# Stored data for newform 363.2.f.i, downloaded from the LMFDB on 25 April 2024. {"label": "363.2.f.i", "space_label": "363.2.f", "level": 363, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029140649902443, "dim": 32, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [28561, 0, 17576, 0, 8619, 0, 3952, 0, 1769, 0, 304, 0, 51, 0, 8, 0, 1]], [5, [28561, 0, -21970, 0, 14703, 0, -9620, 0, 6269, 0, -740, 0, 87, 0, -10, 0, 1]], [7, [4096, 0, -512, 0, 64, 0, -8, 0, 1]]], "char_order": 10, "char_parity": 1, "char_degree": 4, "char_conductor": 33, "char_orbit_label": "f", "char_is_real": false, "Nk2": 1452, "analytic_conductor": 2.898569593372478, "level_radical": 33, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [363, 10, [122, 244], [5, 7]], "inner_twist_count": 16, "level_primes": [3, 11], "conrey_indexes": [161, 215, 233, 239], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c10", "trace_display": [0, 4, 0, 0], "traces": [32, 0, 4, -16, 0, 0, 0, 0, 8, 0, 0, 16, 0, 0, -4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 40, 0, 0, -96, 0, 40, 56, 0, 0, 0, 0, -64, 0, 0, -160, 0, 0, -28, 8, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 28, 0, 0, 0, 16, 0, 0, 64, 0, 0, 16, 0, 0, 0, 0, -24, 0, 0, 240, 0, 0, 8, -96, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, -56, 0, 0, 0, -32, 0, 0, 192, 0, 36, -88, 0, 0, 0, 0, 44, 0, 0, 16, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 16, 0, 0, 0, -24, 0, 0, 0, 0, -76, 96, 0, 0, 0, 0, 32, 0, 0, -160, 0, 0, -4, 160, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, -20, 0, 0, 0, -16, 0, 0, -416, 0, -48, -56, 0, 0, 0, 0, 52, 0, 0, -352, 0, 0, 32, 8, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 52, 0, 0, 0, 16, 0, 0, -32, 0, 8, -88, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 48, 0, 0, 0, -72, 0, 0, 0, 0, -24, -8, 0, 0, 0, 0, 76, 0, 0, 464, 0, 0, 12, -24, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, -96, 0, 0, 0, 24, 0, 0, 448, 0, 12, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -144, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 28, 0, 0, 0, 56, 0, 0, 0, 0, -24, 96, 0, 0, 0, 0, -120, 0, 0, -128, 0, 0, -84, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, -72, 0, 0, 320, 0, -104, 24, 0, 0, 0, 0, 44, 0, 0, -288, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, -152, 0, 48, 0, 0, 0, -104, 0, 0, -576, 0, 8, 80, 0, 0, 0, 0, -16, 0, 0, -208, 0, 0, 32, 120, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, -36, 0, 0, 0, -80, 0, 0, -512, 0, -48, -96, 0, 0, 0, 0, 16, 0, 0, 48, 0, 0, 200, -200, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, -8, 0, 0, 0, 64, 0, 0, -96, 0, 68, 48, 0, 0, 0, 0, 152, 0, 0, 32, 0, 0, 52, 192, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 96, 0, 0, 0, 0, 0, 0, -96, 0, 128, 104, 0, 0, 0, 0, -8, 0, 0, 288, 0, 0, -112, -40, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -64, 0, 0, 0, 0, 0, 0, 736, 0, 104, -248, 0, 0, 0, 0, -144, 0, 0, -256, 0, 0, -132, -128, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 104, 0, 0, 0, 408, 0, 0, 736, 0, 56, -96, 0, 0, 0, 0, -184, 0, 0, 368, 0, 0, -100, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 72, 0, 0, 672, 0, 88, 184, 0, 0, 0, 0, -48, 0, 0, -32, 0, 0, -136, -80, 0, 0, 0, 0, 0, 0, 0, 0, -152, 0, 4, 0, 0, 0, 40, 0, 0, -576, 0, -64, 0, 0, 0, 0, 0, 16, 0, 0, -512, 0, 0, -208, 232, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 104, 0, 0, -704, 0, 128, -80, 0, 0, 0, 0, -172, 0, 0, 608, 0, 0, 80, 72, 0, 0, 0, 0, 0, 0, 0, 0, -176, 0, 132, 0, 0, 0, -128, 0, 0, -64, 0, 84, 312, 0, 0, 0, 0, -24, 0, 0, -256, 0, 0, 72, -40, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 60, 0, 0, 0, 104, 0, 0, -320, 0, -156, 72, 0, 0, 0, 0, 108, 0, 0, -160, 0, 0, 320, -176, 0, 0, 0, 0, 0, 0, 0, 0, 272, 0, -136, 0, 0, 0, -176, 0, 0, -704, 0, 104, 40, 0, 0, 0, 0, 4, 0, 0, -672, 0, 0, -24, 80, 0, 0, 0, 0, 0, 0, 0, 0, -136, 0, -144, 0, 0, 0, -16, 0, 0, 96, 0, -232, -48, 0, 0, 0, 0, 76, 0, 0, 560, 0, 0, 24, -144, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 192, 0, 0, 0, -216, 0, 0, 96, 0, 92, -104, 0, 0, 0, 0, 192, 0, 0, 32, 0, 0, 76, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, -360, 0, 0, 1408, 0, 0, -32, 0, 0, 0, 0, -40, 0, 0, -352, 0, 0, 96, -184, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, -200, 0, 0, 0, 144, 0, 0, -352, 0, -192, -248, 0, 0, 0, 0, -56, 0, 0, 208, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 32, 0, 0, 0, 160, 0, 0, 768, 0, -156, -32, 0, 0, 0, 0, 144, 0, 0, 192, 0, 0, -216, -24, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, -156, 0, 0, 0, -56, 0, 0, -384, 0, 112, 104, 0, 0, 0, 0, 88, 0, 0, 384, 0, 0, 84, 56, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 264, 0, 0, 0, -80, 0, 0, 224, 0, -172, -168, 0, 0, 0, 0, 0, 0, 0, 384, 0, 0, -220, 160, 0, 0, 0, 0, 0, 0, 0, 0, 248, 0, -108, 0, 0, 0, -120, 0, 0, 192, 0, 112, 64, 0, 0, 0, 0, -100, 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, 3, 2, -1, 2, 0], [1, 1, 11, 2, -1, 2, 0], [1, 3, 11, 3, 1, 5, 0], [1, 3, 11, 4, -1, 10, 0], [1, 1, 33, 4, 1, 2, 0], [1, 3, 33, 6, 1, 10, 0], [1, 3, 33, 8, -1, 10, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "363.2.d.e", "char_is_minimal": false, "conrey_index": 161, "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}