# Stored data for newform 324.3.f.b, downloaded from the LMFDB on 19 April 2024.
{"label": "324.3.f.b", "space_label": "324.3.f", "level": 324, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4503943275086148, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 672363718091524329, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [49, -7, 1]], [7, [75, 15, 1]], [11, [75, 15, 1]]], "qexp_display": "q-2q^{2}+4q^{4}+(7-7\\zeta_{6})q^{5}+(-10+\\cdots)q^{7}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 36, "char_orbit_label": "f", "char_is_real": false, "Nk2": 2916, "analytic_conductor": 8.82836056527362, "hecke_ring_index": 1, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.172", "prec": 17}, "analytic_rank_proved": true, "char_values": [324, 6, [163, 245], [3, 4]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [55, 271], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.041", "prec": 17}, {"__RealLiteral__": 0, "data": "1.939", "prec": 17}, {"__RealLiteral__": 0, "data": "0.281", "prec": 17}, {"__RealLiteral__": 0, "data": "11.446", "prec": 20}, {"__RealLiteral__": 0, "data": "3.514", "prec": 17}, {"__RealLiteral__": 0, "data": "95.120", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.3.c6", "trace_display": [-4, 0, 7, -15], "traces": [0, 2, -4, 0, 8, 7, 0, -15, -16, 0, -14, -15, 0, -20, 30, 0, 32, 16, 0, 0, 28, 0, 30, -6, 0, -24, 40, 0, -60, 10, 0, 93, -64, 0, -32, 0, 0, -20, 0, 0, -56, -50, 0, 30, -60, 0, 12, -150, 0, 26, 48, 0, -80, 94, 0, 0, 120, 0, -20, -60, 0, 64, -186, 0, 128, 140, 0, -150, 64, 0, 0, 0, 0, -110, 40, 0, 0, 75, 0, 12, 112, 0, 100, -51, 0, 56, -60, 0, 120, -20, 0, 0, -24, 0, 300, 126, 0, 25, -52, 0, -96, -155, 0, -240, 160, 0, -188, 0, 0, 268, 0, 0, -240, -74, 0, -42, 40, 0, 120, -120, 0, -46, -128, 0, 372, 14, 0, 0, -256, 0, -280, -285, 0, -90, 300, 0, -128, -62, 0, 300, 0, 0, 0, 0, 0, 140, 220, 0, -80, 115, 0, 75, 0, 0, -150, 651, 0, -20, -24, 0, -224, 60, 0, 0, -200, 0, 102, 426, 0, -231, -112, 0, 120, 127, 0, 360, -240, 0, 40, 0, 0, 112, 0, 0, 48, -70, 0, -120, -600, 0, -252, -60, 0, -65, -50, 0, 104, -506, 0, 0, 192, 0, 310, -150, 0, 350, 480, 0, -320, -90, 0, -258, 376, 0, 0, 0, 0, -930, -536, 0, 0, -160, 0, -60, 480, 0, 148, 156, 0, -146, 84, 0, -80, -668, 0, 0, -240, 0, 240, 30, 0, -134, 92, 0, 256, -182, 0, -360, -744, 0, -28, 0, 0, 60, 0, 0, 512, 268, 0, 150, 560, 0, 570, 750, 0, 329, 180, 0, -600, 700, 0, 0, 256, 0, 124, 360, 0, 520, -600, 0, 0, -440, 0, 570, 0, 0, 0, 0, 0, -450, -280, 0, -440, -218, 0, -420, 160, 0, -230, 120, 0, -150, -150, 0, 0, 896, 0, 0, 300, 0, -1302, -510, 0, -485, 40, 0, 48, 217, 0, -150, 448, 0, -120, 0, 0, 960, 0, 0, 400, 750, 0, 750, -204, 0, -852, -1050, 0, 310, 462, 0, 224, -930, 0, 0, -240, 0, -254, -375, 0, -74, -720, 0, 480, 394, 0, 0, -80, 0, 0, 0, 0, 506, -224, 0, 0, -385, 0, 975, -96, 0, 140, -705, 0, 40, 240, 0, 1200, -400, 0, 0, 504, 0, 120, 624, 0, -525, 130, 0, 100, 475, 0, -48, -208, 0, 1012, 0, 0, 520, 0, 0, -384, -740, 0, -1860, -620, 0, 300, 150, 0, -659, -700, 0, -960, 600, 0, 0, 640, 0, 180, 1020, 0, 496, 516, 0, -752, -192, 0, -960, 0, 0, 0, 0, 0, -470, 1860, 0, 1072, 36, 0, -717, 0, 0, 320, -996, 0, -70, 120, 0, -960, 940, 0, 0, -296, 0, -312, -2100, 0, 325, 292, 0, -168, 655, 0, -285, 160, 0, 1336, 0, 0, 1500, 0, 0, 480, -150, 0, 432, -480, 0, -60, 570, 0, 200, 268, 0, -184, 350, 0, 0, -512, 0, 364, -375, 0, 80, 720, 0, 1488, 0, 0, -78, 56, 0, 0, 0, 0, -2170, -120, 0, 0, 265, 0, 825, -1024, 0, -536, -1680, 0, 750, -300, 0, -1120, 760, 0, 0, -1140, 0, -1500, 744, 0, -517, -658, 0, -360, -1000, 0, 1575, 1200, 0, -1400, 0, 0, -1064, 0, 0, -512, 938, 0, 1560, -248, 0, -720, -180, 0, -60, -1040, 0, 1200, 178, 0, 0, 0, 0, 880, 525, 0, 518, -1140, 0, 0, 100, 0, 588, 0, 0, 0, 0, 0, -1460, 900, 0, 560, 255, 0, -705, 880, 0, 436, 1389, 0, -558, 840, 0, -320, -1964, 0, 0, 460, 0, -240, 390, 0, -251, 300, 0, 300, 322, 0, 660, 0, 0, -1792, 0, 0, 1300, 0, 0, -600, -758, 0, 300, 2604, 0, 1020, 150, 0, 649, 970, 0, -80, -160, 0, 0, -96, 0, -434, -315, 0, 520, 300, 0, -896, 910, 0, -60, 240, 0, 0, 0, 0, 600, -1920, 0, 0, 103, 0, -1995, -800, 0, -1500, -105, 0, -578, -1500, 0, 408, -1260, 0, 0, 1704, 0, 2100, -960, 0, -845, -620, 0, -924, -1154, 0, -375, -448, 0, 1860, 0, 0, -868, 0, 0, 480, -940, 0, -852, 508, 0, 750, 2100, 0, -400, 148, 0, 1440, 430, 0, 0, -960, 0, -788, 2325, 0, 532, 0, 0, 160, -186, 0, -2100, 0, 0, 0, 0, 0, 2400, -1012, 0, 448, 240, 0, 2145, 0, 0, 770, 240, 0, -950, -1950, 0, 192, 1500, 0, 0, -280, 0, 1410, -1500, 0, -805, -80, 0, -480, -1125, 0, -303, -2400, 0, 800, 0, 0, 1660, 0, 0, -1008, -560, 0, -2010, -240, 0, -1248, 1200, 0, 331, 1050, 0, -260, -596, 0, 0, -200, 0, -950, -900, 0, 0, 96, 0, 416, 140, 0, 1920, -2024, 0, 0, 0, 0, -2560, -1040, 0, 0, 1303, 0, -1200, 768, 0, 1480, 825, 0, 210, 3720, 0, 1240, 340, 0, 0, -600, 0, -300, 1260, 0, 180, 1318, 0, 1400, 1090, 0, -1635, 1920, 0, -1200, 0, 0, 1084, 0, 0, -1280, 208, 0, 2982, -360, 0, -2040, 1200, 0, 741, -992, 0, -1032, -3234, 0, 0, 1504, 0, 384, 60, 0, -290, 1920, 0, 0, -368, 0, 1848, 0, 0, 0, 0, 0, 1778, 940, 0, -3720, -60, 0, 3000, -2144, 0, -72, -105, 0, 1330, 1434, 0, 0, -2120, 0, 0, -640, 0, 1992, 1236, 0, 225, 140, 0, -240, -900, 0, -2835, 1920, 0, -1880, 0, 0, 752, 0, 0, 592, 392, 0, -2310, 624, 0, 4200, -2670, 0, 255, -650, 0, -584, 2850, 0, 0, 336, 0, -1310, 0, 0, 240, 570, 0, -320, -1340, 0, 468, -2672, 0, 0, 0, 0, -2450, -3000, 0, 0, 115, 0, 300, -960, 0, 300, 1191, 0, 1100, -864, 0, 960, 88, 0, 0, 120, 0, -1140, 930, 0, 1922, -400, 0, -536, 455, 0, 435, 368, 0, -700, 0, 0, -3000, 0, 0, 1024, 346, 0, 150, -728, 0, 750, -1374, 0, -1771, -160, 0, -1440, -120, 0, 0, -2976, 0, 0, -1575, 0, -260, 156, 0, -112], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 36, 6, -1, 6, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "108.3.d.a", "char_is_minimal": false, "conrey_index": 55, "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], [-2, 0], [0, 0], [4, 0], [7, -7], [0, 0], [-10, 5], [-8, 0], [0, 0], [-14, 14], [-10, 5], [0, 0], [-20, 20], [20, -10], [0, 0], [16, 0], [8, 0], [0, 0], [-6, 12], [28, -28], [0, 0], [20, -10], [-2, -2], [0, 0], [0, -24], [40, -40], [0, 0], [-40, 20], [0, 10], [0, 0], [31, 31], [-32, 0], [0, 0], [-16, 0], [-35, 70], [0, 0], [-10, 0], [12, -24], [0, 0], [-56, 56], [-50, 50], [0, 0], [20, -10], [-40, 20], [0, 0], [4, 4], [-100, 50], [0, 0], [26, -26], [0, 48], [0, 0], [-80, 80], [47, 0], [0, 0], [-35, 70], [80, -40], [0, 0], [0, -20], [-20, -20], [0, 0], [0, 64], [-62, -62], [0, 0], [64, 0], [0, 140], [0, 0], [-50, -50], [32, 0], [0, 0], [70, -140], [0, 0], [0, 0], [-55, 0], [20, 0], [0, 0], [-24, 48], [75, -75], [0, 0], [8, -4], [112, -112], [0, 0], [100, -100], [-34, 17], [0, 0], [56, -56], [-40, 20], [0, 0], [80, -40], [-10, 0], [0, 0], [100, -200], [-8, -8], [0, 0], [200, -100], [42, 42], [0, 0], [0, 25], [-52, 52], [0, 0], [0, -96]]}