# Stored data for newform 680.2.f.e, downloaded from the LMFDB on 16 September 2025.
{"Nk2": 2720, "analytic_conductor": 5.429827337447066, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 8, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 2, "char_parity": 1, "char_values": [680, 2, [511, 341, 137, 241], [2, 1, 2, 2]], "cm_discs": [], "conrey_index": 341, "dim": 30, "has_non_self_twist": 1, "hecke_cutters": [[3, [173056, 0, 6620160, 0, 66162432, 0, 234516224, 0, 423668032, 0, 459219008, 0, 326182336, 0, 159829696, 0, 55654464, 0, 13975408, 0, 2536540, 0, 329324, 0, 29781, 0, 1779, 0, 63, 0, 1]], [7, [4096, 16384, -55936, -160032, 211936, 125200, -151952, -26040, 42928, -280, -5408, 508, 300, -42, -6, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014742140420776, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "680.2.f.e", "level": 680, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 5, 17], "level_radical": 170, "minimal_twist": "680.2.f.e", "prim_orbit_index": 2, "related_objects": [], "relative_dim": 30, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "680.2.f", "trace_display": [0, 0, 0, 12], "traces": [30, 0, 0, -2, 0, -8, 12, 6, -36, 2, 0, 8, 0, -10, -14, -2, 30, 6, 0, 4, 0, -6, 12, -46, -30, 4, 0, 22, 0, 6, -26, -10, 12, 0, 0, 32, 0, 6, 2, 4, -20, 48, 0, 22, 0, 38, -22, 24, 30, 0, 0, 48, 0, -66, 32, -6, -26, -32, 0, -14, 0, -46, -4, -50, 6, -44, 0, -2, 0, -2, 58, -14, -18, 56, 0, -6, 0, 12, -60, 0, -42, -24, 0, 72, 0, 48, 6, 18, 6, -14, 0, 74, 0, -16, -30, 22, 38, -16, 0, 2, 0, -8, -32, -82, 0, -80, 0, 10, 0, 6, 12, -66, -2, 6, 0, -32, 0, 82, 12, 12, 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"embedded_related_objects": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}