# Stored data for newform 75.3.c.d, downloaded from the LMFDB on 23 April 2024.
{"label": "75.3.c.d", "space_label": "75.3.c", "level": 75, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13510936371396683, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 473481263581881440, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 0, 1]], [7, [0, 1]], [13, [0, 1]]], "qexp_display": "q+iq^{2}+3iq^{3}+3q^{4}-3q^{6}+7iq^{8}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "c", "char_is_real": true, "Nk2": 675, "analytic_conductor": 2.043601982702227, "hecke_ring_index": 1, "level_radical": 15, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.761", "prec": 17}, "analytic_rank_proved": true, "char_values": [75, 2, [26, 52], [1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [3, 5], "conrey_indexes": [26], "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": "1.874", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.943", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "287.170", "prec": 24}], "related_objects": [], "self_twist_discs": [-15], "cm_discs": [-15], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.1.d2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, 6, 0, -6, 0, 0, -18, 0, 0, 0, 0, 0, 0, 10, 0, 0, 44, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 0, 4, 0, 0, 28, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, -98, 0, 84, 0, 0, 54, 0, 0, 0, 0, 0, 0, -236, 0, 0, -26, 0, 0, 0, 0, 204, 0, 0, 0, 0, 0, 0, 132, 0, 0, -196, 0, 162, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, -198, 0, 0, 0, 0, 0, 0, 0, 0, 0, -172, 0, 0, 44, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 0, 242, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 0, 0, 524, 0, 84, 0, 0, -90, 0, 0, 0, 0, 0, 0, -476, 0, 0, 0, 0, 0, 0, 0, -516, 0, 0, 0, 0, 0, 0, 308, 0, 0, -338, 0, -396, 0, 0, 0, 0, 0, 0, 0, 0, 0, 244, 0, 0, 476, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -294, 0, 0, 284, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 724, 0, 0, -212, 0, 378, 0, 0, 0, 0, 0, 0, 0, 0, 0, -412, 0, 0, -436, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -956, 0, 0, -708, 0, 0, 0, 0, 924, 0, 0, 0, 0, 0, 0, -342, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 964, 0, 0, -452, 0, 612, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 186, 0, 0, 0, 0, 294, 0, 0, 0, 0, 0, 0, 0, 0, 0, 220, 0, -252, 0, 0, 0, 0, 0, 0, 0, 0, 0, -588, 0, 0, 0, 0, -636, 0, 0, 486, 0, 0, 0, 0, 0, 0, 244, 0, 0, 508, 0, 0, 0, 0, -1236, 0, 0, 0, 0, 0, 0, 308, 0, 0, -916, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 246, 0, 0, 0, 0, 708, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 0, 0, 1484, 0, 0, 0, 0, -714, 0, 0, 0, 0, 0, 0, -952, 0, 0, 748, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 284, 0, -1356, 0, 0, -612, 0, 0, 0, 0, 0, 0, 1204, 0, 0, -1204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132, 0, 0, 1244, 0, 882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 268, 0, -924, 0, 0, -756, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, 588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 726, 0, -486, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, -1876, 0, 1524, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -932, 0, 0, 0, 0, 924, 0, 0, 0, 0, 0, 0, -892, 0, 0, -1254, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2156, 0, 0, 924, 0, 0, 0, 0, 2124, 0, 0, 0, 0, 0, 0, 1572, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, -716, 0, 0, 0, 0, 234, 0, 0, 0, 0, 0, 0, 0, 0, 0, 788, 0, 0, 88, 0, 2244, 0, 0, 0, 0, 0, 0, 0, 0, 0, 484, 0, 0, -1428, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1396, 0, -1836, 0, 0, 0, 0, 0, 0, 0, 0, 0, -476, 0, 0, 268, 0, -1548, 0, 0, 0, 0, 0, 0, 0, 0, 0, 616, 0, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 0, -1676, 0, 0, 2156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1014, 0, 0, 0, 0, 804, 0, 0, -1188, 0, 0, 0, 0, 0, 0, 2644, 0, 0, -1172, 0, 0, 0, 0, 204, 0, 0, 0, 0, 0, 0, 548, 0, 0, 1484, 0, 1764, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 732, 0, -726, 0, 0, -1458, 0, 0, 0, 0, 0, 0, 2244, 0, 0, 2924, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, -2876, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1372, 0, 0, -1156, 0, -2796, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -490, 0, 0, 0, 0, -2676, 0, 0, 0, 0, 0, 0, 852, 0, 0, -392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2164, 0, 0, 0, 0, 420, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1004, 0, 0, 0, 0, -1572, 0, 0, 0, 0, 0, 0, 1682, 0, 0, 2172, 0, -252, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1484, 0, 0, -436, 0, 0, 0, 0, 1782, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1496, 0, 0, 0, 0, 2364, 0, 0, 0, 0, 0, 0, -1132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2408, 0, 0, -2884, 0, 1428, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1308, 0, 0, -2596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2156, 0, 0, -692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 804, 0, 0, 1548, 0, 0, 0, 0, 0, 0, -1914, 0, 0, -2868, 0, 0, 0, 0, 1848, 0, 0, 0, 0, 0, 0, -1180, 0, 0, 0, 0, -396, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1916, 0, 0, 0, 0, 2772, 0, 0, 0, 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, 15, 4, -1, 2, -15], [1, 1, 3, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "15.3.d.a", "char_is_minimal": true, "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], [1, 0], [0, 1], [0, 3], [3, 0], [0, 0], [-3, 0], [0, 0], [0, 7], [-9, 0], [0, 0], [0, 0], [0, 9], [0, 0], [0, 0], [0, 0], [5, 0], [0, -14], [0, -9], [22, 0], [0, 0], [0, 0], [0, 0], [0, -34], [-21, 0], [0, 0], [0, 0], [0, -27], [0, 0], [0, 0], [0, 0], [2, 0], [0, 33], [0, 0], [14, 0], [0, 0], [-27, 0], [0, 0], [0, 22], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [34, 0], [0, -14], [0, 15], [-49, 0], [0, 0], [42, 0], [0, 0], [0, 86], [27, 0], [0, 0], [0, 0], [0, 66], [0, 0], [0, 0], [0, 0], [-118, 0], [0, 2], [0, 0], [-13, 0], [0, 0], [0, 0], [0, 0], [0, -42], [102, 0], [0, 0], [0, 0], [0, -63], [0, 0], [0, 0], [0, 0], [66, 0], [0, 0], [0, 0], [-98, 0], [0, 0], [81, 0], [0, 0], [0, -154], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -102], [0, 6], [14, 0], [0, 0], [-99, 0], [0, 0], [0, -49], [0, 0], [0, 0]]}