^{5}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "357.2.a", "trace_display": [2, -4, -2, 4], "trace_hash": 1850763880121356412, "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "3.681", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "36.411", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "559.815", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.009", "prec": 17}, "traces": [0, 4, 2, -4, 6, -2, -2, 4, 6, 4, 4, 2, -6, 2, 2, 2, 6, -4, 2, 10, 4, -4, 20, 6, -6, 10, -4, -4, 6, -4, -4, -4, 14, -2, -2, -2, 6, 0, -16, -2, -20, -18, -2, 26, -8, -2, -20, -4, -6, 4, 10, 4, -4, 20, -2, 2, 6, -10, -28, 4, -4, -4, -12, 4, -2, -30, -20, 28, -6, -6, 4, 4, 6, 8, -24, -10, 8, 2, 4, -8, -44, 4, -28, 28, -6, 2, -20, 4, 8, -28, 4, 2, -16, 4, -12, 14, -14, 4, 2, 2, -46, -28, 2, 2, 20, 2, 0, 30, -6, 24, 16, 0, 6, -14, 16, 38, -20, 2, 20, -4, 20, 6, -24, 18, 48, -6, 2, 10, 30, -26, -20, -6, 8, 10, 0, 2, -6, 12, 20, 36, 4, 4, -64, -2, 6, -8, 68, -4, 4, 8, -10, 20, -32, -4, 20, -16, 4, -2, 76, -20, -20, 6, 2, -4, -84, -2, 0, 18, -6, -22, -4, 10, 0, 14, 28, 10, 24, -4, -4, 20, 4, -8, -4, 4, -80, -32, 12, -2, 48, -4, 36, -12, 2, -4, 52, 30, 6, -14, 20, -8, -30, -28, -80, -4, 6, -34, 0, 6, 44, -30, -4, -40, 84, -4, 20, -30, -6, -4, 40, -8, 24, -2, 24, 6, 14, 10, -24, 46, -8, 20, 72, -2, -36, 10, -4, -16, 24, 8, -2, 20, 44, -12, -58, -4, -52, -2, 28, -14, 56, -28, 40, 16, 6, -18, 28, -2, 30, 4, 20, 0, 16, -4, 24, 56, -8, -28, -16, 28, -8, -50, -4, 2, -6, -2, -8, 76, 16, 32, 56, -4, -20, -4, 12, -28, -72, -14, -16, -18, 14, 4, 0, -4, 4, -76, -2, -72, 12, -2, -28, -38, 46, 26, 48, 28, -72, -92, -2, 40, -8, -2, -76, 0, -20, 12, -20, -2, 48, -8, 0, -40, 28, -30, -20, -10, 6, 16, -16, -24, -60, -4, -16, 58, -8, 0, -48, -28, -6, -68, -6, 14, -4, -76, -16, 4, -16, -38, 36, 28, 20, -46, 10, -2, -48, 24, -20, -36, -28, 4, 88, -36, -20, 10, 60, -6, -4, 12, 24, 0, -144, -18, -36, 20, -48, 20, -20, 6, 56, 8, -2, -64, 24, -10, -24, -40, -30, 2, -40, 26, 84, 28, 20, -6, 6, 6, -56, 12, -8, 20, 20, -10, -14, -26, 0, 16, -52, -2, -28, -52, 6, 70, -4, -12, -112, 4, -20, -28, 20, -36, 104, 28, -4, 46, -20, -4, 92, -10, 64, -4, 120, 2, 48, -40, -6, 22, -12, 8, 68, 102, -68, -24, -48, 4, 4, 40, -4, 72, 32, -8, -2, -60, 10, 10, 76, -20, 32, -30, 32, 26, -4, 4, 56, -16, -20, -44, -52, 16, 24, -20, -4, 28, -76, 2, 112, -14, -76, 4, -6, 20, -20, 18, 20, 32, 36, -6, 6, 80, -2, 20, 20, 4, 4, 68, 84, 4, -36, 2, 64, 4, 0, -16, 112, -18, 12, -54, 6, 20, 92, 22, 40, -60, 4, 8, -82, -10, 32, 54, 0, -76, -24, -14, 0, -10, -28, 24, -16, -10, 88, 4, -24, 70, -52, 4, 8, 34, 4, 54, -8, -20, 28, 2, -4, -28, -104, 8, -14, -24, 4, -20, -100, -4, -32, 32, 80, -8, 20, 32, 168, 20, -12, 30, -44, 2, -44, 12, -48, 22, 4, 4, -104, 36, -36, -48, -24, 12, -28, 44, -2, 6, 2, 4, 24, 28, -52, -64, 52, -30, 28, 112, -6, -8, -84, 14, 20, 56, -20, 2, -124, 8, -72, 12, 30, 8, -20, 28, 144, 32, 80, -28, 16, 4, -52, 16, -6, -30, 16, 34, 8, -20, 0, -28, -112, -6, -80, -28, -44, 68, 136, 30, 76, 0, 4, -50, 120, 40, 84, -46, -84, 2, 8, 4, 12, -2, -20, 64, -16, 30, 16, 4, 6, 20, -60, 4, -56, -18, -40, -122, -36, 8, -12, -32, -24, 50, -36, 2, -8, 14, -24, 40, -8, -6, 64, 0, -14, 32, -80, -10, -94, 22, 24, 4, 20, -46, 36, 22, 8, -60, 2, -20, -32, 28, -72, -32, -44, 2, 48, 68, 36, 18, -44, -10, -46, -12, 4, 16, 64, 16, 40, -28, -24, 72, 48, -8, -76, -76, 2, -86, 72, -20, 12, -30, -44, 2, -122, 12, -20, -20, 58, 56, 20, 4, 32, -26, 52, 56, 0, 2, -72, 36, -28, 14, -8, 14, 0, -12, -56, 12, -28, 28, 8, 30, -40, 48, 64, -16, 0, 76, -6, -78, -24, 18, -8, -32, -28, 24, -96, 2, -44, 72, -30, -50, 16, -4, -52, -36, -20, -192, 52, 0, -20, -50, -16, -52, 20, 4, 6, 38, -24, 40, -60, -56, -60, -14, 8, 92, -168, 28, -16, -68, 16, 4, -142, -28, -88, 140, 8, 38, 76, 50, -124, -34, 4, 20, -20, -2, 20, -12, 6, 114, -92, 2, 96, -58, 8, -84, -168, -76, 20, 30, -16, -24, 64, -32, -28, -4, -56, -58, -104, 4, 112, 22, 20, -60, 208, 4, 8, 0, -12, 6, 100, 28, -10, -20, 72, 56, -24, 14, 56, 72, 16, -88, 104, 18, -72, -28, -14, 14, -52, -4, 48, 96, 0, 28, 108, 4, 0, -6, -4, -52, -116, 76, -120, -16, 2, -6, 4, 72, -4, -50, -12, 10, 16, 2, -48, -8, 28, 20, 30, 38, -76, 24, -46, -20, -152, -26, 44, 20, -48, -52, 112, -28, -20, -46, 72, 36, 64, 92, 116, -6, 2, -170, 16, -40, -64, 36, 8, -60, 32, 2, -20, 82, 76, 10, 12, 0, 88, -2, 20, 20, 0, -12, -112, 0, 20, -18, 200, 2, 140, 60, -48, -12, 152, 8, -6, 72, 0, -172, 48, 40, 32, 12, -28, 80, 36, 30, -12, -44, 20, 54, -90, 10, 8, -52, -6, 36, -88, -16, 92, 0, 16, -8, 4, 24, 0, -26, 60, 38, 28, 4, -24, 110, 16, -32, 176, -58, -64, 36, 8, -64, -156, 0, 40], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 0, 0], [1, 0, -1, -1], [0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 0], [0, -1, -2, -1], [1, 0, 0, 0], [2, 1, 1, 1], [0, 0, -1, 1], [-1, 0, 1, 1], [0, -1, 0, 0], [0, 0, -1, 0], [0, -1, 0, 0], [-1, -2, -3, -1], [-1, 0, 0, 0], [0, 0, -1, 0], [4, 1, 2, 0], [2, 0, 2, 2], [-1, 0, 0, 0], [6, 1, 1, -1], [4, 2, 3, 1], [0, 1, 2, 1], [3, 0, 1, 3], [-2, -1, -1, -1], [-1, 0, 0, 0], [1, 0, -1, -1], [0, 0, 2, 0], [-2, -1, -1, -1], [-2, -1, -1, -3], [2, -1, -2, -3], [0, 0, 1, -1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, -1, -1], [0, -1, 1, -1], [-4, 1, -1, 3], [0, 1, 0, 0], [-4, 0, 2, 0], [-4, -1, 2, 2], [0, 0, 1, 0], [8, 0, 3, 1], [-4, 0, -4, 0], [0, 1, 0, 0], [-2, 3, 3, 5], [-2, -1, -1, -3], [1, 2, 3, 1], [1, 0, 0, 0], [6, 3, 4, 1], [1, 0, 0, 0], [-2, 0, -2, -2], [4, -1, -1, -3], [0, 0, 1, 0], [2, 3, 0, 0], [0, -1, -2, -1], [-4, -1, -2, 0], [-6, 0, 2, 2], [-2, -3, -3, -1], [-2, 0, -2, -2], [-2, -3, 1, 1], [-8, -4, -6, -2], [1, 0, 0, 0], [-3, 0, -5, -1], [-8, 0, -1, -3], [-6, -1, -1, 1], [8, 0, 2, 2], [-1, 0, 1, 1], [-4, -2, -3, -1], [2, 1, 1, 1], [4, 0, 6, 2], [0, -1, -2, -1], [0, 0, -4, 2], [-8, -2, -2, 0], [-3, 0, -1, -3], [6, 2, 6, 0], [0, 0, -1, 1], [2, 1, 1, 1], [-6, -1, -7, -1], [-10, 0, 2, -2], [1, 0, 0, 0], [-2, 1, 9, 1], [8, 0, 2, 2], [-1, 0, 1, 1], [0, -1, 0, 0], [-6, 1, -3, 3], [0, 0, -2, 0], [0, -2, -2, -2], [-6, 2, 0, 0], [2, 1, 1, 1], [0, -1, 0, 0], [4, 4, 12, 4], [2, 1, 1, 3], [-8, -4, -6, -2], [4, 2, -1, 1], [-2, 1, 2, 3], [0, 2, -4, -2], [0, 0, -1, 0], [0, 0, -1, 1], [-9, 4, 1, 1]]}