# Stored data for newform 90.3.g.b, downloaded from the LMFDB on 25 April 2024.
{"label": "90.3.g.b", "space_label": "90.3.g", "level": 90, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4504011994562650, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 363704759835060183, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [8, -4, 1]], [11, [-8, 1]]], "qexp_display": "q+(1+i)q^{2}+2iq^{4}+5iq^{5}+(2+2i)q^{7}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "g", "char_is_real": false, "Nk2": 810, "analytic_conductor": 2.452322379242672, "hecke_ring_index": 1, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.248", "prec": 17}, "analytic_rank_proved": true, "char_values": [90, 4, [11, 37], [4, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [37, 73], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.950", "prec": 17}, {"__RealLiteral__": 0, "data": "0.023", "prec": 17}, {"__RealLiteral__": 0, "data": "11.405", "prec": 20}, {"__RealLiteral__": 0, "data": "0.620", "prec": 17}, {"__RealLiteral__": 0, "data": "92.032", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.3.c4", "trace_display": [2, 0, 0, 4], "traces": [0, 2, 2, 0, 0, 0, 0, 4, -4, 0, -10, 16, 0, 6, 0, 0, -8, -14, 0, 0, -20, 0, 16, 4, 0, -50, 12, 0, -8, 0, 0, 104, -8, 0, 0, -20, 0, -6, 40, 0, -20, 16, 0, -84, 0, 0, 8, 36, 0, 0, -50, 0, 12, -106, 0, 0, -16, 0, 80, 0, 0, -96, 104, 0, 0, 30, 0, 124, 28, 0, -40, 56, 0, -94, 0, 0, 80, 32, 0, 0, 0, 0, 16, -36, 0, 70, -168, 0, -32, 0, 0, 24, 8, 0, 0, 200, 0, -126, 82, 0, 0, -124, 0, 236, 0, 0, -212, -284, 0, 0, -80, 0, -16, -46, 0, 20, 160, 0, -40, 0, 0, -114, -96, 0, 0, 0, 0, -236, 16, 0, 0, 256, 0, 80, 0, 0, 56, 126, 0, 0, -40, 0, 56, 48, 0, 400, -188, 0, 12, 0, 0, 104, 80, 0, 0, 0, 0, 54, 0, 0, 40, 16, 0, -164, 0, 0, -72, -124, 0, 0, 140, 0, -168, 214, 0, -100, -64, 0, 160, 0, 0, 4, 24, 0, 0, 30, 0, -112, -72, 0, 200, -424, 0, -114, 0, 0, 164, 6, 0, 0, 100, 0, -124, 160, 0, 0, 472, 0, -24, 0, 0, -656, -212, 0, 0, -420, 0, 208, 20, 0, -160, -84, 0, 276, 0, 0, -92, -4, 0, 0, 0, 0, 160, -366, 0, -180, -80, 0, 56, 0, 0, 464, -114, 0, 0, 410, 0, -120, -208, 0, 250, 96, 0, 32, 0, 0, 32, 626, 0, 0, -60, 0, 256, 524, 0, -530, 160, 0, -248, 0, 0, 504, 56, 0, 0, -400, 0, 534, -280, 0, 0, -624, 0, -524, 0, 0, 96, 32, 0, 0, 400, 0, -188, -486, 0, -200, 24, 0, -300, 0, 0, -336, 104, 0, 0, 0, 0, -36, -64, 0, -520, 776, 0, 366, 0, 0, 0, 426, 0, 0, 80, 0, 16, -280, 0, -150, -328, 0, -32, 0, 0, 464, -72, 0, 0, -620, 0, 834, -302, 0, 140, 832, 0, 360, 0, 0, 428, -404, 0, 0, 0, 0, -64, 894, 0, 0, 320, 0, -440, 0, 0, -78, 4, 0, 0, -470, 0, -236, -16, 0, 60, -424, 0, -214, 0, 0, -144, -240, 0, 0, 0, 0, -424, 684, 0, -160, -228, 0, 252, 0, 0, -56, 164, 0, 0, 0, 0, -646, 240, 0, 200, -1284, 0, 312, 0, 0, 320, -48, 0, 0, -80, 0, 472, -80, 0, -180, -48, 0, 320, 0, 0, -416, -656, 0, 0, 350, 0, -192, 568, 0, 0, 1576, 0, -734, 0, 0, 40, -80, 0, 0, -160, 0, -84, -756, 0, 800, 552, 0, 32, 0, 0, 128, -92, 0, 0, 0, 0, -786, -240, 0, -40, -1244, 0, 556, 0, 0, -732, 76, 0, 0, -360, 0, -80, -672, 0, 0, 112, 0, 240, 0, 0, -36, 464, 0, 0, 630, 0, 1044, 192, 0, 410, 656, 0, -560, 0, 0, -416, 112, 0, 0, 500, 0, 96, 84, 0, 0, 64, 0, 472, 0, 0, -376, 32, 0, 0, 1180, 0, 288, 24, 0, -120, 516, 0, 516, 0, 0, 1048, -728, 0, 0, 0, 0, 160, 48, 0, 1420, -496, 0, 20, 0, 0, -676, 504, 0, 0, 100, 0, -1116, -252, 0, -400, -1600, 0, 0, 0, 0, -560, 6, 0, 0, 80, 0, -624, 84, 0, -230, -1048, 0, -112, 0, 0, 784, 96, 0, 0, -100, 0, -946, 382, 0, 0, -144, 0, -848, 0, 0, -972, 396, 0, 0, -200, 0, 24, 94, 0, 280, -600, 0, 24, 0, 0, -656, -336, 0, 0, 0, 0, 924, -160, 0, 480, 216, 0, 1446, 0, 0, -128, -654, 0, 0, -1040, 0, 776, 320, 0, 1250, 732, 0, -108, 0, 0, -1096, 0, 0, 0, 1180, 0, -246, 640, 0, 80, 1136, 0, -684, 0, 0, -560, 236, 0, 0, -300, 0, -328, -906, 0, 0, -64, 0, -144, 0, 0, 1024, 464, 0, 0, 400, 0, -160, 248, 0, -1240, -768, 0, 386, 0, 0, -604, -314, 0, 0, 0, 0, 832, -876, 0, -630, 720, 0, 336, 0, 0, 2064, 428, 0, 0, -1400, 0, -112, 880, 0, 200, 256, 0, -120, 0, 0, 1788, -248, 0, 0, -280, 0, 320, 208, 0, 240, -880, 0, -800, 0, 0, 944, -78, 0, 0, 0, 0, -1116, -48, 0, 0, 1176, 0, -1654, 0, 0, -32, 992, 0, 0, 60, 0, -424, 764, 0, -1500, -428, 0, 224, 0, 0, -1176, -144, 0, 0, 0, 0, 1974, -680, 0, -400, 316, 0, 40, 0, 0, 1368, 120, 0, 0, -320, 0, -228, -486, 0, -2600, 504, 0, 780, 0, 0, 448, -56, 0, 0, -270, 0, 524, -12, 0, 0, -184, 0, -288, 0, 0, 480, -534, 0, 0, 200, 0, -1284, -752, 0, 0, 624, 0, 248, 0, 0, -416, 320, 0, 0, -820, 0, 1680, 300, 0, -160, 3136, 0, -1124, 0, 0, -160, -1524, 0, 0, 0, 0, -48, -574, 0, 620, 640, 0, 600, 0, 0, -1518, -416, 0, 0, -1510, 0, -228, 424, 0, 0, -24, 0, 2246, 0, 0, 1136, -834, 0, 0, 840, 0, 1576, 484, 0, 1070, -1468, 0, -416, 0, 0, 744, 40, 0, 0, 500, 0, -906, -1120, 0, 0, -1424, 0, 236, 0, 0, -1512, 2316, 0, 0, 800, 0, 552, 720, 0, -2200, 64, 0, -820, 0, 0, 1484, 128, 0, 0, 0, 0, 284, 8, 0, -120, -2344, 0, -288, 0, 0, -480, 512, 0, 0, -80, 0, -1244, 168, 0, 150, 1112, 0, -320, 0, 0, -1640, -732, 0, 0, 560, 0, -466, -496, 0, -360, 156, 0, 32, 0, 0, -1344, -124, 0, 0, -1000, 0, 112, 2034, 0, 0, 480, 0, -880, 0, 0, 3486, -36, 0, 0, -570, 0, 1004, 228, 0, 1260, -1984, 0, -560, 0, 0, 384, 1566, 0, 0, 0, 0, 656, -2116, 0, -30, -1120, 0, 240, 0, 0, -136, -416, 0, 0, 1200, 0, -1546, -760, 0, 500], "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, 5, 3, -1, 4, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "10.3.c.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], [1, 1], [0, 0], [0, 2], [0, 5], [0, 0], [2, 2], [-2, 2], [0, 0], [-5, 5], [8, 0], [0, 0], [3, -3], [0, 4], [0, 0], [-4, 0], [-7, -7], [0, 0], [0, -20], [-10, 0], [0, 0], [8, 8], [2, -2], [0, 0], [-25, 0], [6, 0], [0, 0], [-4, 4], [0, -40], [0, 0], [52, 0], [-4, -4], [0, 0], [0, -14], [-10, 10], [0, 0], [-3, -3], [20, -20], [0, 0], [-10, -10], [8, 0], [0, 0], [-42, 42], [0, 16], [0, 0], [4, 0], [18, 18], [0, 0], [0, -41], [-25, -25], [0, 0], [6, 6], [-53, 53], [0, 0], [0, 40], [-8, 0], [0, 0], [40, -40], [0, 20], [0, 0], [-48, 0], [52, 52], [0, 0], [0, -8], [15, 15], [0, 0], [62, 62], [14, -14], [0, 0], [-20, 0], [28, 0], [0, 0], [-47, 47], [0, -6], [0, 0], [40, 0], [16, 16], [0, 0], [0, 0], [0, -20], [0, 0], [8, 8], [-18, 18], [0, 0], [35, -35], [-84, 0], [0, 0], [-16, 16], [0, -80], [0, 0], [12, 0], [4, 4], [0, 0], [0, 36], [100, 0], [0, 0], [-63, -63], [41, -41], [0, 0], [0, -50]]}