# Stored data for newform 936.2.w.g, downloaded from the LMFDB on 08 December 2024. {"Nk2": 3744, "analytic_conductor": 7.473997629191844, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 104, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 23, "char_orbit_label": "w", "char_order": 4, "char_parity": 1, "char_values": [936, 4, [703, 469, 209, 145], [2, 2, 4, 1]], "cm_discs": [], "conrey_index": 307, "dim": 4, "field_disc": 43264, "field_disc_factorization": [[2, 8], [13, 2]], "field_poly": [169, 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": [[5, [169, 0, 0, 0, 1]], [7, [169, 0, 0, 0, 1]]], "hecke_orbit": 7, "hecke_orbit_code": 27023109626266536, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, 0], [1, 1, 13, 4, -1, 4, 0], [1, 1, 104, 13, 1, 4, 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": false, "label": "936.2.w.g", "level": 936, "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, 13], "level_radical": 78, "minimal_twist": "104.2.m.a", "nf_label": "4.0.43264.3", "prim_orbit_index": 13, "qexp_display": "q+(1-\\beta _{2})q^{2}-2\\beta _{2}q^{4}+\\beta _{1}q^{5}-\\beta _{3}q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "936.2.w", "trace_display": [4, 0, 0, 0], "trace_hash": 1443973343006396938, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.757", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "84.066", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2582.988", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.622", "prec": 17}, "traces": [0, 4, 4, 0, 0, 0, 0, 0, -8, 0, 0, -4, 0, 0, 0, 0, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 12, 52, 0, 0, 0, 0, 0, -24, 0, 0, -8, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 12, 24, 0, 52, 0, 0, -24, 0, 0, -16, 0, 0, 0, 0, 0, 0, -20, 0, 0, -4, 0, 0, 8, 0, -52, 0, 0, 0, 0, 0, -28, -24, 0, 64, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -16, 0, 52, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, -52, -28, 0, 0, 0, 0, 24, 20, 0, -60, 0, 0, 0, 0, 0, 52, -48, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 36, 48, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 16, 0, 16, 0, 0, 0, -52, 0, 0, 52, 0, 12, 0, 0, 0, 0, 0, 36, 0, 0, -48, 0, 0, 0, 64, 0, 0, -52, 0, 0, 0, 0, 0, -16, 0, 28, 0, 0, 8, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, -16, 48, 0, 0, 104, 0, 0, 0, 0, -52, -64, 0, 0, 0, 0, -56, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, -104, 0, -28, 0, 0, -52, 0, 0, -24, 0, 0, 0, 0, 0, 40, 32, 0, 0, -60, 0, -104, -64, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, -48, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, -32, 0, 0, -40, 0, 0, 104, 0, 0, -124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 72, 0, 96, 0, 0, 84, 40, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, -8, 0, 0, 28, 0, 0, 0, 0, 32, -20, 0, 0, 16, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 52, 0, 0, 0, 0, 0, -52, 0, -92, 0, 0, 0, 0, 0, -52, 72, 0, 56, 0, 0, 0, -48, 0, 0, -52, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -104, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, -16, -20, 0, 0, 28, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 0, -12, 0, 48, 0, 0, 0, 0, 0, -8, 0, 0, 104, 0, 0, 0, 0, 0, 44, 0, 0, 0, -52, 0, 0, -4, 0, 64, 0, 0, 0, 0, 0, -52, -112, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156, 0, 8, 0, 0, -40, 0, 0, -104, 0, 0, 0, 0, 0, 0, 64, 0, 12, -52, 0, 0, -52, 0, -104, 12, 0, -24, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -48, 0, 0, -24, 0, 0, 0, 0, -48, 0, 0, 92, 40, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, -208, 0, -128, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 32, 0, -104, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, -116, 0, 0, 0, 0, -104, 0, 0, 148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, -80, 0, 0, 48, 0, -88, 208, 0, 0, 0, 0, 4, -124, 0, 0, 0, 0, 0, 0, 0, 0, 156, 0, 0, 0, 0, 0, 0, 0, 60, -104, 0, 48, 0, 0, 0, 0, 0, 72, 0, 0, 0, 96, 0, 52, -120, 0, 0, 0, 0, 80, 104, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 104, 0, 0, 0, 0, 0, 0, -116, 0, 0, 0, 0, 0, 52, 0, 24, 0, 0, 28, 0, 0, -72, 0, 0, 0, 0, 0, 0, 32, 0, 0, -104, 0, 0, 156, 0, 0, 104, 0, -52, 72, 0, 0, 0, 0, -52, 44, 0, 0, 0, 0, 0, 104, 0, 0, 12, 0, 0, 0, 0, 0, -24, 0, -8, 0, 0, 104, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, 0, 0, 16, 0, 52, 0, 0, 0, 0, 0, -32, -104, 0, 72, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, -8, 0, 0, 0, -104, 0, 0, 60, 0, -96, -104, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 72, 0, -312, 0, 0, -20, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, -96, 52, 0, 0, 0, 0, -16, 0, 0, 40, 0, 0, 0, 0, 0, 52, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 156, 0, 0, 0, 0, 0, 0, 0, 0, -24, 104, 0, 0, 48, 0, 32, -156, 0, 0, -96, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -48, 88, 0, -8, 0, 0, -128, 0, 0, 0, 0, 0, 0, 128, 0, 0, -140, 0, 0, 128, 0, 0, 0, 0, 260, 0, 0, 0, 0, 0, 0, -52, 0, -112, 0, 0, 0, -72, 0, 0, -188, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156, 260, 0, 0, 0, 0, 0], "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], [1, 0, -1, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [-2, 0, -2, 0], [0, 0, 0, 0], [0, 1, 0, -1], [-1, 0, -1, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, -1, 0, -1], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 0], [2, 0, -2, 0], [0, 0, 0, -2], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 1, 0, -1], [0, 0, 0, 0], [0, 0, 8, 0], [0, -1, 0, 1], [0, 0, 0, 0], [0, -2, 0, 0], [0, -1, 0, -1], [0, 0, 0, 0], [0, 2, 0, 0], [-4, 0, 4, 0], [0, 0, 0, 0], [3, 0, 3, 0], [13, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, -4, 0], [0, 0, 0, 0], [0, -2, 0, -2], [-6, 0, 6, 0], [0, 0, 0, 0], [0, 0, -1, 0], [-2, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, -6, 0], [8, 0, 8, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 1, 0, 1], [0, 0, 0, 0], [0, -1, 0, -1], [0, -2, 0, 2], [0, 0, 0, 0], [0, -2, 0, 0], [-8, 0, -8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, -2], [0, 0, 0, 0], [0, 0, 8, 0], [0, 0, -13, 0], [0, 0, 0, 0], [3, 0, -3, 0], [6, 0, 0, 0], [0, 0, 0, 0], [13, 0, -13, 0], [0, 3, 0, 0], [0, 0, 0, 0], [-6, 0, -6, 0], [0, -1, 0, -1], [0, 0, 0, 0], [-4, 0, -4, 0], [0, -1, 0, 1], [0, 0, 0, 0], [0, 1, 0, 1], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, 12, 0], [-5, 0, 5, 0], [0, 0, 0, 0], [0, 0, 0, 3], [-1, 0, -1, 0], [0, 0, 0, 0], [0, 0, 4, 0], [2, 0, 2, 0], [0, 0, 0, 0], [-13, 0, 0, 0], [0, -2, 0, -2], [0, 0, 0, 0], [0, 1, 0, 1], [0, 2, 0, -2], [0, 0, 0, 0], [-7, 0, 7, 0], [-6, 0, -6, 0], [0, 0, 0, 0], [16, 0, 0, 0]]}