# Stored data for newform 324.2.h.e, downloaded from the LMFDB on 23 April 2024. {"label": "324.2.h.e", "space_label": "324.2.h", "level": 324, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014879579373892, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 1281354402008989800, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [28561, 0, -4732, 0, 615, 0, -28, 0, 1]], [7, [0, 1]]], "qexp_display": "q-\\zeta_{24}^{3}q^{2}+(2-2\\zeta_{24})q^{4}+(\\zeta_{24}^{5}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 36, "char_orbit_label": "h", "char_is_real": false, "Nk2": 1296, "analytic_conductor": 2.5871530254894846, "hecke_ring_index": 729, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 24, "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": "0.759", "prec": 17}, "analytic_rank_proved": true, "char_values": [324, 6, [163, 245], [3, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 8, "level_primes": [2, 3], "conrey_indexes": [107, 215], "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[3, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.016", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "740.288", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "132272.708", "prec": 34}], "related_objects": [], "self_twist_discs": [-4], "cm_discs": [-4], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.1.d6", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 16, 0, 0, 0, 0, 0, 28, 0, 0, -20, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 144, 0, 0, 0, 0, 0, 40, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, -136, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 56, 0, 0, 0, 0, 0, 88, 0, 0, -4, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -80, 0, 0, 0, 0, 0, -124, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 64, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, -88, 0, 0, 0, 0, 0, -44, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, 0, -424, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 52, 0, 0, -152, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 136, 0, 0, -80, 0, 0, 0, 0, 0, 296, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, -88, 0, 0, 0, 0, 0, 28, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, -80, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, -268, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -136, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 236, 0, 0, -272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -152, 0, 0, 88, 0, 0, 0, 0, 0, 100, 0, 0, -56, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, -288, 0, 0, 0, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, -200, 0, 0, 88, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 152, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, -416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, -56, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, -352, 0, 0, 0, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -116, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 200, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 232, 0, 0, 180, 0, 0, -224, 0, 0, 0, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -172, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -124, 0, 0, 64, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, -244, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, -496], "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, 4, 2, -1, 2, -4], [1, 1, 3, 2, -1, 2, 0], [1, 1, 9, 3, 1, 3, 0], [1, 1, 9, 4, -1, 6, 0], [1, 1, 12, 2, 1, 2, 0], [1, 1, 36, 6, -1, 6, 0], [1, 1, 36, 8, 1, 6, 0]], "char_orbit_index": 8, "prim_orbit_index": 8, "minimal_twist": "324.2.b.a", "char_is_minimal": false, "conrey_index": 107, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, -2, 2], [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, 0, 0], [0, 9, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, -2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, -1, 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, 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], [-7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -10, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 2, 0, 0, 0, 0, 0], [0, 0, 0, 5, 0, -5, 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, 0, 0, 0, 0], [7, -7, 1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 12, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 2, 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, 0, 0, 0], [8, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, -1, 0, 0, 4, -4], [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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, -4, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [11, -11, -2, 0, 2, 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, 7, 0, -7, 0, 1], [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, 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, -8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 0, -7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [18, 0, 0, 0, -2, 0, 0, 0]]}