# Stored data for newform 170.2.r.a, downloaded from the LMFDB on 25 April 2024. {"label": "170.2.r.a", "space_label": "170.2.r", "level": 170, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1168264659114, "dim": 32, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [3844, 6944, 511984, 3415488, 9758552, 11929408, 9219984, 5453424, 355464, -6040352, -6066072, -1473728, 432188, -562448, -103008, 1423672, 1318261, 369864, 92088, 129128, 49692, -11864, -5752, -1784, -192, -472, 248, 168, -48, -8, 0, 0, 1]]], "char_order": 16, "char_parity": 1, "char_degree": 8, "char_conductor": 85, "char_orbit_label": "r", "char_is_real": false, "Nk2": 680, "analytic_conductor": 1.3574568343617666, "level_radical": 170, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [170, 16, [137, 71], [12, 15]], "inner_twist_count": 2, "level_primes": [2, 5, 17], "conrey_indexes": [23, 37, 97, 107, 113, 143, 163, 167], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c16", "trace_display": [0, 0, 0, 0], "traces": [32, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -48, 0, 0, 16, 0, 0, 0, 0, 0, 0, -24, 8, 24, -8, -8, -16, -16, 0, 64, 24, 32, 0, -32, 0, -32, 0, 16, -24, -16, -16, -24, 0, 0, 0, -16, -32, 32, -16, 16, 24, -8, 8, -24, -16, -64, 40, -24, -40, -24, 0, 32, 0, 16, 0, 0, 40, 8, -16, 32, 8, -56, 0, 24, 32, 72, 8, 48, 48, 16, 0, 8, -64, 40, 32, 16, 24, 48, 24, -8, 8, 56, 0, -48, 0, -64, -8, 0, 16, 48, -8, -8, -16, 40, -24, -32, 8, 24, 0, -32, 8, -144, -16, 56, 0, 64, 0, -144, -24, 0, -24, 96, 48, 0, 0, -48, -16, -64, 0, -16, 0, -8, 24, -16, 8, 128, -16, -32, 16, -120, 0, 24, -32, -64, 8, 48, 56, 40, 16, -48, 0, -24, -32, -16, -72, -104, 0, 80, -64, -8, 64, 192, 16, 64, -24, -48, -32, -96, -16, -176, 16, -56, 0, 232, 16, 96, 8, 72, -48, 64, -24, -56, 0, -40, -16, 160, 8, -16, 0, 8, -80, -32, -16, -112, -112, -32, 0, -128, 32, 144, 48, 8, -24, -152, 0, -64, -24, 80, 0, -168, 8, 32, -24, 0, 64, 48, -40, -32, -80, -64, 0, -16, 16, 16, 88, -88, 24, -120, -8, 48, 0, 160, 64, 128, -24, 0, -16, -80, 128, 24, -32, 0, 128, -16, 0, 0, 120, 144, 16, -40, -80, 72, -32, 16, 64, 64, 16, 80, 64, 96, 0, 104, 80, -24, 48, -96, 0, 0, 0, 144, 16, 200, 32, 88, 16, -40, 24, 80, 32, 0, 16, -112, -120, -24, 16, 64, 32, -128, -64, 0, 128, 120, -32, 16, -32, -112, -24, -168, 0, -32, 0, -80, -152, -144, -24, 136, 16, -8, 32, -72, -136, 8, -48, -176, -104, 128, 8, 176, 160, 24, 0, -24, 8, -112, -64, -144, -144, 16, -16, 96, 184, 8, 0, 112, -96, -352, -96, 32, -32, 160, 0, -168, 24, 80, 24, 136, -80, -40, 0, -144, -232, -296, 0, -72, 0, 136, -8, -96, 72, 0, 16, -88, 40, -24, 0, 144, -176, -32, 8, 0, 88, 0, 8, -280, 0, -96, -24, 8, -48, -112, 0, -72, -8, 0, 16, 56, 16, 160, 0, 64, -112, 64, 112, -56, 72, 0, -8, -48, 80, 72, -32, 80, 176, 64, -16, 0, 80, 144, -32, 72, 0, -248, 8, 80, 112, 240, 56, 112, -96, 24, 0, 72, 96, 80, 88, -160, -40, 80, 72, 16, 64, 256, -72, -80, 128, 48, 16, 0, 88, 48, 24, 104, 16, 144, 8, -48, 136, -176, 32, 120, -64, -240, 88, 80, -48, -64, 32, 24, -136, 0, -8, -192, -16, 96, -104, -88, -32, -232, 0, -48, -40, 64, 8, -16, 0, 152, 0, 96, 0, -64, -144, -88, -88, -240, -32, 112, 8, 64, -16, -120, 0, -88, 0, 80, 0, -112, -16, 8, -96, 120, 24, 304, 0, 136, 0, -304, -208, 80, 0, -40, 48, -8, 0, 136, 80, 280, 64, -48, -80, -112, -64, -280, 0, 96, -64, 80, 88, 0, 80, 152, -24, -184, 0, -128, -104, -64, -72, 80, -96, 64, 8, 144, -16, -112, 0, -8, -104, 24, -72, 16, 128, 40, -64, 0, 216, -96, -48, 96, -16, -240, 32, 64, 32, 16, 8, -16, -112, 96, 24, 272, -32, 56, 0, 80, -32, 0, 40, -8, 0, 112, 16, -24, -8, -80, 32, 216, 128, 144, -16, -144, -16, -8, 160, -40, 176, 128, 24, 16, 72, 128, -40, 240, -16, 48, 0, -288, 120, 0, 80, 144, -64, 56, -32, -176, -40, -80, 120, -16, 80, -136, 0, -16, -72, 240, -32, -104, 176, -56, -80, 0, 16, -104, -120, 232, 24, 48, -8, -144, 0, -24, 32, 88, 40, -80, 64, 80, -48, -224, 88, -40, -136, 0, -48, -264, -144, 144, 104, 88, 64, -344, 0, -16, -96, -192, -184, -56, -152, -168, 40, 48, 240, 200, 48, 112, -144, -192, -56, -240, -200, -320, 48, -64, 16, -24, 48, 96, -104, -16, -24, -208, -80, -248, 0, -104, -80, 176, -96, -128, -40, -48, -32, 144, -32, -176, -56, -328, -32, -16, -16, 224, 128, -32, 80, -48, 0, -112, 48, 160, -80, -80, 0, -8, 16, 0, 64, 144, 104, -128, -160, 0, -24, 176, 0, 16, 16, 0, 120, -168, -96, 104, 0, -64, 88, 128, -88, 0, 240, -96, 64, 176, -40, 136, -160, 16, 96, 328, 88, 80, 216, 144, 64, -32, -160, -80, 0, 64, -72, 64, 88, 128, 64, -96, -16, 64, 192, -208, -144, 0, 200, 16, 48, 200, -160, 240, 40, 56, 216, 152, 16, 152, 248, 112, 72, 0, -144, -160, -16, 176, 80, 0, 16, 232, 104, 120, 0, 112, -208, -192, 0, -320, -72, 176, 48, 96, 0, 16, 40, 152, 80, -160, -24, -496, -56, 8, 0, 208, -16, 296, 16, -8, 0, -24, -112, 224, -240, -96, 8, -160, 48, 88, 112, -184, -48, 16, 0, -304, -40, -64, -168, -40, 0, -64, -24, 288, 0, 112, -24, 104, -80, -272, -72, 88, 0, -176, -64, 312, 176, 96, -72, -104, -64, 8, 48, -248, -184, -176, 8, 224, 0, -128, 48, 8, -64, 216, 0, -80, -184, 192, 48, -16, 16, 48, -8, 0, 240, -288, -176, 376, -48, -48, 32, -128, 72, 112, 80, -160, 64, -120, 8, 112, 16, 176, 56, 144, 16, 0, -8, -160, -320, 264, 120, -208, 136, -120, -16, 112, 192, 0, -48, -40, -48, 24, 64, -128, 72, 32, 80, -96, 8, 24, -64, 528, 80, 0, -32, 64, 48, 0, -48, -304, -160, -48, -32, -152, -128, 32, 24, -288, -48, 184, 16, -48, -64, 512, 16, 256, 64, -192, 152, 0, 128, 112, -24, 64, 176, -64, 48, -96, 0, -32, 96, 176, -136, -176, 16, 168, 32, 16, 24, -152, 48, -104, -96, -8, -112, -32, -104], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 85, 18, 1, 16, 0]], "char_orbit_index": 18, "prim_orbit_index": 18, "minimal_twist": "170.2.o.a", "char_is_minimal": true, "conrey_index": 23, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}