# Stored data for newform 475.3.c.d, downloaded from the LMFDB on 16 April 2024.
{"label": "475.3.c.d", "space_label": "475.3.c", "level": 475, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13510936371397083, "dim": 4, "is_polredabs": true, "nf_label": "4.0.7600.1", "trace_hash": 723346349161734572, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [19, 0, 16, 0, 1]], [7, [0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(\\beta _{1}-\\beta _{2})q^{3}+(-4+3\\beta _{3})q^{4}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 19, "char_orbit_label": "c", "char_is_real": true, "Nk2": 4275, "analytic_conductor": 12.942812557114102, "hecke_ring_index": 4, "level_radical": 95, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.885", "prec": 17}, "analytic_rank_proved": true, "char_values": [475, 2, [77, 401], [2, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [5, 19], "conrey_indexes": [151], "field_disc": 7600, "field_disc_factorization": [[2, 4], [5, 2], [19, 1]], "field_poly": [19, 0, 9, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.042", "prec": 17}, {"__RealLiteral__": 0, "data": "3.428", "prec": 17}, {"__RealLiteral__": 0, "data": "3.238", "prec": 17}, {"__RealLiteral__": 0, "data": "160.524", "prec": 24}, {"__RealLiteral__": 0, "data": "215.797", "prec": 24}, {"__RealLiteral__": 0, "data": "8382.187", "prec": 27}], "related_objects": [], "self_twist_discs": [-95], "cm_discs": [-95], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.1.d2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, -16, 0, -28, 0, 0, -36, 0, 0, 0, 0, 0, 0, 116, 0, 0, 76, 0, 0, 0, 0, 300, 0, -172, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 0, 0, -8, 0, 0, 0, 0, 360, 0, 0, 0, 0, -196, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, 0, 0, 0, 0, -464, 0, 600, 0, 0, 0, 0, 0, 0, 0, 92, 0, -304, 0, 0, 0, 0, -244, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -812, 0, 0, 240, 0, 0, 0, 0, 540, 0, 772, 0, 0, 0, 0, -632, 0, 0, -532, 0, 0, 0, 0, 0, 0, 236, 0, 0, 0, 0, 0, 0, 0, 0, 0, -472, 0, 0, -692, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1524, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2072, 0, 0, 248, 0, 0, 0, 0, 0, 0, 0, 0, 0, -676, 0, -684, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1208, 0, 0, -868, 0, 784, 0, 0, -1288, 0, 392, 0, 0, 0, 0, 1268, 0, 0, 0, 0, 0, 0, 0, 1708, 0, -840, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1612, 0, 0, 0, 0, 0, 0, 0, 1908, 0, 0, 0, 0, -392, 0, 0, 0, 0, 3240, 0, 0, 0, 0, 0, 0, -728, 0, 0, -1348, 0, 484, 0, 0, 0, 0, 0, 0, 0, -2520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1080, 0, 0, -1156, 0, 808, 0, 0, 1372, 0, 1620, 0, 0, 0, 0, 0, 0, 0, 2204, 0, 0, 0, 0, 2392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1352, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1052, 0, 0, 0, 0, -2408, 0, 0, 0, 0, 0, 0, -652, 0, 0, 2072, 0, 1360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1444, 0, 0, 0, 0, 5400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3032, 0, 0, 3900, 0, -3068, 0, 0, 2968, 0, 0, 0, 0, 0, 0, -4200, 0, 0, 0, 0, 0, 0, 0, -5400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4988, 0, 0, -1832, 0, 0, 0, 0, -3060, 0, 0, 0, 0, 4080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1764, 0, 0, -472, 0, -2588, 0, 0, 0, 0, 0, 0, 0, -212, 0, 5700, 0, 0, 0, 0, -2392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2632, 0, 0, -944, 0, 1708, 0, 0, 0, 0, 1192, 0, 0, -3268, 0, 0, 0, 0, 0, 0, -2072, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -388, 0, 0, 0, 0, -3848, 0, 0, 0, 0, 1888, 0, 0, 0, 0, -2116, 0, 0, 0, 0, 0, 0, 900, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 5400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5736, 0, 0, -3112, 0, 0, 0, 0, 0, 0, -4508, 0, 0, 0, 0, 0, 0, 0, -1680, 0, -6120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9000, 0, 0, 0, 0, 0, 0, 0, 4588, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8392, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1652, 0, -9512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 728, 0, 6480, 0, 0, -5012, 0, 904, 0, 0, 0, 0, 4232, 0, 0, 5016, 0, 0, 0, 0, 5432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4680, 0, 0, 0, 0, -808, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1652, 0, 0, 2196, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5608, 0, -152, 0, 0, 0, 0, -188, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4832, 0, 2708, 0, 0, 0, 0, 4648, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 0, -5684, 0, 3304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5152, 0, 0, 0, 0, 0, 0, 0, 7912, 0, 0, 0, 0, 4472, 0, 0, 0, 0, 3240, 0, 0, 0, 0, 0, 0, 488, 0, 0, -10980, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9000, 0, 6840, 0, 0, 0, 0, 3364, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9180, 0, 0, 6808, 0, 0, 0, 0, 5800, 0, -2572, 0, 0, 0, 0, -6712, 0, 0, 0, 0, 0, 0, 0, -5512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2160, 0, 0, -10200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12060, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 0, 11160, 0, 0, 6328, 0, 6152, 0, 0, 0, 0, 0, 0, 0, 3512, 0, -3724, 0, 0, 0, 0, -10020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7288, 0, 0, -8988, 0, 1568, 0, 0, 0, 0, 3844, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1708, 0, -12960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2000, 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, 95, 4, -1, 2, -95], [1, 1, 5, 2, 1, 2, 0], [1, 1, 19, 2, -1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "95.3.d.c", "char_is_minimal": true, "conrey_index": 151, "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, 1, -1, 0], [-4, 0, 0, 3], [0, 0, 0, 0], [-7, 0, 0, 5], [0, 0, 0, 0], [0, -6, 3, 0], [-9, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 6], [0, -13, 1, 0], [0, 5, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [29, 0, 0, -12], [0, 0, 0, 0], [0, -13, 2, 0], [19, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -12, 6, 0], [0, 0, 0, 0], [75, 0, 0, -21], [0, 0, 0, 0], [-43, 0, 0, 9], [0, -6, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 29, 0, 0], [0, -18, -6, 0], [0, 0, 0, 0], [0, 0, 0, 0], [66, 0, 0, -35], [0, -1, -15, 0], [0, 19, 0, 0], [-2, 0, 0, 34], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [90, 0, 0, -24], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 65, -17, 0], [-49, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -41, 21, 0], [0, -23, -9, 0], [50, 0, 0, -14], [0, 0, 0, 0], [0, 0, 0, 0], [0, 19, -19, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 54], [0, 0, 0, 0], [0, 0, 0, 0], [-116, 0, 0, 39], [0, 0, 0, 0], [150, 0, 0, -42], [0, 19, 21, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 84, -27, 0], [0, 0, 0, 0], [23, 0, 0, 27], [0, 0, 0, 0], [-76, 0, 0, 57], [0, 0, 0, 0], [0, -70, 34, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-61, 0, 0, -18], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 90, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-203, 0, 0, 145], [0, 23, 33, 0], [0, -49, 0, 0], [60, 0, 0, -54], [0, 0, 0, 0]]}