# Stored data for newform 783.2.k.f, downloaded from the LMFDB on 26 September 2025.
{"Nk2": 3132, "analytic_conductor": 6.252286478266254, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 29, "char_degree": 6, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 11, "char_orbit_label": "k", "char_order": 7, "char_parity": 1, "char_values": [783, 7, [407, 379], [7, 2]], "cm_discs": [], "conrey_index": 82, "dim": 60, "has_non_self_twist": 1, "hecke_cutters": [[2, [41209, 0, -32685842, 0, 16749257077, 0, 137756473190, 0, 486708349540, 0, 986828625279, 0, 1613244471175, 0, 1913899489513, 0, 1997842043463, 0, 1861663206684, 0, 1629630101361, 0, 1323467625965, 0, 942831515945, 0, 515458664355, 0, 252219872019, 0, 103451840127, 0, 41044537806, 0, 15923522014, 0, 5253485109, 0, 1405917769, 0, 327640570, 0, 70121099, 0, 14292353, 0, 2768405, 0, 475150, 0, 69070, 0, 9533, 0, 1289, 0, 154, 0, 15, 0, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22518685365175055, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 29, 4, 1, 7, 0], [1, 1, 87, 10, -1, 14, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "783.2.k.f", "level": 783, "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": [3, 29], "level_radical": 87, "minimal_twist": "783.2.k.f", "prim_orbit_index": 4, "related_objects": [], "relative_dim": 10, "rm_discs": [], "sato_tate_group": "1.2.3.c7", "self_twist_discs": [], "self_twist_type": 0, "space_label": "783.2.k", "trace_display": [0, 0, 0, 4], "traces": [60, 0, 0, -10, 0, 0, 4, 0, 0, 4, 0, 0, -24, 0, 0, -26, 0, 0, 4, 0, 0, -8, 0, 0, -16, 0, 0, 112, 0, 0, -4, 0, 0, 26, 0, 0, -18, 0, 0, -78, 0, 0, -8, 0, 0, 72, 0, 0, 14, 0, 0, -12, 0, 0, 24, 0, 0, -162, 0, 0, -10, 0, 0, 116, 0, 0, 60, 0, 0, -12, 0, 0, 66, 0, 0, -120, 0, 0, 46, 0, 0, -84, 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-786, 0, 0, -226, 0, 0, 396, 0, 0, 420, 0, 0, 236, 0, 0, -528, 0, 0, -266, 0, 0, -514, 0, 0, -30, 0, 0, -808, 0, 0, -248, 0, 0, -344, 0, 0, -356, 0, 0, 4, 0, 0, 1234, 0, 0, 288, 0, 0, 568, 0, 0, 504, 0, 0, -184, 0, 0, 268, 0, 0, 218, 0, 0, 78, 0, 0, 140, 0, 0, 448, 0, 0, -418, 0, 0, -18, 0, 0, -262, 0, 0, 484, 0, 0, 108, 0, 0, 300, 0, 0, -384, 0, 0, 288, 0, 0, 492, 0, 0, 478, 0, 0, 98, 0, 0, -14, 0, 0, -26, 0, 0, -74], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "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}