# Stored data for newform 342.3.d.a, downloaded from the LMFDB on 18 April 2024. {"label": "342.3.d.a", "space_label": "342.3.d", "level": 342, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 206208762198, "dim": 2, "is_polredabs": true, "nf_label": "2.0.8.1", "trace_hash": 489673958850425110, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-1, 1]]], "qexp_display": "q-\\beta q^{2}-2q^{4}+q^{5}+5q^{7}+2\\beta q^{8}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 19, "char_orbit_label": "d", "char_is_real": true, "Nk2": 3078, "analytic_conductor": 9.318825041122153, "hecke_ring_index": 1, "level_radical": 114, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [342, 2, [191, 325], [2, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 19], "conrey_indexes": [37], "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.892", "prec": 17}, {"__RealLiteral__": 0, "data": "0.103", "prec": 17}, {"__RealLiteral__": 0, "data": "14.826", "prec": 20}, {"__RealLiteral__": 0, "data": "1.479", "prec": 17}, {"__RealLiteral__": 0, "data": "146.747", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 2, 10], "traces": [0, 2, 0, 0, -4, 2, 0, 10, 0, 0, 0, -10, 0, 0, 0, 0, 8, 50, 0, 38, -4, 0, 0, 20, 0, -48, -48, 0, -20, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 10, 20, 0, 0, -10, 0, -48, 0, 0, 0, 0, 0, -10, 0, 0, -120, 0, 0, 190, -120, 0, -16, 0, 0, 0, -100, 0, 0, 0, 0, -50, -72, 0, -76, -50, 0, 0, 8, 0, 120, 260, 0, 50, 0, 0, 0, 0, 0, 0, -40, 0, 0, 38, 0, 0, 0, 0, 96, -100, 0, 0, 96, 0, 72, 0, 0, 0, 0, 0, 40, 0, 0, 20, 0, 0, -240, 250, 0, -192, 0, 0, 0, -98, 0, 0, 0, 0, -48, 326, 0, 190, 312, 0, 0, -190, 0, 250, -20, 0, 0, 0, 0, 0, 0, 0, 0, -430, 0, 0, 0, 0, 0, 0, 0, -380, 120, 0, 0, 100, 0, 220, 0, 0, 0, 0, 0, -238, 0, 0, -20, 0, 0, -240, -40, 0, 360, 0, 0, 0, -240, 0, 0, 0, 0, -250, 20, 0, 0, -586, 0, 0, 48, 0, 96, 140, 0, 346, 0, 0, 0, 0, 0, 0, -48, 0, 0, -190, 0, 0, 0, 0, 288, 10, 0, 0, 360, 0, 20, 0, 0, 0, 0, 0, -312, 0, 0, -290, 0, 0, 240, -670, 0, -10, 0, 0, 0, -394, 0, 0, 0, 0, -380, -48, 0, 0, 240, 0, 0, -346, 0, -100, 648, 0, 32, 0, 0, 0, 0, 0, 0, 710, 0, 0, 0, 0, 0, 0, 0, 220, 200, 0, 0, 240, 0, -530, 0, 0, 0, 0, 0, 250, 0, 0, 240, 0, 0, 672, -120, 0, 100, 0, 0, 0, 144, 0, 0, 0, 0, 50, -240, 0, 152, 190, 0, 0, 100, 0, -120, 470, 0, -620, 0, 0, 0, 0, 0, 0, -16, 0, 0, 950, 0, 0, 0, 0, -240, -50, 0, 0, -520, 0, -168, 0, 0, 0, 0, 0, -100, 0, 0, -730, 0, 0, 528, -250, 0, 46, 0, 0, 0, -820, 0, 0, 0, 0, 360, 950, 0, 722, -720, 0, 0, -50, 0, 460, 80, 0, -72, 0, 0, 0, 0, 0, 0, -1440, 0, 0, -76, 0, 0, 0, 0, -50, 168, 0, 0, 1106, 0, 500, 0, 0, 0, 0, 0, 670, 0, 0, -192, 0, 0, -1440, 200, 0, -600, 0, 0, 0, 120, 0, 0, 0, 0, 260, -192, 0, 0, -124, 0, 0, 240, 0, -144, -1200, 0, 950, 0, 0, 0, 0, 0, 0, -600, 0, 0, 380, 0, 0, 0, 0, -1200, -730, 0, 0, -1032, 0, -80, 0, 0, 0, 0, 0, -192, 0, 0, -530, 0, 0, -40, 1106, 0, 970, 0, 0, 0, 230, 0, 0, 0, 0, 480, -50, 0, -912, -500, 0, 0, 980, 0, -864, 840, 0, 384, 0, 0, 0, 0, 0, 0, 164, 0, 0, -912, 0, 0, 0, 0, 970, 196, 0, 0, 500, 0, -100, 0, 0, 0, 0, 0, -250, 0, 0, 192, 0, 0, 50, -360, 0, 96, 0, 0, 0, -652, 0, 0, 0, 0, -858, 72, 0, -380, 1440, 0, 0, -624, 0, 1080, 240, 0, -50, 0, 0, 0, 0, 0, 0, 380, 0, 0, 0, 0, 0, 0, 0, -500, 1490, 0, 0, 40, 0, -1200, 0, 0, 0, 0, 0, 0, 0, 0, 2140, 0, 0, 600, -480, 0, -50, 0, 0, 0, 1300, 0, 0, 0, 0, -528, -1450, 0, 0, -240, 0, 0, -1300, 0, 250, 860, 0, -480, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 2110, 792, 0, 0, 1010, 0, -260, 0, 0, 0, 0, 0, 1102, 0, 0, 760, 0, 0, -950, -240, 0, 528, 0, 0, 0, 600, 0, 0, 0, 0, -1910, -200, 0, 0, -1930, 0, 0, 1152, 0, -440, -1870, 0, 326, 0, 0, 0, 0, 0, 0, 840, 0, 0, 190, 0, 0, 0, 0, 312, -950, 0, 0, -1488, 0, 476, 0, 0, 0, 0, 0, 600, 0, 0, -190, 0, 0, 40, 864, 0, -1430, 0, 0, 0, 250, 0, 0, 0, 0, 480, 860, 0, 0, 80, 0, 0, -500, 0, -764, 0, 0, -720, 0, 0, 0, 0, 0, 0, 230, 0, 0, 0, 0, 0, 0, 0, -2150, 480, 0, 0, 250, 0, 1060, 0, 0, 0, 0, 0, -1094, 0, 0, 360, 0, 0, -430, -192, 0, 500, 0, 0, 0, -40, 0, 0, 0, 0, 2110, -720, 0, 0, -430, 0, 0, 1172, 0, 408, -2880, 0, -290, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -192, -380, 0, 0, -280, 0, 120, 0, 0, 0, 0, 0, -692, 0, 0, -250, 0, 0, -600, 250, 0, 100, 0, 0, 0, 914, 0, 0, 0, 0, 360, 220, 0, 190, 2040, 0, 0, -334, 0, -2630, 96, 0, -1200, 0, 0, 0, 0, 0, 0, -1200, 0, 0, 380, 0, 0, 0, 0, -1918, 840, 0, 0, -238, 0, -960, 0, 0, 0, 0, 0, 1540, 0, 0, -576, 0, 0, 1114, -20, 0, 1440, 0, 0, 0, -648, 0, 0, 0, 0, 3744, -720, 0, 0, -490, 0, 0, 2280, 0, -40, 50, 0, 1930, 0, 0, 0, 0, 0, 0, 360, 0, 0, -190, 0, 0, 0, 0, 2160, -3600, 0, 0, -600, 0, 624, 0, 0, 0, 0, 0, -240, 0, 0, -1300, 0, 0, 580, 1630, 0, -1076, 0, 0, 0, 0, 0, 0, 0, 0, -480, 1484, 0, -912, 1340, 0, 0, -250, 0, 670, 1560, 0, 20, 0, 0, 0, 0, 0, 0, 2420, 0, 0, 0, 0, 0, 0, 0, -586, 788, 0, 0, -950, 0, -1678, 0, 0, 0, 0, 0, 700, 0, 0, 48, 0, 0, 1250, -1728, 0, 760, 0, 0, 0, 96, 0, 0, 0, 0, 140, -3000, 0, 0, 100, 0, 0, -480, 0, 0, 346, 0, -530, 0, 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, 19, 2, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "38.3.b.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], [1, 0], [0, -1], [0, 0], [-2, 0], [1, 0], [0, 0], [5, 0], [0, 2], [0, 0], [0, -1], [-5, 0], [0, 0], [0, -12], [0, -5], [0, 0], [4, 0], [25, 0], [0, 0], [19, 0], [-2, 0], [0, 0], [0, 5], [10, 0], [0, 0], [-24, 0], [-24, 0], [0, 0], [-10, 0], [0, -30], [0, 0], [0, -30], [0, -4], [0, 0], [0, -25], [5, 0], [0, 0], [0, -18], [0, -19], [0, 0], [0, 2], [0, 30], [0, 0], [5, 0], [10, 0], [0, 0], [0, -10], [-5, 0], [0, 0], [-24, 0], [0, 24], [0, 0], [0, 24], [0, 18], [0, 0], [-5, 0], [0, 10], [0, 0], [-60, 0], [0, -60], [0, 0], [95, 0], [-60, 0], [0, 0], [-8, 0], [0, -12], [0, 0], [0, 78], [-50, 0], [0, 0], [0, -5], [0, 0], [0, 0], [-25, 0], [-36, 0], [0, 0], [-38, 0], [-25, 0], [0, 0], [0, 30], [4, 0], [0, 0], [60, 0], [130, 0], [0, 0], [25, 0], [0, -5], [0, 0], [0, -10], [0, 90], [0, 0], [0, -60], [-20, 0], [0, 0], [0, 5], [19, 0], [0, 0], [0, 12], [0, 24], [0, 0], [48, 0]]}