# Stored data for newform 324.4.e.d, downloaded from the LMFDB on 20 April 2024.
{"label": "324.4.e.d", "space_label": "324.4.e", "level": 324, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13511073827127620, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1185301677693870233, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [0, 1]], [7, [289, 17, 1]]], "qexp_display": "q+(-17+17\\zeta_{6})q^{7}-89\\zeta_{6}q^{13}+107q^{19}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 5184, "analytic_conductor": 19.11661884185996, "hecke_ring_index": 1, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [324, 3, [163, 245], [3, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [109, 217], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "1.868", "prec": 17}, {"__RealLiteral__": 0, "data": "0.220", "prec": 17}, {"__RealLiteral__": 0, "data": "16.864", "prec": 20}, {"__RealLiteral__": 0, "data": "2.103", "prec": 17}, {"__RealLiteral__": 0, "data": "208.891", "prec": 24}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.1.d3", "trace_display": [0, 0, 0, -17], "traces": [0, 2, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, -89, 0, 0, 0, 0, 0, 214, 0, 0, 0, 0, 0, 125, 0, 0, 0, 0, 0, -308, 0, 0, 0, 0, 0, -866, 0, 0, 0, 0, 0, 520, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 901, 0, 0, 0, 0, 0, -1007, 0, 0, 0, 0, 0, -542, 0, 0, 0, 0, 0, -503, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3026, 0, 0, 0, 0, 0, -1853, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, -1292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1331, 0, 0, 0, 0, 0, 760, 0, 0, 0, 0, 0, -1819, 0, 0, 0, 0, 0, 3043, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3709, 0, 0, 0, 0, 0, 3850, 0, 0, 0, 0, 0, -758, 0, 0, 0, 0, 0, -5724, 0, 0, 0, 0, 0, 2125, 0, 0, 0, 0, 0, -9398, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5111, 0, 0, 0, 0, 0, 8746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2071, 0, 0, 0, 0, 0, 10472, 0, 0, 0, 0, 0, 3220, 0, 0, 0, 0, 0, -4466, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4769, 0, 0, 0, 0, 0, -9523, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7361, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16202, 0, 0, 0, 0, 0, 4030, 0, 0, 0, 0, 0, -5600, 0, 0, 0, 0, 0, -9826, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8840, 0, 0, 0, 0, 0, 21280, 0, 0, 0, 0, 0, 9109, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22250, 0, 0, 0, 0, 0, 10891, 0, 0, 0, 0, 0, -12293, 0, 0, 0, 0, 0, -13498, 0, 0, 0, 0, 0, -1367, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9180, 0, 0, 0, 0, 0, -9413, 0, 0, 0, 0, 0, 12601, 0, 0, 0, 0, 0, 29374, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2380, 0, 0, 0, 0, 0, -27412, 0, 0, 0, 0, 0, -8297, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6679, 0, 0, 0, 0, 0, 15317, 0, 0, 0, 0, 0, -5180, 0, 0, 0, 0, 0, -14924, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12710, 0, 0, 0, 0, 0, -11969, 0, 0, 0, 0, 0, 34238, 0, 0, 0, 0, 0, 13375, 0, 0, 0, 0, 0, 38537, 0, 0, 0, 0, 0, -12206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4607, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23762, 0, 0, 0, 0, 0, 12167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3778, 0, 0, 0, 0, 0, -21293, 0, 0, 0, 0, 0, -8551, 0, 0, 0, 0, 0, -92560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23941, 0, 0, 0, 0, 0, 54646, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32956, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29302, 0, 0, 0, 0, 0, -6137, 0, 0, 0, 0, 0, 25702, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, -15625, 0, 0, 0, 0, 0, 52918, 0, 0, 0, 0, 0, 4806, 0, 0, 0, 0, 0, -13160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33731, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9899, 0, 0, 0, 0, 0, -31501, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16072, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92662, 0, 0, 0, 0, 0, 8623, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -646, 0, 0, 0, 0, 0, 10780, 0, 0, 0, 0, 0, -15050, 0, 0, 0, 0, 0, 62752, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17569, 0, 0, 0, 0, 0, 48274, 0, 0, 0, 0, 0, 10982, 0, 0, 0, 0, 0, 34417, 0, 0, 0, 0, 0, -77000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14653, 0, 0, 0, 0, 0, -160378, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78736, 0, 0, 0, 0, 0, 55640, 0, 0, 0, 0, 0, -45611, 0, 0, 0, 0, 0, 60154, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24389, 0, 0, 0, 0, 0, -45254, 0, 0, 0, 0, 0, -8279, 0, 0, 0, 0, 0, 49807, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -89623, 0, 0, 0, 0, 0, 36793, 0, 0, 0, 0, 0, 104218, 0, 0, 0, 0, 0, -6460, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4607, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5512, 0, 0, 0, 0, 0, -54125, 0, 0, 0, 0, 0, 5778, 0, 0, 0, 0, 0, 30454, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24119, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -65073, 0, 0, 0, 0, 0, -53927, 0, 0, 0, 0, 0, -103462, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 119338, 0, 0, 0, 0, 0, -28910, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 9, 3, 1, 3, 0], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "108.4.a.c", "char_is_minimal": false, "conrey_index": 109, "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, 0], [0, 0], [0, 0], [0, 0], [-17, 17], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -89], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [107, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [125, -125], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -308], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-433, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [520, -520], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 54], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [901, -901], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -1007], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-271, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-503, 503], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [1513, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-1853, 1853], [0, 0], [0, 0], [0, 0]]}