# Stored data for newform 1008.2.cz.d, downloaded from the LMFDB on 16 April 2024. {"label": "1008.2.cz.d", "space_label": "1008.2.cz", "level": 1008, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13516090315375600, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2264316416331195, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [0, 1]], [11, [12, -6, 1]]], "qexp_display": "q+(2-\\zeta_{6})q^{3}+(2-3\\zeta_{6})q^{7}+(3-3\\zeta_{6})q^{9}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 252, "char_orbit_label": "cz", "char_is_real": false, "Nk2": 4032, "analytic_conductor": 8.048920523745062, "hecke_ring_index": 1, "level_radical": 42, "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": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.176", "prec": 17}, "analytic_rank_proved": true, "char_values": [1008, 6, [127, 757, 785, 577], [3, 6, 4, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [367, 607], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.912", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.449", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "96.238", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 3, 0, 1], "traces": [0, 2, 0, 3, 0, 0, 0, 1, 0, 3, 0, 6, 0, -3, 0, 0, 0, 3, 0, 5, 0, -3, 0, -6, 0, -5, 0, 0, 0, -3, 0, -2, 0, 6, 0, 0, 0, -7, 0, -3, 0, -3, 0, -3, 0, 0, 0, 18, 0, -13, 0, 6, 0, 9, 0, 0, 0, 15, 0, 30, 0, 0, 0, -12, 0, 0, 0, 0, 0, -12, 0, 0, 0, 3, 0, -15, 0, -6, 0, 0, 0, -9, 0, 9, 0, 0, 0, 0, 0, 3, 0, 3, 0, -3, 0, 0, 0, -3, 0, 0, 0, -24, 0, -8, 0, 0, 0, 3, 0, -11, 0, -21, 0, 9, 0, 0, 0, 0, 0, 6, 0, 1, 0, -3, 0, 0, 0, 0, 0, -6, 0, 12, 0, 25, 0, 0, 0, 18, 0, -5, 0, 27, 0, -6, 0, 0, 0, -24, 0, 6, 0, -30, 0, 9, 0, 0, 0, 0, 0, 0, 0, -12, 0, 27, 0, 0, 0, -21, 0, -10, 0, 30, 0, 0, 0, -25, 0, 45, 0, 21, 0, 0, 0, -3, 0, 0, 0, 12, 0, -27, 0, 0, 0, -34, 0, 0, 0, 12, 0, -1, 0, 27, 0, 12, 0, 0, 0, -18, 0, 30, 0, -21, 0, 18, 0, 0, 0, -1, 0, 6, 0, -6, 0, 5, 0, -30, 0, 12, 0, 24, 0, -24, 0, 21, 0, 0, 0, 3, 0, 39, 0, -36, 0, -27, 0, 0, 0, -15, 0, 0, 0, 0, 0, -24, 0, 0, 0, -48, 0, -35, 0, 9, 0, -54, 0, 0, 0, 3, 0, 39, 0, 1, 0, 12, 0, -30, 0, 14, 0, -3, 0, -15, 0, 62, 0, 0, 0, 3, 0, -14, 0, -6, 0, 45, 0, 0, 0, -18, 0, 12, 0, -6, 0, -24, 0, 0, 0, -16, 0, 0, 0, 6, 0, 0, 0, 0, 0, -42, 0, 0, 0, 3, 0, 0, 0, 15, 0, 0, 0, 9, 0, 0, 0, -42, 0, 0, 0, -11, 0, 27, 0, -6, 0, -20, 0, 0, 0, 0, 0, 45, 0, 9, 0, -36, 0, 0, 0, 3, 0, -21, 0, -6, 0, 0, 0, 0, 0, 8, 0, 0, 0, -36, 0, 10, 0, 0, 0, 0, 0, 0, 0, 18, 0, 24, 0, 0, 0, -9, 0, -18, 0, -6, 0, 0, 0, 0, 0, 27, 0, 30, 0, -30, 0, 3, 0, 0, 0, -42, 0, 0, 0, 54, 0, 15, 0, 0, 0, -15, 0, 15, 0, 5, 0, 27, 0, 0, 0, -9, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 50, 0, -33, 0, 0, 0, 0, 0, 0, 0, 36, 0, -6, 0, -30, 0, 0, 0, -2, 0, 9, 0, -39, 0, 63, 0, 0, 0, -15, 0, 81, 0, -21, 0, -12, 0, 25, 0, -27, 0, 0, 0, 21, 0, -6, 0, 0, 0, -27, 0, 27, 0, 15, 0, -9, 0, 0, 0, 54, 0, -6, 0, -63, 0, 48, 0, 0, 0, 0, 0, -60, 0, 6, 0, 45, 0, 0, 0, 54, 0, 33, 0, 39, 0, 13, 0, -30, 0, -3, 0, -11, 0, 45, 0, 3, 0, 0, 0, 42, 0, -48, 0, -43, 0, 24, 0, 0, 0, -15, 0, -9, 0, -30, 0, 9, 0, 0, 0, 33, 0, 6, 0, 18, 0, -42, 0, 0, 0, -45, 0, 6, 0, 0, 0, 3, 0, 0, 0, -45, 0, -51, 0, -36, 0, 0, 0, 0, 0, -27, 0, -5, 0, 18, 0, 15, 0, 0, 0, 0, 0, 0, 0, -63, 0, 81, 0, 0, 0, 32, 0, 27, 0, -27, 0, -35, 0, 0, 0, -27, 0, 28, 0, -18, 0, -3, 0, -25, 0, 60, 0, 0, 0, 0, 0, -21, 0, 0, 0, 24, 0, 54, 0, -6, 0, -13, 0, 0, 0, 15, 0, 90, 0, 3, 0, -30, 0, 0, 0, 9, 0, -39, 0, 0, 0, -9, 0, 0, 0, 18, 0, 0, 0, -6, 0, -7, 0, -45, 0, 0, 0, -6, 0, 36, 0, -75, 0, 0, 0, 48, 0, 0, 0, 10, 0, -54, 0, 0, 0, -6, 0, 63, 0, 36, 0, 35, 0, 0, 0, 24, 0, -74, 0, 9, 0, 6, 0, 0, 0, 39, 0, -27, 0, 32, 0, -36, 0, 30, 0, -35, 0, -54, 0, -3, 0, 36, 0, 0, 0, 54, 0, -27, 0, -30, 0, -21, 0, 0, 0, -27, 0, -3, 0, 30, 0, 0, 0, 0, 0, 4, 0, -36, 0, -84, 0, 44, 0, 0, 0, -45, 0, 9, 0, -96, 0, -57, 0, 5, 0, -42, 0, -15, 0, 36, 0, 27, 0, 0, 0, -26, 0, -54, 0, 45, 0, 3, 0, 0, 0, 57, 0, 27, 0, 0, 0, 12, 0, 0, 0, 78, 0, 9, 0, -104, 0, 3, 0, 0, 0, 0, 0, 27, 0, -66, 0, 0, 0, -60, 0, 0, 0, 27, 0, 42, 0, -15, 0, 0, 0, 0, 0, -27, 0, 20, 0, 0, 0, 0, 0, -4, 0, 93, 0, 0, 0, 93, 0, 0, 0, -12, 0, -4, 0, 12, 0, -45, 0, 0, 0, -42, 0, 6, 0, -27, 0, -9, 0, 0, 0, 46, 0, 45, 0, 0, 0, 0, 0, 0, 0, -12, 0, 54, 0, -54, 0, 45, 0, 0, 0, 18, 0, 3, 0, 27, 0, -3, 0, 0, 0, -66, 0, 0, 0, -99, 0, 0, 0, 0, 0, -48, 0, 39, 0, -24, 0, -18, 0, -35, 0, 24, 0, 0, 0, -10, 0, 9, 0, 0, 0, 0, 0, -51, 0, 0, 0, 12, 0, 0, 0, 0, 0, -6, 0, -63, 0, -36, 0, 0, 0, 18, 0, 90, 0, -60, 0, 0, 0, 0, 0, 27, 0, 15, 0, -15, 0, -25, 0, 30, 0, 102, 0, 6, 0, 33, 0, -12, 0, 0, 0, -27, 0, 6, 0, -63, 0, -9, 0, 0, 0, 96, 0, -63, 0, 24, 0, 45, 0, 0, 0, 90, 0, -100, 0, -33, 0, -72, 0, 0, 0, 54, 0, 102, 0, -63, 0, -6, 0, 15, 0, -3, 0, -3, 0, -18, 0, 26, 0, 0, 0, 3, 0, -10, 0, 39, 0, -24, 0, 0, 0, 90, 0, 21, 0, 9, 0, 27, 0, 0, 0, 30, 0, -36, 0, 9, 0, 112, 0, 0, 0, -12, 0, 0, 0, -9, 0, 42, 0, 0, 0, -21, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 0, -3, 0, -39, 0, 5, 0, 0, 0, -45, 0, -63, 0, 24, 0, 0, 0, 0, 0, 9, 0, 108, 0, -48, 0, -81, 0, 0, 0, -11, 0, 0, 0, 75, 0, -44, 0, 0, 0, 30, 0, 50, 0, -9, 0, 0, 0, 0, 0, -42, 0, -27, 0, -27, 0, 54, 0, 0, 0, 7, 0, 0, 0, 3, 0, 63, 0, 0, 0, -3, 0, 15, 0, -9, 0, 45, 0, 0, 0, -54, 0, -105, 0, -9, 0, -18, 0, -45, 0, 6, 0, -36, 0, 0, 0, 40, 0, 0, 0, -3, 0, 0, 0, 27, 0, 0, 0, 0, 0, 15, 0, 0, 0, -10, 0, 0, 0, 0, 0, -18, 0, 3, 0, 99, 0, -34, 0, 0, 0, -87, 0, -54, 0, -84, 0, 9, 0, 10, 0, 51, 0, 78, 0, -31, 0, 108, 0, 0, 0, -24, 0, -45, 0, 3, 0, 54, 0, 0, 0, 9, 0, -48, 0, -30, 0, 42, 0, 0, 0, 45, 0, -24, 0, 6, 0, 0, 0, 0, 0, 72, 0, 0, 0, 3, 0, -135, 0, -15, 0, 51, 0, 29, 0, -15, 0, -90, 0, 0, 0, 18, 0, -3, 0, -34, 0, 90, 0, 0, 0, -47, 0, -24, 0, -51, 0, -87, 0, 0, 0, 138, 0, 6, 0, -30, 0, 24, 0, 0, 0, 75, 0, -42, 0, 0, 0, -27, 0, -90, 0, 0, 0, -45, 0, 0, 0, 3, 0, 0, 0, 9, 0, 0, 0, -18, 0, -3, 0, 0, 0, 54, 0, -90, 0, -17, 0, 0, 0, 0, 0, -90, 0, 0, 0, -108, 0, -27, 0, 0, 0, 87, 0, -12, 0, -3, 0, 69, 0, 0, 0, 0, 0, 6, 0, -50, 0, -78, 0, 0, 0, 0, 0, 63, 0, -3, 0, 4, 0, 0, 0, 36, 0, 31, 0, -45, 0, -6, 0, 0, 0, 135, 0, -30, 0, 27, 0, -63, 0, 0, 0, 0, 0, -18, 0, 33, 0, -21, 0, 0, 0, 27, 0, 53, 0, -81, 0, 0, 0, 0, 0, 0, 0, 57, 0, 0, 0, 42, 0, 0, 0, 10, 0, 18, 0, 0, 0, 46, 0, 0, 0, -18, 0, 11, 0, -54, 0, 60, 0, 0, 0, 0, 0, -27, 0, -21, 0, 15, 0, -75, 0, 21, 0, -9, 0, 6, 0, -19, 0, 0, 0, 48, 0, -108, 0, 90, 0, -39, 0, 0, 0, -12, 0, 39, 0, -15, 0, -126, 0, 0, 0, 108, 0, 72, 0, 144, 0, 6, 0, 0, 0, 21, 0, 13, 0, 30, 0, 102, 0, -15, 0, -120, 0, -30, 0, 73, 0, 3, 0, 0, 0, 27, 0, 45, 0, 54, 0, -130, 0, 0, 0, -3, 0, -43, 0, 54, 0, 45, 0, 0, 0, 99, 0, 138, 0, -20, 0, 78, 0, 0, 0, 16, 0, 39, 0, -114, 0, 0, 0, -15, 0, 90, 0, 0, 0, -6, 0, 0, 0, 0, 0, -33, 0, 60, 0, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 51, 0, 48, 0, 0, 0, 0, 0, 45, 0, 63, 0, 60, 0, 0, 0, -66, 0, 39, 0, 5, 0, -129, 0, 0, 0, -28, 0, 72, 0, 105, 0, 36, 0, 0, 0, 0, 0, 0, 0, -30, 0, -9, 0, 0, 0, -18, 0, -3, 0, -18, 0, -45, 0, 0, 0, 111, 0, 15, 0, -60, 0, 90, 0, 0, 0, 81, 0, 0, 0, 0, 0, -39, 0, 135, 0, 9, 0, -6, 0, -38, 0, 18, 0, 0, 0, 36, 0, -63, 0, 15, 0, 0, 0, 0, 0, 0, 0, -110, 0, -54, 0, 0, 0, 0, 0, 9, 0, -156, 0, -45, 0, -69, 0, 0, 0, -48, 0, 9, 0, -3, 0, -129, 0, 30, 0, -42, 0, -30, 0, -90, 0, 78, 0, 0, 0, -51, 0, -63, 0, -24, 0, -81, 0, 0, 0, -27, 0, -54, 0, -24, 0, 36, 0, 0, 0, 0, 0, -126, 0, 0, 0, 6, 0, 0, 0, -15, 0, 9, 0, -12, 0, 18, 0, 90, 0, 93, 0, 15, 0, -54, 0, 37, 0, 0, 0, 78, 0, -34, 0, 3, 0, 54, 0, 0, 0, 63, 0, -96, 0, 53, 0, -126, 0, 0, 0, 15, 0, 162, 0, 114, 0, 14, 0, 0, 0, 6, 0, 6, 0, 0, 0, -66, 0, 0, 0, 45, 0, -30, 0, 0, 0, -27, 0, 0, 0, -126, 0, 0, 0, 54, 0, 0, 0, 0, 0, -39, 0, -40, 0, -81, 0, -33, 0, 0, 0, 84, 0, 0, 0, -27, 0, 0, 0, 0, 0, 4, 0, -12, 0, -9, 0, -83, 0, 0, 0, 21, 0, 64, 0, 90, 0, 78, 0, 0, 0, -21, 0, 0, 0, 0, 0, -54, 0, 0, 0, 5, 0, 0, 0, 30, 0, 66, 0, 0, 0, 27, 0, -54, 0, 33, 0, -6, 0, 0, 0, 108, 0, -120, 0, 0, 0, -18, 0, -60, 0, -27, 0, -39, 0, 63, 0, 1, 0, 0, 0, 0, 0, 70, 0, 0, 0, -81, 0, 0, 0, 90, 0, 0, 0, -70, 0, 12, 0, 0, 0, -80, 0, 0, 0, -126, 0, 30, 0, 0, 0, 60, 0, 84, 0, 9, 0, 81, 0, 15, 0, -78, 0, -15, 0, 31, 0, 15, 0, 0, 0, -35, 0, -9, 0, 48, 0, 84, 0, 0, 0, 69, 0, 33, 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, 252, 36, 1, 6, 0]], "char_orbit_index": 78, "prim_orbit_index": 36, "minimal_twist": "1008.2.bf.b", "char_is_minimal": true, "conrey_index": 367, "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], [2, -1], [0, 0], [0, 0], [0, 0], [2, -3], [0, 0], [3, -3], [0, 0], [4, -2], [0, 0], [-2, 1], [0, 0], [0, 0], [0, 0], [1, 1], [0, 0], [0, 5], [0, 0], [1, -5], [0, 0], [-2, -2], [0, 0], [0, -5], [0, 0], [3, -6], [0, 0], [-3, 3], [0, 0], [-1, 0], [0, 0], [6, -6], [0, 0], [0, 0], [0, 0], [0, -7], [0, 0], [-3, 3], [0, 0], [-2, 1], [0, 0], [-1, -1], [0, 0], [0, 0], [0, 0], [9, 0], [0, 0], [-5, -3], [0, 0], [3, 0], [0, 0], [9, -9], [0, 0], [0, 0], [0, 0], [5, 5], [0, 0], [15, 0], [0, 0], [1, -2], [0, 0], [-3, -6], [0, 0], [0, 0], [0, 0], [-9, 18], [0, 0], [-6, 0], [0, 0], [-6, 12], [0, 0], [1, 1], [0, 0], [-5, -5], [0, 0], [2, -10], [0, 0], [-1, 2], [0, 0], [0, -9], [0, 0], [9, -9], [0, 0], [0, 0], [0, 0], [-3, 6], [0, 0], [2, -1], [0, 0], [-1, 5], [0, 0], [-2, 1], [0, 0], [0, 0], [0, 0], [-1, -1], [0, 0], [6, -12], [0, 0]]}