# Stored data for newform 324.3.c.a, downloaded from the LMFDB on 16 April 2024.
{"label": "324.3.c.a", "space_label": "324.3.c", "level": 324, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 137489285444, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2304.1", "trace_hash": 1574510874205247564, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [81, 0, 36, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{5}+(-1+\\beta _{2})q^{7}-\\beta _{3}q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "c", "char_is_real": true, "Nk2": 2916, "analytic_conductor": 8.82836056527362, "hecke_ring_index": 81, "level_radical": 6, "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": 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, 2, [163, 245], [2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [161], "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [1, 0, 4, 0, 1], "hecke_ring_index_factorization": [[3, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.020", "prec": 17}, {"__RealLiteral__": 0, "data": "3.835", "prec": 17}, {"__RealLiteral__": 0, "data": "1.165", "prec": 17}, {"__RealLiteral__": 0, "data": "72.251", "prec": 20}, {"__RealLiteral__": 0, "data": "46.284", "prec": 20}, {"__RealLiteral__": 0, "data": "1888.954", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, -4], "traces": [0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 308, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 220, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, 188, 0, 0, 0, 0, 0, -468, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, -460, 0, 0, 0, 0, 0, 568, 0, 0, 0, 0, 0, 584, 0, 0, 0, 0, 0, 468, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -616, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 296, 0, 0, 0, 0, 0, -952, 0, 0, 0, 0, 0, 828, 0, 0, 0, 0, 0, 524, 0, 0, 0, 0, 0, 656, 0, 0, 0, 0, 0, -828, 0, 0, 0, 0, 0, -1012, 0, 0, 0, 0, 0, 616, 0, 0, 0, 0, 0, -844, 0, 0, 0, 0, 0, -220, 0, 0, 0, 0, 0, -648, 0, 0, 0, 0, 0, 1184, 0, 0, 0, 0, 0, 1108, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, -396, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, -304, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -1940, 0, 0, 0, 0, 0, 936, 0, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, 440, 0, 0, 0, 0, 0, -724, 0, 0, 0, 0, 0, -1692, 0, 0, 0, 0, 0, 620, 0, 0, 0, 0, 0, -916, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 608, 0, 0, 0, 0, 0, 396, 0, 0, 0, 0, 0, 1452, 0, 0, 0, 0, 0, -352, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 900, 0, 0, 0, 0, 0, -1144, 0, 0, 0, 0, 0, 1264, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -648, 0, 0, 0, 0, 0, -508, 0, 0, 0, 0, 0, -908, 0, 0, 0, 0, 0, -172, 0, 0, 0, 0, 0, -1312, 0, 0, 0, 0, 0, -1332, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 1328, 0, 0, 0, 0, 0, 304, 0, 0, 0, 0, 0, 1424, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, 1044, 0, 0, 0, 0, 0, 1508, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, -716, 0, 0, 0, 0, 0, -648, 0, 0, 0, 0, 0, 428, 0, 0, 0, 0, 0, -1412, 0, 0, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 1460, 0, 0, 0, 0, 0, -1216, 0, 0, 0, 0, 0, -1064, 0, 0, 0, 0, 0, 1996, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, -568, 0, 0, 0, 0, 0, -868, 0, 0, 0, 0, 0, 1656, 0, 0, 0, 0, 0, 3016, 0, 0, 0, 0, 0, -2556, 0, 0, 0, 0, 0, 1244, 0, 0, 0, 0, 0, -100, 0, 0, 0, 0, 0, -1696, 0, 0, 0, 0, 0, -1576, 0, 0, 0, 0, 0, -632, 0, 0, 0, 0, 0, -2464, 0, 0, 0, 0, 0, -348, 0, 0, 0, 0, 0, -688, 0, 0, 0, 0, 0, 504, 0, 0, 0, 0, 0, 1764, 0, 0, 0, 0, 0, 344, 0, 0, 0, 0, 0, 4500, 0, 0, 0, 0, 0, -2140, 0, 0, 0, 0, 0, -2216, 0, 0, 0, 0, 0, 900, 0, 0, 0, 0, 0, 596, 0, 0, 0, 0, 0, 4284, 0, 0, 0, 0, 0, 148, 0, 0, 0, 0, 0, 2468, 0, 0, 0, 0, 0, 612, 0, 0, 0, 0, 0, 448, 0, 0, 0, 0, 0, -1204, 0, 0, 0, 0, 0, -2920, 0, 0, 0, 0, 0, -1360, 0, 0, 0, 0, 0, -684, 0, 0, 0, 0, 0, -172, 0, 0, 0, 0, 0, -688, 0, 0, 0, 0, 0, -2780, 0, 0, 0, 0, 0, -2524, 0, 0, 0, 0, 0, 2168, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 668, 0, 0, 0, 0, 0, -1880, 0, 0, 0, 0, 0, 4536, 0, 0, 0, 0, 0, 2088, 0, 0, 0, 0, 0, -2656, 0, 0, 0, 0, 0, 5224, 0, 0, 0, 0, 0, 2984, 0, 0, 0, 0, 0, 656, 0, 0, 0, 0, 0, -2052, 0, 0, 0, 0, 0, -4052, 0, 0, 0, 0, 0, -2572, 0, 0, 0, 0, 0, -1720, 0, 0, 0, 0, 0, 3248, 0, 0, 0, 0, 0, 2484, 0, 0, 0, 0, 0, 628, 0, 0, 0, 0, 0, -3088, 0, 0, 0, 0, 0, 5192, 0, 0, 0, 0, 0, -512, 0, 0, 0, 0, 0, -504, 0, 0, 0, 0, 0, -1332, 0, 0, 0, 0, 0, 2720, 0, 0, 0, 0, 0, 5184, 0, 0, 0, 0, 0, -2548, 0, 0, 0, 0, 0, 716, 0, 0, 0, 0, 0, -492, 0, 0, 0, 0, 0, 164, 0, 0, 0, 0, 0, -4896, 0, 0, 0, 0, 0, -1688, 0, 0, 0, 0, 0, -3276, 0, 0, 0, 0, 0, 300, 0, 0, 0, 0, 0, -3796, 0, 0, 0, 0, 0, 496, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 1476, 0, 0, 0, 0, 0, 5900, 0, 0, 0, 0, 0, -3544, 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, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "324.3.c.a", "char_is_minimal": true, "conrey_index": 161, "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], [-1, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [-1, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -5, 0, 2], [0, 0, 0, 0], [-7, 0, 5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 6, 0, 1], [0, 0, 0, 0], [7, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -5, 0, -3], [0, 0, 0, 0], [8, 0, 6, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -6, 0, 1], [0, 0, 0, 0], [14, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 12, 0, -1], [0, 0, 0, 0], [-13, 0, 9, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 10, 0, -2], [0, 0, 0, 0], [-21, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 3], [0, 0, 0, 0], [9, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -14, 0, 2], [0, 0, 0, 0], [-16, 0, -9, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -11, 0, 2], [0, 0, 0, 0], [5, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, -7], [0, 0, 0, 0], [-64, 0, -9, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, -4], [0, 0, 0, 0], [77, 0, -7, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 10], [0, 0, 0, 0], [72, 0, -21, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 19, 0, -1], [0, 0, 0, 0], [55, 0, -3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -32, 0, 5], [0, 0, 0, 0], [-40, 0, -22, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}