# Stored data for newform 155.3.c.b, downloaded from the LMFDB on 24 May 2024. {"Nk2": 1395, "analytic_conductor": 4.223444097584602, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 155, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": -1, "char_values": [155, 2, [32, 96], [1, 1]], "cm_discs": [-155], "conrey_index": 154, "dim": 2, "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 10, "has_non_self_twist": 1, "hecke_cutters": [[2, [0, 1]], [3, [-5, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503737116655771, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 155, 3, -1, 2, -155], [1, 1, 5, 2, 1, 2, 0], [1, 1, 31, 2, -1, 2, 0]], "is_cm": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": true, "label": "155.3.c.b", "level": 155, "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": true, "level_primes": [5, 31], "level_radical": 155, "minimal_twist": "155.3.c.b", "nf_label": "2.2.5.1", "prim_orbit_index": 3, "qexp_display": "q-\\beta q^{3}+4q^{4}+5q^{5}-4q^{9}-4\\beta q^{12}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "2.2.1.d2", "self_twist_discs": [-155], "self_twist_type": 1, "space_label": "155.3.c", "trace_display": [0, 0, 10, 0], "trace_hash": 80065404248381985, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.942", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "23.177", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "307.605", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.760", "prec": 17}, "traces": [0, 2, 0, 0, 8, 10, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 32, 0, 0, 14, 40, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, -62, 0, 0, 0, 0, -32, 0, 0, -60, 0, -146, 0, 0, 0, -40, 0, 0, 0, 98, 0, -150, 0, 0, 0, 0, 0, 0, 0, -74, 0, 0, 0, 0, 128, 0, 0, 0, 0, 180, 0, -274, 0, 0, 0, 0, 56, 0, 0, 0, 160, -58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 200, -154, 0, 0, 0, 0, 0, 0, 0, 374, 0, 330, 0, 0, 0, 0, 0, 0, 0, 0, 0, 242, 0, 0, -248, 250, 0, 0, 0, -270, 0, -34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 286, 0, 0, 0, 0, 0, -310, -240, 0, 0, -30, 0, 0, 0, 0, -584, 0, 0, 0, 0, 22, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -476, 0, 0, 0, -300, 392, 0, 0, 0, 0, 0, 0, 0, -600, -730, 0, 0, 0, 0, 0, 596, 0, 0, 0, 0, 0, 0, 0, 450, 0, 900, 0, 0, 0, -200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -296, 0, 0, 0, 0, 0, 0, 0, 0, 490, 0, 0, 0, 690, 0, 0, 0, 0, 0, -750, 512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 720, 0, 0, 248, 0, 566, 0, 0, -1096, 0, 0, 0, 0, 1672, 0, 0, 0, 0, 0, -370, 0, 0, 0, -1080, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 934, 0, 0, 0, 0, 0, 0, 0, 0, 640, 0, 0, 0, -232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 900, 0, 0, 0, -1394, 0, 780, 0, 0, 0, -1370, 0, 0, 0, -796, 0, -624, 0, 0, 0, 0, 0, 0, 0, 584, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1274, 280, -300, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2700, 0, 0, 0, 0, 0, 0, 0, 0, 800, 0, 0, 0, -616, -290, 0, 0, 0, 0, 0, -990, 0, 0, 0, 0, 0, 0, 0, 1366, 0, -1106, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1166, 0, 0, 0, 0, 1496, 0, 0, -1034, 0, -392, 0, 0, 1320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1950, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 350, 0, 0, 0, 676, 0, -1980, 0, 0, 968, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -992, 0, 0, 0, 1000, -270, 0, 0, 0, -770, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1080, 0, 0, 0, 0, 1526, 0, 0, -136, 0, 0, 0, 0, 2182, 0, 296, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1804, 0, 0, 0, 1870, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1650, 0, 0, 0, 1620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -434, 0, 1380, 0, 0, 0, 0, 1144, 0, 0, 164, 0, 0, 0, 0, 0, 1210, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1240, -2340, 0, 0, -960, 1250, 0, 0, 0, -4950, 0, 0, 0, 0, 0, 0, -120, 0, 0, 1096, 0, 0, 0, 0, 0, -1350, 0, 0, 0, 0, 0, 0, 0, 0, 0, -170, -2336, 0, 0, -2386, 0, -394, 0, 0, 0, 0, 0, 0, 0, 330, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 180, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -640, 0, 0, 0, 0, 0, 0, 0, 0, 1402, 0, 4050, 0, 0, 0, 0, 0, 0, 0, 0, 0, -420, 0, 0, 0, 1430, 0, 0, 0, 0, 0, 2756, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1904, 0, 0, 0, 0, 286, 0, 0, 0, 0, 0, -1550, 0, 0, 0, -1022, -1200, 0, 0, 0, 1568, 0, 0, 0, 0, 1290, 0, 0, 0, 0, 0, -150, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 454, 0, 0, 0, 0, -2400, 0, 0, 0, -2920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2370, 0, 0, 0, 0, 0, 0, 0, -1666, 0, 1682, 0, 0, 2384, 110, 0, 0, 0, 0, 0, 5940, 0, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1800, 0, 0, 0, 0, 0, 0, 0, 3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -800, 450, 0, 0, 0, 0, 0, 0, 0, 616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3614, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 686, 0, 0, 0, 0, 0, 0, 0, -1230, 0, 0, 0, 0, -1184, 0, 0, 0, 0, -2700, 0, 0, 0, 0, 0, -2380, 0, 0, 0, 0, 0, 1922, 0, 0, 0, 0, 0, 0, 0, -1050, 0, -3866, 0, 0, 0, -1500, 0, 0, 0, 0, 1960, -1496, 0, 0, 0, 0, 0, 0, 0, -4860, 0, 0, 0, 0, 0, 0, 2760, 0, 0, -4290, 0], "weight": 3, "weight_parity": -1, "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, 0], [0, -1], [4, 0], [5, 0], [0, 0], [0, 0], [0, 0], [-4, 0], [0, 0], [0, 0], [0, -4], [0, 6], [0, 0], [0, -5], [16, 0], [0, 15], [0, 0], [7, 0], [20, 0], [0, 0], [0, 0], [0, -18], [0, 0], [25, 0], [0, 0], [0, 13], [0, 0], [0, 0], [0, 0], [-31, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-16, 0], [0, -33], [0, 0], [-30, 0], [0, 0], [-73, 0], [0, 0], [0, 27], [0, 0], [-20, 0], [0, 0], [0, 0], [0, -16], [49, 0], [0, 0], [-75, 0], [0, 24], [0, 3], [0, 0], [0, 0], [0, 0], [0, -7], [0, 0], [-37, 0], [0, -20], [0, 0], [0, 0], [0, 0], [64, 0], [0, 30], [0, 0], [0, 0], [0, 60], [90, 0], [0, 0], [-137, 0], [0, 0], [0, -45], [0, 0], [0, -25], [28, 0], [0, 0], [0, 0], [0, 0], [80, 0], [-29, 0], [0, 0], [0, -69], [0, 0], [0, 75], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -72], [0, 31], [0, 0], [35, 0], [0, 0], [0, 0], [0, 0], [0, 0], [100, 0]]}