# Stored data for newform 324.5.g.d, downloaded from the LMFDB on 18 April 2024.
{"label": "324.5.g.d", "space_label": "324.5.g", "level": 324, "weight": 5, "hecke_orbit": 4, "hecke_orbit_code": 13511211282858308, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 696172496356326394, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [6561, 0, -81, 0, 1]], [7, [25, 5, 1]]], "qexp_display": "q+\\zeta_{12}q^{5}-5\\zeta_{12}^{2}q^{7}+(-13\\zeta_{12}+\\cdots)q^{11}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "g", "char_is_real": false, "Nk2": 8100, "analytic_conductor": 33.49186803916556, "hecke_ring_index": 81, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [324, 6, [163, 245], [6, 5]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [53, 269], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [[3, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.081", "prec": 17}, {"__RealLiteral__": 0, "data": "3.796", "prec": 17}, {"__RealLiteral__": 0, "data": "1.801", "prec": 17}, {"__RealLiteral__": 0, "data": "87.823", "prec": 20}, {"__RealLiteral__": 0, "data": "64.212", "prec": 20}, {"__RealLiteral__": 0, "data": "3094.638", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "4.2.3.c6", "trace_display": [0, 0, 0, -10], "traces": [0, 4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, -1088, 0, 0, 0, 0, 0, 1394, 0, 0, 0, 0, 0, -2992, 0, 0, 0, 0, 0, -5236, 0, 0, 0, 0, 0, 4752, 0, 0, 0, 0, 0, -4212, 0, 0, 0, 0, 0, -12808, 0, 0, 0, 0, 0, 10436, 0, 0, 0, 0, 0, -18076, 0, 0, 0, 0, 0, -15004, 0, 0, 0, 0, 0, 8100, 0, 0, 0, 0, 0, -680, 0, 0, 0, 0, 0, -21142, 0, 0, 0, 0, 0, 11660, 0, 0, 0, 0, 0, -20080, 0, 0, 0, 0, 0, 11016, 0, 0, 0, 0, 0, -1904, 0, 0, 0, 0, 0, 36908, 0, 0, 0, 0, 0, 640, 0, 0, 0, 0, 0, -19624, 0, 0, 0, 0, 0, -38232, 0, 0, 0, 0, 0, 51110, 0, 0, 0, 0, 0, -42328, 0, 0, 0, 0, 0, 135320, 0, 0, 0, 0, 0, 54810, 0, 0, 0, 0, 0, -5440, 0, 0, 0, 0, 0, -78016, 0, 0, 0, 0, 0, 105300, 0, 0, 0, 0, 0, -103054, 0, 0, 0, 0, 0, 182660, 0, 0, 0, 0, 0, 12312, 0, 0, 0, 0, 0, -26248, 0, 0, 0, 0, 0, -13940, 0, 0, 0, 0, 0, 157700, 0, 0, 0, 0, 0, -17740, 0, 0, 0, 0, 0, 95256, 0, 0, 0, 0, 0, -66844, 0, 0, 0, 0, 0, -4352, 0, 0, 0, 0, 0, -286416, 0, 0, 0, 0, 0, 7480, 0, 0, 0, 0, 0, -19278, 0, 0, 0, 0, 0, 433292, 0, 0, 0, 0, 0, -61432, 0, 0, 0, 0, 0, 127952, 0, 0, 0, 0, 0, -475916, 0, 0, 0, 0, 0, -104652, 0, 0, 0, 0, 0, -26180, 0, 0, 0, 0, 0, 25640, 0, 0, 0, 0, 0, -321922, 0, 0, 0, 0, 0, 248508, 0, 0, 0, 0, 0, -73984, 0, 0, 0, 0, 0, 66572, 0, 0, 0, 0, 0, 255380, 0, 0, 0, 0, 0, -95540, 0, 0, 0, 0, 0, -407584, 0, 0, 0, 0, 0, -118260, 0, 0, 0, 0, 0, -504900, 0, 0, 0, 0, 0, -302158, 0, 0, 0, 0, 0, 12956, 0, 0, 0, 0, 0, 396032, 0, 0, 0, 0, 0, 10530, 0, 0, 0, 0, 0, 550800, 0, 0, 0, 0, 0, -653752, 0, 0, 0, 0, 0, -47396, 0, 0, 0, 0, 0, -215050, 0, 0, 0, 0, 0, 197316, 0, 0, 0, 0, 0, -268840, 0, 0, 0, 0, 0, -64040, 0, 0, 0, 0, 0, 448748, 0, 0, 0, 0, 0, 409286, 0, 0, 0, 0, 0, 159732, 0, 0, 0, 0, 0, -320112, 0, 0, 0, 0, 0, -13354, 0, 0, 0, 0, 0, -477598, 0, 0, 0, 0, 0, -104360, 0, 0, 0, 0, 0, 69632, 0, 0, 0, 0, 0, -50864, 0, 0, 0, 0, 0, 1325048, 0, 0, 0, 0, 0, 955800, 0, 0, 0, 0, 0, -90100, 0, 0, 0, 0, 0, -472068, 0, 0, 0, 0, 0, 45190, 0, 0, 0, 0, 0, -619164, 0, 0, 0, 0, 0, -858568, 0, 0, 0, 0, 0, 189406, 0, 0, 0, 0, 0, 19602, 0, 0, 0, 0, 0, 2180624, 0, 0, 0, 0, 0, 982844, 0, 0, 0, 0, 0, -75020, 0, 0, 0, 0, 0, -356048, 0, 0, 0, 0, 0, 384912, 0, 0, 0, 0, 0, -1179436, 0, 0, 0, 0, 0, 736376, 0, 0, 0, 0, 0, -250614, 0, 0, 0, 0, 0, -89216, 0, 0, 0, 0, 0, -81000, 0, 0, 0, 0, 0, 1032230, 0, 0, 0, 0, 0, 973148, 0, 0, 0, 0, 0, -758200, 0, 0, 0, 0, 0, -22780, 0, 0, 0, 0, 0, -490622, 0, 0, 0, 0, 0, -26860, 0, 0, 0, 0, 0, -161568, 0, 0, 0, 0, 0, -1094896, 0, 0, 0, 0, 0, 2720952, 0, 0, 0, 0, 0, 76950, 0, 0, 0, 0, 0, 1372640, 0, 0, 0, 0, 0, -2599776, 0, 0, 0, 0, 0, -429454, 0, 0, 0, 0, 0, -105710, 0, 0, 0, 0, 0, -407592, 0, 0, 0, 0, 0, -1368952, 0, 0, 0, 0, 0, 615600, 0, 0, 0, 0, 0, 191488, 0, 0, 0, 0, 0, 639296, 0, 0, 0, 0, 0, -71604, 0, 0, 0, 0, 0, -116600, 0, 0, 0, 0, 0, -1727746, 0, 0, 0, 0, 0, -415216, 0, 0, 0, 0, 0, -3214360, 0, 0, 0, 0, 0, -296622, 0, 0, 0, 0, 0, 2131970, 0, 0, 0, 0, 0, 3001640, 0, 0, 0, 0, 0, 50200, 0, 0, 0, 0, 0, 1466762, 0, 0, 0, 0, 0, -1516672, 0, 0, 0, 0, 0, -1537380, 0, 0, 0, 0, 0, -1005448, 0, 0, 0, 0, 0, -870944, 0, 0, 0, 0, 0, -2381400, 0, 0, 0, 0, 0, 55080, 0, 0, 0, 0, 0, -1324288, 0, 0, 0, 0, 0, 335104, 0, 0, 0, 0, 0, 1082390, 0, 0, 0, 0, 0, 158504, 0, 0, 0, 0, 0, -492804, 0, 0, 0, 0, 0, 841126, 0, 0, 0, 0, 0, 19040, 0, 0, 0, 0, 0, 66068, 0, 0, 0, 0, 0, -687208, 0, 0, 0, 0, 0, 1663092, 0, 0, 0, 0, 0, -354824, 0, 0, 0, 0, 0, 1392188, 0, 0, 0, 0, 0, -5792512, 0, 0, 0, 0, 0, -92270, 0, 0, 0, 0, 0, -374058, 0, 0, 0, 0, 0, 1927800, 0, 0, 0, 0, 0, -749656, 0, 0, 0, 0, 0, -1282554, 0, 0, 0, 0, 0, 2627108, 0, 0, 0, 0, 0, 813824, 0, 0, 0, 0, 0, -304128, 0, 0, 0, 0, 0, 780692, 0, 0, 0, 0, 0, 837216, 0, 0, 0, 0, 0, -307292, 0, 0, 0, 0, 0, -253368, 0, 0, 0, 0, 0, 875424, 0, 0, 0, 0, 0, 1567238, 0, 0, 0, 0, 0, 196240, 0, 0, 0, 0, 0, 2076516, 0, 0, 0, 0, 0, -1087830, 0, 0, 0, 0, 0, 3524972, 0, 0, 0, 0, 0, 1380332, 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, 9, 3, 1, 3, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 7, "prim_orbit_index": 4, "minimal_twist": "108.5.c.c", "char_is_minimal": false, "conrey_index": 53, "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, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, -5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -13, 0, 13], [0, 0, 0, 0], [34, 0, -34, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -50], [0, 0, 0, 0], [-64, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 68, 0, 0], [0, 0, 0, 0], [0, 0, -544, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -118, 0, 118], [0, 0, 0, 0], [697, 0, -697, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -5], [0, 0, 0, 0], [-748, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 76, 0, 0], [0, 0, 0, 0], [0, 0, -2618, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 294, 0, -294], [0, 0, 0, 0], [2376, 0, -2376, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 119], [0, 0, 0, 0], [-1053, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -646, 0, 0], [0, 0, 0, 0], [0, 0, -6404, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 34, 0, -34], [0, 0, 0, 0], [5218, 0, -5218, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 730], [0, 0, 0, 0], [-4519, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 65, 0, 0], [0, 0, 0, 0], [0, 0, -7502, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 609, 0, -609], [0, 0, 0, 0], [4050, 0, -4050, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -986], [0, 0, 0, 0], [-170, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -64, 0, 0], [0, 0, 0, 0], [0, 0, -10571, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}