# Stored data for newform 1470.2.m.a, downloaded from the LMFDB on 24 April 2024.
{"label": "1470.2.m.a", "space_label": "1470.2.m", "level": 1470, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 824667276734, "dim": 8, "is_polredabs": true, "nf_label": "8.0.16777216.1", "trace_hash": 79578698620748253, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [62, -8, -24, 0, 1]], [13, [99856, -45504, 10368, 1504, 152, -80, 32, 8, 1]]], "qexp_display": "q+\\zeta_{16}^{3}q^{2}-\\zeta_{16}^{3}q^{3}-\\zeta_{16}^{2}q^{4}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 35, "char_orbit_label": "m", "char_is_real": false, "Nk2": 5880, "analytic_conductor": 11.738009097128216, "hecke_ring_index": 98, "level_radical": 210, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 16, "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": "0.285", "prec": 17}, "analytic_rank_proved": true, "char_values": [1470, 4, [491, 1177, 1081], [4, 1, 2]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [97, 1273], "field_disc": 16777216, "field_disc_factorization": [[2, 24]], "field_poly": [1, 0, 0, 0, 0, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 1], [7, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.102", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "189.465", "prec": 24}, {"__RealLiteral__": 0, "data": "28.573", "prec": 20}, {"__RealLiteral__": 0, "data": "7846.931", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, -8, 0], "traces": [0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, -8, 0, 16, 16, 0, -8, -24, 8, -24, 0, 0, 0, 0, -16, 0, 0, 8, 0, 0, -8, 8, -8, 0, 0, 0, 0, 32, 0, 16, 0, -16, 0, 0, 0, 0, 8, -32, 8, 0, 0, 8, -16, -16, 0, 0, -8, 0, 0, -8, 0, -16, -8, 0, 0, 32, 0, -16, 0, 0, 0, 0, -8, 0, 8, -8, 16, 0, 0, 24, -32, 16, 8, -64, 0, 0, -24, 8, -32, -16, 0, -32, 0, 0, -32, 0, 8, 48, 0, 0, -48, 16, 0, 0, -8, 0, 0, -16, 0, 72, 0, 8, -8, 0, -8, 8, -16, -16, -16, 88, 0, 16, 0, 32, 0, 0, -8, 0, 0, 0, 0, 24, 24, -48, 0, 32, -8, -80, 0, 0, 0, 0, -8, 0, 32, -16, 8, -8, 0, 32, 0, -48, 16, 48, 0, 0, 0, 0, -16, 8, 0, 32, 0, 0, 0, 0, 32, -56, 0, 0, 0, 8, 0, 0, 8, 0, 0, 16, 0, 8, 16, 8, -16, 0, -8, 96, 0, 8, -80, 0, 0, 32, 8, 80, 0, 0, -8, 0, 0, 32, 0, -24, 8, 16, 0, -64, -32, 8, 0, -96, 0, 0, -32, 0, 0, 0, 8, -32, 0, -32, 0, -48, -8, 144, 0, 0, -16, 32, 0, 48, 0, -16, 0, 0, 0, 0, -8, 0, 0, 0, 16, -16, -8, 0, 0, 0, 0, 0, 0, 0, 8, -24, -32, 0, -24, 0, 40, 40, 0, 96, 0, 0, 16, -48, -8, 0, 8, 0, 0, 0, 0, 40, 56, -16, 0, 16, 16, -24, 0, 8, 0, 0, 0, 0, 48, 80, 16, -24, 0, 16, -16, -8, 0, 48, 0, 0, -8, 8, -16, 0, 0, -16, 0, 0, 24, 0, -8, 0, 80, 0, -16, 32, 32, 0, -16, 0, 0, -16, 0, 56, 64, 32, 16, 0, 0, 64, 0, -8, -96, -16, 0, 8, 16, 0, -8, 0, 8, 0, 0, 0, 0, -48, 16, 0, 0, 0, 8, -56, 0, -32, 0, 0, 40, 0, 0, -104, 0, 8, 0, -16, 0, -80, 24, -16, 32, 0, 8, 40, -64, 0, 0, -64, 0, 0, 32, 0, 24, -64, -8, 0, 16, 32, -32, 0, 24, 0, 0, -40, 0, 32, 0, 16, -24, 0, 24, -64, -16, 80, 16, 8, 0, -104, -8, 160, -48, 0, -48, 0, 0, 0, 0, -56, -16, 64, 0, -128, 48, -16, 0, -8, 0, 0, -16, 0, 32, 80, 0, -96, 0, -48, 32, -48, -16, -64, -24, 0, 80, -64, 16, 64, 0, 0, 0, 0, 0, 0, -16, 8, 80, 0, 16, -88, 32, 0, -24, 0, 0, 96, 0, -24, -128, 0, 8, 0, 32, -80, 8, -40, 16, -48, 0, -32, 56, 32, 16, 0, -80, 0, 0, 96, 0, 48, -16, -64, 0, 112, -16, 72, 0, 0, 0, 0, 0, 0, -16, 96, 80, 96, 0, -32, 48, -16, -16, 0, 8, 0, 0, -8, -80, 48, 0, 120, 0, 0, 0, 0, -16, 56, 16, 0, 48, -88, -8, 0, 48, 0, 0, -144, 0, 16, 0, -40, -16, 0, 0, 16, 24, 0, 0, -64, 0, 16, -24, 0, 56, 0, -24, 0, 0, -32, 0, 32, -8, 80, 0, 64, 16, 16, 0, 48, 0, 0, 8, 0, -32, -96, 80, -24, 0, -24, 8, 32, -8, -16, 0, 0, 32, -48, -16, -24, 0, -48, 0, 0, -8, 0, -8, 88, 0, 0, 96, 24, 0, 0, -24, 0, 0, 16, 0, -8, -16, -144, 8, 0, 48, -144, 8, -8, -64, 48, 0, 88, 48, -32, 16, 0, 16, 0, 0, -56, 0, 16, -48, -112, 0, -112, 16, -48, 0, 16, 0, 0, 72, 0, 0, -48, 16, 56, 0, -32, 16, -64, 0, 0, 0, 0, 0, 16, -32, -32, 0, 16, 0, 0, 24, 0, -80, -80, 48, 0, -16, 0, 32, 0, 0, 0, 0, 40, 0, 0, -72, 24, 16, 0, 0, -80, -56, -48, -16, 24, 0, -32, -32, 256, 24, 0, 56, 0, 0, 48, 0, -32, 80, 128, 0, -160, -8, 0, 0, -32, 0, 0, -8, 0, -8, -16, 0, -48, 0, -80, 48, -56, 56, 192, -16, 0, -32, 80, 48, 0, 0, -160, 0, 0, 32, 0, 16, -128, -112, 0, 0, -152, 16, 0, 24, 0, 0, -48, 0, -192, -16, 0, 8, 0, 16, -144, 16, -80, -112, 16, 0, 8, -64, -48, -24, 0, 16, 0, 0, -8, 0, 32, 0, 0, 0, 80, 8, 56, 0, -64, 0, 0, 0, 0, 0, 48, 0, 16, 0, 144, -16, 32, -32, -48, -48, 0, 8, -160, 48, -48, 0, 24, 0, 0, 0, 0, -48, 48, 0, 0, 160, 16, -8, 0, 0, 0, 0, -24, 0, 0, 0, 96, 0, 0, 16, 0, 24, 128, 32, -56, 0, -80, 24, -32, -96, 0, -8, 0, 0, -96, 0, 8, 32, 0, 0, -40, 80, -16, 0, 144, 0, 0, 32, 0, 0, -48, -8, 160, 0, 32, 48, -40, -80, 80, 32, 0, 72, 96, -8, -56, 0, 8, 0, 0, 0, 0, -32, -32, 48, 0, 16, 136, 56, 0, 0, 0, 0, 48, 0, 8, 0, 48, 8, 0, 0, 0, 32, 0, -96, -96, 0, 0, -16, 176, 24, 0, 0, 0, 0, -96, 0, -48, -48, 16, 0, 80, -8, -112, 0, -48, 0, 0, -8, 0, 0, 64, -48, -64, 0, -56, 0, -48, 16, 80, -16, 0, 32, -16, -64, -24, 0, 144, 0, 0, -16, 0, 48, -48, 16, 0, -128, -96, -16, 0, 56, 0, 0, -8, 0, -96, 32, -72, 16, 0, 0, -8, 112, -16, -64, -24, 0, -48, 8, -16, 80, 0, 0, 0, 0, 0, 0, 64, 0, -144, 0, 32, -120, 112, 0, 32, 0, 0, 16, 0, -24, -144, 8, 80, 0, -80, -48, -128, -16, 16, 0, 0, -32, -64, 16, 0, 0, -16, 0, 0, 24, 0, 0, -56, 72, 0, -16, -16, 40, 0, 0, 0, 0, 56, 0, -64, 16, -144, -24, 0, -64, 48, 32, 8, -64, -24, 0, -16, -56, -32, 8, 0, -64, 0, 0, -16, 0, -80, 40, -80, 0, 96, 40, 8, 0, 64, 0, 0, 0, 0, -32, 128, 8, 112, 0, 8, 0, 176, 0, -32, -96, 0, 16, -24, -48, 32, 0, -56, 0, 0, 16, 0, 0, 32, -96, 0, -48, 96, 8, 0, 96, 0, 0, 40, 0, -32, 0, -24, -16, 0, 0, 112, -32, -72, 0, 0, 0, -16, -40, 32, -24, 0, -56, 0, 0, -32, 0, 120, 96, 16, 0, -16, -8, 104, 0, -16, 0, 0, -16, 0, 0, 112, 24, 32, 0, 144, -32, 64, -48, 80, 24, 0, -112, -16, -32, -144, 0, -40, 0, 0, 0, 0, 0, -16, 112, 0, -40, 208, -8, 0, -16, 0, 0, -48, 0, -96, 240, 0, 16, 0, 0, 256, 24, 0, -80, -16, 0, 128, 0, 16, -32, 0, 32, 0, 0, 48, 0, 0, -8, -64, 0, -48, 0, 72, 0, -64, 0, 0, 24, 0, 0, -288, 16, 48, 0, 128, 0, 128, 8, -160, -8, 0, 8, 104, -112, 0, 0, 104, 0, 0, 0, 0, 128, 160, 0, 0, -64, 0, -16, 0, -16, 0, 0, -24, 0, -16, -32, 72, 8, 0, -8, -112, -24, 144, 0, 96, 0, 72, 8, -128, 0, 0, 0, 0, 0, -32, 0, -32, 72, 16, 0, -128, -88, -80, 0, 0, 0, 0, -32, 0, 32, 128, -32, -32, 0, 0, 96, 136, 8, -48, -8, 0, -32, 32, -48, 72, 0, 80, 0, 0, -32, 0, -16, -72, 32, 0, 8, 8, 96, 0, 8, 0, 0, 0, 0, 0, -80, 0, 32, 0, -120, -48, -16, -48, -16, -120, 0, -56, -8, -32, 0, 0, 32, 0, 0, -32, 0, 112, 0, 0, 0, 48, -8, -104, 0, 0, 0, 0, -32, 0, -48, 96, -16, -32, 0, 48, -80, 16, -8, 80, -24, 0, 16, 0, -112, 192, 0, 48, 0, 0, -24, 0, 48, -56, -48, 0, -128, 152, 8, 0, 0, 0, 0, -32, 0, 0, 32, 8, -128, 0, 0, 352, -88, 48, 80, 40, 0, -48, 48, 0, 56, 0, -16, 0, 0, 16, 0, -48, -32, 64, 0, 64, -80, 0, 0, -16, 0, 0, -8, 0, 16, -32, 56, -48, 0, -24, -16, -48, 16, 128, 64, 0, 16, 160, 64, -56, 0, 128, 0, 0, 64, 0, 40, -104, -32, 0, -48, -16, 80, 0, 0, 0, 0, -112, 0, 80, 64, -64, 0, 0, -16, 144, -8, 104, 80, -80, 0, -72, 0, 0, -48, 0, 104, 0, 0, -24, 0, 0, -80, -256, 0, 32, 24, 120, 0, 48, 0, 0, -48, 0, 16, -96, -16, 0, 0, 24, -32, -16, -8, 0, 0, 0, 40, 160, 48, -48, 0, 16, 0, 0, 0, 0, 8, 32, 32, 0, -16, -48, -64, 0, -8, 0, 0, 128, 0, -24, 128, -160, 0, 0, 16, -72, 96, -160, 16, 0, 0, -40, -24, 16, 0, 0, 64, 0, 0, 48, 0, -176, -144, -16, 0, 96, 24, 48, 0, 64, 0, 0, -32, 0, -8, 64, 32, -72, 0, 0, -192, 56, 48, 64, -8, 0, -192, 64, 48, 0, 0, 80, 0, 0, -80, 0, -40, -40, 0, 0, -48, 48, -40, 0, 16, 0, 0, 96, 0, 32, 64, 0, 16, 0, 32, 80, 24, -8, 224, -192, 0, 200, -56, 0, 32, 0, 0, 0, 0, 96, 0, 192, -16, 160, 0, 48, 80, 24, 0, 48, 0, 0, -144, 0, -16, 128, -40, 0, 0, -72, 96, 56, 104, 48, -64, 0, -8, -96, -128, -96, 0, -8, 0, 0, 16, 0, 16, -32, 0, 0, -48, 16, -48, 0, 0, 0, 0, 32, 0, -64, 0, -48, 128, 0, 0, 320, 40, -64, 0, 24, 0, 288, 56, -208, 96, 0, 16, 0, 0, 112, 0, -96, 32, 96, 0, -88, -136, 8, 0, 8, 0, 0, -48, 0, -48, -128, 16, -152, 0, 0, 48, -40, -24, 96, 56, 0, -48, -32, 32, 96, 0, 48, 0, 0, -24, 0, -16, 112, -80, 0, 32, -144, -120, 0, -64, 0, 0, -112, 0, 0, -144, -80, 0, 0, -160, -112, 96, 208, 40, -48, 0, 8, 0, -368, 16, 0, -48, 0, 0, 0, 0, 32, -48, -240, 0, -96, -16, 112, 0, 0, 0, 0, -24, 0, 8, 80, -32, 272, 0, -56, -160, 0, -80, -192, 32, 0, -64, -32, 256, -96, 0, 16, 0, 0, -128, 0, 8, 0, 16, 0, -32, 96, 0, 0, -120, 0, 0, 104, 0, 96, -32, -24, 104, 0, 0, -272, 144, -16, 128, 104, 0, -80, 16, 0, 0, 0, -8, 0, 0, 8, 0, -48, -8, -16, 0, 112, 56, -112, 0, 112, 0, 0, 88, 0, 0, -224, -32, -128, 0, 240, 0, 232, 88, 64, -72, 0, 16, 16, 32, 16, 0, -48, 0, 0, -64, 0, 96, -48, 32, 0, 0, -8, 48, 0, 8, 0, 0, 24, 0, -120, 0, -8, 0, 0, 64, 0, -8, 88, -80, 0, 0, -80, 0, 16, -64, 0, 88, 0, 0, 192, 0, -72, 8, 16, 0, 96, -40, 88, 0, -256, 0, 0, 160, 0, -64, 160, 32, -96, 0, -32, 64, -48, 32, 0, 24, 0, 56, -16, -96, -64, 0, -8, 0, 0, 8, 0, -168, 32, -160, 0, 48, -144, -80, 0, -16, 0, 0, -88, 0, 32, -8, 144, 16, 0, -32, -32, -64, -200, -8, 384, 0, -96, -48, -160, -8, 0, 16, 0, 0, -96, 0, 128, 0, 80, 0, 208, -32, -288, 0, 120, 0, 0, 16, 0, 96, 16, -72, -40, 0, -64, -16, 8, 96, -16, 0, 0, 56, -32, 16, -48, 0, -80, 0, 0, -24, 0, 0, 0, -96, 0, -64, -32, 8, 0, -88], "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, 35, 6, 1, 4, 0]], "char_orbit_index": 13, "prim_orbit_index": 6, "minimal_twist": "1470.2.m.a", "char_is_minimal": true, "conrey_index": 97, "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, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [-1, 0, 2, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, -2, 0, -1, 0, 0, 0, 0], [0, 1, 0, -1, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, -1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [2, 1, 0, -1, 0, 0, 0, 0], [2, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, -1, 0, 0, 0], [-3, 0, -3, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -4, 0, 0, 0, 0, 0], [0, -1, 0, -1, 1, 1, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, 1, 1, -1, 0], [-2, 0, -1, 0, 0, 0, 0, 0], [0, 1, -2, 1, -1, -1, 1, 0], [0, 0, 0, -1, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, 0, 0], [0, 1, 0, -1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 2, -1, 0, -1, 1], [-1, 0, 1, 2, 0, 0, 0, 0], [0, 1, 0, 1, -1, -1, 0, 0], [0, -1, 0, 2, 0, 0, 0, 0], [0, -2, -2, -2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 0, 0, -1, 1, 1], [0, -1, 0, -1, 0, 0, 1, 0], [2, 0, 1, 0, 0, 0, 0, 0], [0, 3, 0, -3, 0, 0, 0, 0], [-2, 4, -2, 0, 0, -1, -1, -1], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, -3, 0, 0, 0, 0], [0, -1, 0, 1, 0, 0, 0, -1], [1, 0, 1, 0, 0, 0, -1, -1], [-4, 6, -4, 0, 0, 2, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 3, 0, 0, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, -2, 0, 0, 0, 0], [-2, 0, -2, 0, 0, 1, -1, -1], [-2, 1, 0, -1, -1, 1, 0, 0], [0, 1, 0, -2, 0, 0, 0, 0], [0, 2, 0, 2, 0, 0, -2, 0], [-1, 2, -1, 0, 0, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [-1, 0, -3, 0, 0, 0, 3, 1], [0, 1, 0, 1, 0, 0, -1, 0], [-2, 0, 2, 0, 1, 0, -2, 2], [-1, 0, 1, 0, 1, 0, 0, 0], [0, -3, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 1, 0, -1, 2, -2, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [-2, 0, 2, 2, -2, 0, 1, -1], [0, 1, -2, 1, 1, 1, 1, 0], [0, -4, 0, 3, 0, 0, 0, 0], [0, -1, -2, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 0, 1, 1], [0, -2, -2, -2, 0, 0, -2, 0], [1, 0, -2, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 2, 0, 0], [0, 0, 0, -6, 0, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, 0, -2, 1, 0, 0], [-4, -4, 0, 4, 1, -1, 0, 1], [2, 0, 2, 0, 0, -1, 1, 1], [1, 0, 1, 0, 0, -1, 0, 0], [-8, 0, 0, 0, 1, -1, 0, 2], [0, -1, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 3, 0, 0, 0, 0, 0], [1, -2, 1, 0, 0, 1, -1, -1], [-4, 2, 0, -2, -1, 1, 0, 1], [-2, 1, 4, 3, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [-4, 10, -4, 0, 0, -2, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0, 1, 0], [-4, 0, 3, 0, 0, 0, 0, 0]]}