# Stored data for newform 722.2.e.s, downloaded from the LMFDB on 25 April 2024.
{"label": "722.2.e.s", "space_label": "722.2.e", "level": 722, "weight": 2, "hecke_orbit": 19, "hecke_orbit_code": 81065068204131026, "dim": 24, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [4096, 0, 0, -49152, 0, 0, 568320, 0, 0, -259072, 0, 0, 119104, 0, 0, 1152, 0, 0, 400, 0, 0, -8, 0, 0, 1]], [5, [47045881, 0, 0, -72280142, 0, 0, 102640310, 0, 0, -12617792, 0, 0, 1278099, 0, 0, -48048, 0, 0, 1710, 0, 0, 22, 0, 0, 1]], [7, [16, -48, 120, -88, 64, -12, 10, -2, 1]], [13, [51520374361, 0, 0, -1829557198438, 0, 0, 64940441655990, 0, 0, -1049930053408, 0, 0, 11801523939, 0, 0, -67527952, 0, 0, 281870, 0, 0, -642, 0, 0, 1]]], "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 19, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2888, "analytic_conductor": 5.765199025936444, "level_radical": 38, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [722, 9, [363], [1]], "inner_twist_count": 6, "level_primes": [2, 19], "conrey_indexes": [99, 245, 389, 415, 423, 595], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c9", "trace_display": [0, 0, 0, 6], "traces": [24, 0, 0, 0, 0, 0, 6, 12, 0, 0, -6, 6, 0, 0, 0, 0, 0, -24, 0, -12, 0, 0, 0, 0, 0, -54, -12, 0, 0, -12, 78, 0, 0, 0, 0, 0, -24, 0, -36, 0, 0, 0, 0, 0, 66, -30, 0, 0, 36, 18, 0, 0, 0, 0, 0, 12, 0, -12, 0, 0, 0, 0, 0, -12, -12, 0, 0, -18, -60, 0, 0, 0, 0, 0, -48, 0, 24, 0, 0, 0, 0, 0, 36, 12, 0, 0, 78, 6, 0, 0, 0, 0, 0, 72, 0, 12, 0, 0, 0, 0, 0, 6, 102, 0, 0, -24, -36, 0, 0, 0, 0, 0, 72, 0, -120, 0, 0, 0, 0, 0, -36, 0, 0, 0, -126, -66, 0, 0, 0, 0, 0, -96, 0, 60, 0, 0, 0, 0, 0, -18, -48, 0, 0, -12, -12, 0, 0, 0, 0, 0, 72, 0, 276, 0, 0, 0, 0, 0, -72, -6, 0, 0, -18, -36, 0, 0, 0, 0, 0, 108, 0, -60, 0, 0, 0, 0, 0, 48, -84, 0, 0, 12, -150, 0, 0, 0, 0, 0, 48, 0, -144, 0, 0, 0, 0, 0, 72, 66, 0, 0, 120, 30, 0, 0, 0, 0, 0, -108, 0, -72, 0, 0, 0, 0, 0, 12, -24, 0, 0, 78, 36, 0, 0, 0, 0, 0, 48, 0, 132, 0, 0, 0, 0, 0, -78, -24, 0, 0, 18, 12, 0, 0, 0, 0, 0, 96, 0, 156, 0, 0, 0, 0, 0, -24, 18, 0, 0, 60, 54, 0, 0, 0, 0, 0, -216, 0, -408, 0, 0, 0, 0, 0, -144, -42, 0, 0, -150, 12, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 42, 192, 0, 0, -12, 144, 0, 0, 0, 0, 0, 120, 0, 120, 0, 0, 0, 0, 0, 102, -18, 0, 0, -138, 66, 0, 0, 0, 0, 0, -240, 0, -24, 0, 0, 0, 0, 0, 204, -42, 0, 0, 24, -60, 0, 0, 0, 0, 0, -168, 0, 120, 0, 0, 0, 0, 0, -36, -54, 0, 0, -78, 48, 0, 0, 0, 0, 0, 132, 0, 72, 0, 0, 0, 0, 0, 30, -96, 0, 0, -24, 78, 0, 0, 0, 0, 0, -192, 0, 144, 0, 0, 0, 0, 0, -90, 84, 0, 0, 210, -36, 0, 0, 0, 0, 0, 48, 0, 36, 0, 0, 0, 0, 0, 72, -54, 0, 0, 42, 204, 0, 0, 0, 0, 0, 408, 0, 144, 0, 0, 0, 0, 0, -72, 60, 0, 0, -36, -60, 0, 0, 0, 0, 0, 168, 0, 48, 0, 0, 0, 0, 0, 24, -6, 0, 0, 6, -48, 0, 0, 0, 0, 0, -132, 0, -396, 0, 0, 0, 0, 0, 36, -6, 0, 0, 84, -6, 0, 0, 0, 0, 0, -336, 0, -168, 0, 0, 0, 0, 0, -108, 60, 0, 0, -90, 54, 0, 0, 0, 0, 0, -192, 0, -156, 0, 0, 0, 0, 0, -108, 30, 0, 0, 90, 60, 0, 0, 0, 0, 0, -24, 0, 288, 0, 0, 0, 0, 0, 12, -24, 0, 0, 12, -12, 0, 0, 0, 0, 0, -72, 0, -204, 0, 0, 0, 0, 0, 18, -84, 0, 0, -228, 18, 0, 0, 0, 0, 0, 252, 0, -120, 0, 0, 0, 0, 0, -78, -150, 0, 0, -24, -78, 0, 0, 0, 0, 0, 216, 0, 372, 0, 0, 0, 0, 0, 30, -42, 0, 0, 192, 42, 0, 0, 0, 0, 0, 156, 0, -36, 0, 0, 0, 0, 0, -84, 168, 0, 0, -24, -132, 0, 0, 0, 0, 0, -192, 0, 288, 0, 0, 0, 0, 0, 66, 12, 0, 0, -132, -84, 0, 0, 0, 0, 0, -324, 0, 0, 0, 0, 0, 0, 0, -84, 168, 0, 0, 108, -180, 0, 0, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, 210, -132, 0, 0, 42, -72, 0, 0, 0, 0, 0, 72, 0, -216, 0, 0, 0, 0, 0, -12, 84, 0, 0, -162, -234, 0, 0, 0, 0, 0, 324, 0, 192, 0, 0, 0, 0, 0, 96, -36, 0, 0, 246, -78, 0, 0, 0, 0, 0, 288, 0, 12, 0, 0, 0, 0, 0, -210, -54, 0, 0, -48, -186, 0, 0, 0, 0, 0, 312, 0, 288, 0, 0, 0, 0, 0, 204, 96, 0, 0, -156, -84, 0, 0, 0, 0, 0, -48, 0, -84, 0, 0, 0, 0, 0, -24, -132, 0, 0, 36, 120, 0, 0, 0, 0, 0, 360, 0, -192, 0, 0, 0, 0, 0, 198, 6, 0, 0, -132, 132, 0, 0, 0, 0, 0, -264, 0, 348, 0, 0, 0, 0, 0, -204, -48, 0, 0, -72, 168, 0, 0, 0, 0, 0, -132, 0, 132, 0, 0, 0, 0, 0, 120, 366, 0, 0, 102, 6, 0, 0, 0, 0, 0, 12, 0, -96, 0, 0, 0, 0, 0, -102, -108, 0, 0, 150, -108, 0, 0, 0, 0, 0, 276, 0, -96, 0, 0, 0, 0, 0, -42, 66, 0, 0, 78, 24, 0, 0, 0, 0, 0, 120, 0, -72, 0, 0, 0, 0, 0, 102, -204, 0, 0, -240, -126, 0, 0, 0, 0, 0, -888, 0, -156, 0, 0, 0, 0, 0, 42, -36, 0, 0, 204, -114, 0, 0, 0, 0, 0, -132, 0, -156, 0, 0, 0, 0, 0, -18, 66, 0, 0, 36, 192, 0, 0, 0, 0, 0, -660, 0, -576, 0, 0, 0, 0, 0, -60, -60, 0, 0, -30, -84, 0, 0, 0, 0, 0, -96, 0, 36, 0, 0, 0, 0, 0, 60, 156, 0, 0, -30, 420, 0, 0, 0, 0, 0, 468, 0, 144, 0, 0, 0, 0, 0, 84, -150, 0, 0, -180, 144, 0, 0, 0, 0, 0, -72, 0, -324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 36, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -372, -228, 0, 0, 132, 126], "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, 2, 19, 3, 1, 3, 0], [1, 3, 19, 5, 1, 9, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "722.2.a.m", "char_is_minimal": false, "conrey_index": 99, "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}