# Stored data for newform 990.2.c.i, downloaded from the LMFDB on 09 September 2025.
{"Nk2": 3960, "analytic_conductor": 7.905189800106758, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [990, 2, [551, 397, 541], [2, 1, 2]], "cm_discs": [], "conrey_index": 199, "dim": 4, "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[7, [6, 0, 1]], [29, [-20, 4, 1]], [41, [-8, -8, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36028934491472862, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 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": "990.2.c.i", "level": 990, "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, 11], "level_radical": 330, "minimal_twist": "990.2.c.f", "nf_label": "4.0.2304.2", "prim_orbit_index": 2, "qexp_display": "q+\\beta _{2}q^{2}-q^{4}+(1+\\beta _{2}+\\beta _{3})q^{5}+(-\\beta _{1}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "990.2.c", "trace_display": [0, 0, 4, 0], "trace_hash": 1075814951130370877, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.890", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "77.547", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2174.875", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.521", "prec": 17}, "traces": [0, 4, 0, 0, -4, 4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 4, 0, 0, 8, -4, 0, 0, 0, 0, 0, 16, 0, 0, -8, 0, 16, 0, 0, 0, 12, 0, 0, 0, 0, 4, 16, 0, 0, -4, 0, -8, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -16, 0, 0, -4, 28, 0, 0, 0, 0, -12, 24, 0, 0, -8, 0, -8, 0, 0, 0, 4, 0, 0, 0, 0, 24, 24, 0, 0, 0, 0, -24, 0, 0, -8, 8, 0, 0, 0, 0, 0, -40, 0, 0, -16, 0, -24, 0, 0, 16, -4, 0, 0, 0, 0, 4, 8, 0, 0, -48, 0, 4, 0, 0, -16, 28, 0, 0, 0, 0, 4, -56, 0, 0, -24, 0, 0, 0, 0, -8, -12, 0, 0, 0, 0, -32, 24, 0, 0, 8, 0, 32, 0, 0, 0, 40, 0, 0, 0, 0, -4, -24, 0, 0, -16, 0, 16, 0, 0, -36, -24, 0, 0, 0, 0, 0, 4, 0, 0, -16, 0, 24, 0, 0, 8, -32, 0, 0, 0, 0, -8, -8, 0, 0, -24, 0, -4, 0, 0, 80, -4, 0, 0, 0, 0, -8, 64, 0, 0, 8, 0, 56, 0, 0, -24, 48, 0, 0, 0, 0, -4, -48, 0, 0, 0, 0, 0, 0, 0, -72, -20, 0, 0, 0, 0, -20, 0, 0, 0, -48, 0, -8, 0, 0, 16, 4, 0, 0, 0, 0, 28, 32, 0, 0, 16, 0, 4, 0, 0, 48, -28, 0, 0, 0, 0, 12, 0, 0, 0, 24, 0, -32, 0, 0, 48, 0, 0, 0, 0, 0, 12, -72, 0, 0, -24, 0, 16, 0, 0, -28, -16, 0, 0, 0, 0, 24, 8, 0, 0, 8, 0, -48, 0, 0, 8, -28, 0, 0, 0, 0, 8, -40, 0, 0, 8, 0, 0, 0, 0, -8, -4, 0, 0, 0, 0, -16, 48, 0, 0, 24, 0, 24, 0, 0, 16, 24, 0, 0, 0, 0, -24, 16, 0, 0, -24, 0, 8, 0, 0, -32, -48, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -60, 0, 0, 24, 0, 0, 0, 0, 0, 16, -72, 0, 0, 0, 0, 8, 0, 0, -56, -8, 0, 0, 0, 0, 12, 56, 0, 0, 120, 0, -48, 0, 0, -56, 12, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 48, 0, 0, 88, -40, 0, 0, 0, 0, 64, 16, 0, 0, 32, 0, -88, 0, 0, 24, 0, 0, 0, 0, 0, 0, -16, 0, 0, -48, 0, -16, 0, 0, 80, 4, 0, 0, 0, 0, -48, 80, 0, 0, 96, 0, 16, 0, 0, -24, 24, 0, 0, 0, 0, -4, -40, 0, 0, -8, 0, -56, 0, 0, -96, 4, 0, 0, 0, 0, 0, 48, 0, 0, 64, 0, 80, 0, 0, -4, -24, 0, 0, 0, 0, -4, -48, 0, 0, 32, 0, 16, 0, 0, -56, -28, 0, 0, 0, 0, -40, -8, 0, 0, 56, 0, 48, 0, 0, 32, 64, 0, 0, 0, 0, -4, 16, 0, 0, 56, 0, 48, 0, 0, 52, -60, 0, 0, 0, 0, -48, 24, 0, 0, 4, 0, -16, 0, 0, 0, -44, 0, 0, 0, 0, 4, -16, 0, 0, -64, 0, 8, 0, 0, -144, 12, 0, 0, 0, 0, -72, 8, 0, 0, 88, 0, -72, 0, 0, 48, 8, 0, 0, 0, 0, 32, -96, 0, 0, -24, 0, 56, 0, 0, 32, 24, 0, 0, 0, 0, -48, -8, 0, 0, 56, 0, 56, 0, 0, -32, 4, 0, 0, 0, 0, 4, 56, 0, 0, -8, 0, 0, 0, 0, 16, -40, 0, 0, 0, 0, 92, 32, 0, 0, 96, 0, 32, 0, 0, -8, 28, 0, 0, 0, 0, 4, -96, 0, 0, 24, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, -32, 16, 0, 0, -16, 0, -24, 0, 0, -16, 24, 0, 0, 0, 0, -72, -16, 0, 0, 88, 0, 36, 0, 0, 0, 24, 0, 0, 0, 0, 48, 0, 0, 0, 24, 0, 16, 0, 0, 48, 88, 0, 0, 0, 0, 0, -72, 0, 0, -4, 0, -16, 0, 0, -40, -36, 0, 0, 0, 0, 28, 16, 0, 0, -120, 0, 0, 0, 0, -24, -96, 0, 0, 0, 0, 48, -96, 0, 0, 16, 0, -8, 0, 0, 56, 32, 0, 0, 0, 0, 80, -32, 0, 0, 48, 0, -48, 0, 0, 16, -28, 0, 0, 0, 0, 8, 72, 0, 0, 8, 0, -72, 0, 0, 120, -12, 0, 0, 0, 0, 96, 24, 0, 0, 32, 0, 24, 0, 0, 4, -64, 0, 0, 0, 0, 12, 144, 0, 0, -104, 0, -80, 0, 0, 48, 4, 0, 0, 0, 0, -48, 16, 0, 0, -112, 0, 136, 0, 0, -8, 0, 0, 0, 0, 0, 8, -104, 0, 0, -64, 0, -48, 0, 0, 8, -32, 0, 0, 0, 0, -8, -8, 0, 0, -120, 0, -4, 0, 0, -56, 60, 0, 0, 0, 0, -96, 32, 0, 0, 24, 0, 24, 0, 0, 88, -48, 0, 0, 0, 0, -40, -16, 0, 0, 0, 0, 0, 0, 0, -16, -36, 0, 0, 0, 0, 4, 48, 0, 0, 48, 0, -80, 0, 0, -24, -48, 0, 0, 0, 0, -40, 0, 0, 0, -128, 0, -144, 0, 0, 0, -24, 0, 0, 0, 0, 72, -104, 0, 0, -72, 0, 72, 0, 0, -32, 20, 0, 0, 0, 0, 8, -16, 0, 0, 144, 0, 8, 0, 0, 0, 24, 0, 0, 0, 0, 20, -88, 0, 0, 0, 0, 24, 0, 0, -48, 8, 0, 0, 0, 0, 76, 48, 0, 0, 0, 0, 36, 0, 0, 8, 56, 0, 0, 0, 0, -24, 32, 0, 0, 16, 0, -16, 0, 0, 0, -4, 0, 0, 0, 0, -80, 96, 0, 0, 0, 0, -32, 0, 0, 24, 56, 0, 0, 0, 0, -28], "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], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [1, 0, 1, 1], [0, 0, 0, 0], [0, -1, 0, -1], [0, 0, -1, 0], [0, 0, 0, 0], [-1, -1, 1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, -1, -4, -1], [0, 1, 0, -1], [0, 0, 0, 0], [1, 0, 0, 0], [0, -2, 0, -2], [0, 0, 0, 0], [2, 0, 0, 0], [-1, 0, -1, -1], [0, 0, 0, 0], [0, 0, 1, 0], [0, -1, 2, -1], [0, 0, 0, 0], [0, -2, -1, 2], [4, 1, 0, -1], [0, 0, 0, 0], [0, 1, 0, 1], [-2, 2, 0, -2], [0, 0, 0, 0], [4, -2, 0, 2], [0, 0, 1, 0], [0, 0, 0, 0], [0, 2, 0, -2], [3, 0, 3, -2], [0, 0, 0, 0], [0, 2, 2, 2], [0, 0, 2, 0], [0, 0, 0, 0], [1, 1, -1, 0], [4, 2, 0, -2], [0, 0, 0, 0], [0, -2, -6, -2], [-1, 0, 0, 0], [0, 0, 0, 0], [-2, 1, 0, -1], [0, 1, 2, 1], [0, 0, 0, 0], [1, 0, 0, 0], [1, -2, 0, -2], [0, 0, 0, 0], [0, 1, 4, 1], [0, -3, 6, -3], [0, 0, 0, 0], [1, 0, 1, 1], [0, -1, 0, 1], [0, 0, 0, 0], [0, 2, -2, 2], [0, -2, 0, 2], [0, 0, 0, 0], [-4, 1, 0, -1], [0, -2, 4, -2], [0, 0, 0, 0], [-1, 0, 0, 0], [7, 4, -1, -2], [0, 0, 0, 0], [0, -4, 6, -4], [0, 2, 0, 2], [0, 0, 0, 0], [-3, 2, 3, 0], [6, 1, 0, -1], [0, 0, 0, 0], [0, 2, -6, 2], [-2, -2, 0, 2], [0, 0, 0, 0], [-2, 0, 0, 0], [0, -1, 0, -1], [0, 0, 0, 0], [0, -1, 0, 1], [1, 0, 1, 1], [0, 0, 0, 0], [0, 2, 4, 2], [0, -4, -4, -4], [0, 0, 0, 0], [6, 0, 6, -4], [6, 2, 0, -2], [0, 0, 0, 0], [0, 0, -1, 0], [0, 4, 0, -4], [0, 0, 0, 0], [-6, -4, 0, 4], [0, 1, -2, 1], [0, 0, 0, 0], [-2, -1, 0, 1], [2, 0, 2, 2], [0, 0, 0, 0], [0, 0, 6, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 2, 1, -2]]}