# Stored data for newform 405.3.i.b, downloaded from the LMFDB on 20 April 2024. {"label": "405.3.i.b", "space_label": "405.3.i", "level": 405, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4504149433516437, "dim": 4, "is_polredabs": true, "nf_label": "4.0.3600.3", "trace_hash": 45823794284025303, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [25, 0, -5, 0, 1]], [7, [36, -6, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{2}q^{4}+(\\beta _{1}-\\beta _{3})q^{5}+(6+\\cdots)q^{7}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "i", "char_is_real": false, "Nk2": 3645, "analytic_conductor": 11.035450706592025, "hecke_ring_index": 1, "level_radical": 15, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [405, 6, [326, 82], [1, 6]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [3, 5], "conrey_indexes": [26, 296], "field_disc": 3600, "field_disc_factorization": [[2, 4], [3, 2], [5, 2]], "field_poly": [25, 0, -5, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.680", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "83.882", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3016.451", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, 0, 12], "traces": [0, 4, 0, 0, 2, 0, 0, 12, 0, 0, 20, 0, 0, -32, 0, 0, 38, 0, 0, -8, 0, 0, -20, 0, 0, 10, 0, 0, 24, 0, 0, 36, 0, 0, -20, 0, 0, -64, 0, 0, -30, 0, 0, -32, 0, 0, 120, 0, 0, 26, 0, 0, 32, 0, 0, -40, 0, 0, 140, 0, 0, -164, 0, 0, -164, 0, 0, -48, 0, 0, 60, 0, 0, -296, 0, 0, -4, 0, 0, -276, 0, 0, 560, 0, 0, 20, 0, 0, -60, 0, 0, -384, 0, 0, 220, 0, 0, 332, 0, 0, 20, 0, 0, -52, 0, 0, -20, 0, 0, 152, 0, 0, -228, 0, 0, 60, 0, 0, 40, 0, 0, -202, 0, 0, -36, 0, 0, -104, 0, 0, -160, 0, 0, -24, 0, 0, 120, 0, 0, 164, 0, 0, 560, 0, 0, 280, 0, 0, -32, 0, 0, 316, 0, 0, -240, 0, 0, -328, 0, 0, 70, 0, 0, 944, 0, 0, 420, 0, 0, -174, 0, 0, -64, 0, 0, -60, 0, 0, -480, 0, 0, 8, 0, 0, -180, 0, 0, 40, 0, 0, -40, 0, 0, 428, 0, 0, -26, 0, 0, -968, 0, 0, -300, 0, 0, 280, 0, 0, -1216, 0, 0, -4, 0, 0, -900, 0, 0, 432, 0, 0, -20, 0, 0, -172, 0, 0, 280, 0, 0, 564, 0, 0, 420, 0, 0, 440, 0, 0, 120, 0, 0, -524, 0, 0, -328, 0, 0, 64, 0, 0, 50, 0, 0, -240, 0, 0, -362, 0, 0, -192, 0, 0, 120, 0, 0, 20, 0, 0, 48, 0, 0, 328, 0, 0, 540, 0, 0, -48, 0, 0, -360, 0, 0, 288, 0, 0, -320, 0, 0, 1076, 0, 0, -148, 0, 0, 20, 0, 0, -1000, 0, 0, 192, 0, 0, -76, 0, 0, 736, 0, 0, 180, 0, 0, 788, 0, 0, -552, 0, 0, -280, 0, 0, 360, 0, 0, -320, 0, 0, -840, 0, 0, 396, 0, 0, 840, 0, 0, -788, 0, 0, -20, 0, 0, 1488, 0, 0, -60, 0, 0, 724, 0, 0, -280, 0, 0, -560, 0, 0, -860, 0, 0, -1428, 0, 0, -192, 0, 0, 372, 0, 0, -320, 0, 0, 88, 0, 0, 660, 0, 0, -1448, 0, 0, 920, 0, 0, -120, 0, 0, 664, 0, 0, 120, 0, 0, 420, 0, 0, 496, 0, 0, -190, 0, 0, 576, 0, 0, 1680, 0, 0, -916, 0, 0, 52, 0, 0, 840, 0, 0, 40, 0, 0, -1124, 0, 0, 120, 0, 0, 984, 0, 0, -160, 0, 0, 904, 0, 0, 76, 0, 0, 4, 0, 0, 640, 0, 0, 480, 0, 0, -492, 0, 0, -1120, 0, 0, 260, 0, 0, -668, 0, 0, 120, 0, 0, -732, 0, 0, 1620, 0, 0, -576, 0, 0, -60, 0, 0, -20, 0, 0, -2240, 0, 0, 512, 0, 0, 202, 0, 0, -3544, 0, 0, 130, 0, 0, -280, 0, 0, 1368, 0, 0, 4, 0, 0, -2100, 0, 0, -600, 0, 0, -52, 0, 0, -888, 0, 0, 1800, 0, 0, -440, 0, 0, -480, 0, 0, 1504, 0, 0, 260, 0, 0, -698, 0, 0, -48, 0, 0, 900, 0, 0, 1660, 0, 0, -792, 0, 0, 140, 0, 0, -2048, 0, 0, -200, 0, 0, 1656, 0, 0, -164, 0, 0, 1024, 0, 0, 840, 0, 0, 140, 0, 0, -3360, 0, 0, -1924, 0, 0, 1680, 0, 0, -3544, 0, 0, 140, 0, 0, 40, 0, 0, 4200, 0, 0, -72, 0, 0, -608, 0, 0, 240, 0, 0, -960, 0, 0, -4, 0, 0, 632, 0, 0, 1012, 0, 0, -820, 0, 0, 2224, 0, 0, 360, 0, 0, 1604, 0, 0, 1440, 0, 0, -50, 0, 0, 328, 0, 0, -2792, 0, 0, -2020, 0, 0, 416, 0, 0, -1380, 0, 0, -312, 0, 0, 40, 0, 0, -80, 0, 0, 472, 0, 0, 60, 0, 0, 2640, 0, 0, -1364, 0, 0, 1260, 0, 0, 1680, 0, 0, -240, 0, 0, 1788, 0, 0, -348, 0, 0, -1992, 0, 0, 360, 0, 0, 1080, 0, 0, 608, 0, 0, 1516, 0, 0, -1640, 0, 0, 560, 0, 0, 60, 0, 0, 128, 0, 0, 1380, 0, 0, 4, 0, 0, 2880, 0, 0, 320, 0, 0, -1320, 0, 0, -624, 0, 0, 4, 0, 0, -1348, 0, 0, -1480, 0, 0, -1312, 0, 0, 420, 0, 0, 2392, 0, 0, 120, 0, 0, -500, 0, 0, 80, 0, 0, 676, 0, 0, 2240, 0, 0, -2624, 0, 0, 60, 0, 0, 456, 0, 0, -3240, 0, 0, 164, 0, 0, -428, 0, 0, 360, 0, 0, -1980, 0, 0, -1120, 0, 0, 988, 0, 0, 1072, 0, 0, -1380, 0, 0, 5248, 0, 0, -484, 0, 0, -440, 0, 0, -2400, 0, 0, -360, 0, 0, -900, 0, 0, -2232, 0, 0, 320, 0, 0, 64, 0, 0, 560, 0, 0, 428, 0, 0, 120, 0, 0, 1272, 0, 0, 1312, 0, 0, 420, 0, 0, -5320, 0, 0, 278, 0, 0, 4, 0, 0, -2424, 0, 0, 100, 0, 0, 1368, 0, 0, 5400, 0, 0, 1684, 0, 0, -1560, 0, 0, -120, 0, 0, 216, 0, 0, -768, 0, 0, -240, 0, 0, 312, 0, 0, -380, 0, 0, -3856, 0, 0, -900, 0, 0, -312, 0, 0, -344, 0, 0, 860, 0, 0, -1400, 0, 0, -80, 0, 0, -420, 0, 0, -2568, 0, 0, -1920, 0, 0, -840, 0, 0, -564, 0, 0, 1672, 0, 0, -420, 0, 0, -160, 0, 0, 1960, 0, 0, -52, 0, 0, -2020, 0, 0, 2136, 0, 0, 220, 0, 0, 1680, 0, 0, 640, 0, 0, 2368, 0, 0, 360, 0, 0, 1840, 0, 0, 2640, 0, 0, 1274, 0, 0, -1048, 0, 0, -1348, 0, 0, 1660, 0, 0, 1968, 0, 0, 3116, 0, 0, 960, 0, 0, -3640, 0, 0, -420, 0, 0, -64, 0, 0, 3848, 0, 0, -3360, 0, 0, -48, 0, 0, -300], "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, 3, 2, -1, 2, 0], [1, 1, 9, 3, 1, 3, 0], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 9, "prim_orbit_index": 4, "minimal_twist": "15.3.c.a", "char_is_minimal": false, "conrey_index": 26, "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, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, -1], [0, 0, 0, 0], [6, 0, -6, 0], [0, 0, 0, -3], [0, 0, 0, 0], [5, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, -16, 0], [0, 6, 0, -6], [0, 0, 0, 0], [19, 0, -19, 0], [0, 0, 0, 2], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, -10, 0], [0, 6, 0, -6], [0, 0, 0, 0], [5, 0, -5, 0], [0, 0, 0, -16], [0, 0, 0, 0], [6, 0, 0, 0], [0, 14, 0, 0], [0, 0, 0, 0], [0, 0, 18, 0], [0, 7, 0, -7], [0, 0, 0, 0], [-10, 0, 10, 0], [0, 0, 0, -6], [0, 0, 0, 0], [-16, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, -15, 0], [0, 28, 0, -28], [0, 0, 0, 0], [-16, 0, 16, 0], [0, 0, 0, -2], [0, 0, 0, 0], [30, 0, 0, 0], [0, 22, 0, 0], [0, 0, 0, 0], [0, 0, 13, 0], [0, 5, 0, -5], [0, 0, 0, 0], [16, 0, -16, 0], [0, 0, 0, 2], [0, 0, 0, 0], [-10, 0, 0, 0], [0, -18, 0, 0], [0, 0, 0, 0], [0, 0, 70, 0], [0, 2, 0, -2], [0, 0, 0, 0], [-82, 0, 82, 0], [0, 0, 0, 18], [0, 0, 0, 0], [-41, 0, 0, 0], [0, -16, 0, 0], [0, 0, 0, 0], [0, 0, -24, 0], [0, -2, 0, 2], [0, 0, 0, 0], [30, 0, -30, 0], [0, 0, 0, -56], [0, 0, 0, 0], [-74, 0, 0, 0], [0, -16, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, -12, 0, 12], [0, 0, 0, 0], [-138, 0, 138, 0], [0, 0, 0, -19], [0, 0, 0, 0], [140, 0, 0, 0], [0, 42, 0, 0], [0, 0, 0, 0], [0, 0, 10, 0], [0, -16, 0, 16], [0, 0, 0, 0], [-30, 0, 30, 0], [0, 0, 0, 48], [0, 0, 0, 0], [-96, 0, 0, 0], [0, 6, 0, 0], [0, 0, 0, 0], [0, 0, 110, 0], [0, -2, 0, 2], [0, 0, 0, 0], [166, 0, -166, 0], [0, 0, 0, 13], [0, 0, 0, 0], [5, 0, 0, 0]]}