# Stored data for newform 2240.2.n.g, downloaded from the LMFDB on 25 April 2024.
{"label": "2240.2.n.g", "space_label": "2240.2.n", "level": 2240, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27022491150977216, "dim": 8, "is_polredabs": true, "nf_label": "8.0.1731891456.1", "trace_hash": 1114308509450916389, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-4, -1, 1]], [11, [36, 0, -39, 0, 1]], [17, [144, 0, -27, 0, 1]], [23, [-8, 6, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+(-2+\\beta _{5})q^{5}+(-2-\\beta _{2}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 280, "char_orbit_label": "n", "char_is_real": true, "Nk2": 8960, "analytic_conductor": 17.886490052766806, "hecke_ring_index": 16, "level_radical": 70, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.764", "prec": 17}, "analytic_rank_proved": true, "char_values": [2240, 2, [1471, 1541, 897, 1921], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 5, 7], "conrey_indexes": [1119], "field_disc": 1731891456, "field_disc_factorization": [[2, 8], [3, 4], [17, 4]], "field_poly": [256, 0, -144, 0, 65, 0, -9, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.050", "prec": 17}, {"__RealLiteral__": 0, "data": "7.353", "prec": 17}, {"__RealLiteral__": 0, "data": "12.935", "prec": 20}, {"__RealLiteral__": 0, "data": "616.440", "prec": 24}, {"__RealLiteral__": 0, "data": "2582.178", "prec": 27}, {"__RealLiteral__": 0, "data": "75430.618", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 4, -16, -16], "traces": [0, 8, 0, 4, 0, -16, 0, -16, 0, 12, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, -24, 0, 24, 0, 28, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -24, 0, -12, 0, 0, 0, 56, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -56, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 68, 0, 0, 0, -16, 0, -96, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 48, 0, 56, 0, 0, 0, 84, 0, -56, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 76, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, -16, 0, -104, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 0, -60, 0, 56, 0, -24, 0, -28, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -72, 0, 200, 0, 48, 0, -36, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 80, 0, -112, 0, 0, 0, 24, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, -56, 0, -272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -48, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 60, 0, 0, 0, 112, 0, 168, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 160, 0, 8, 0, 0, 0, -100, 0, -96, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 128, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, -24, 0, 216, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, -160, 0, 24, 0, 112, 0, -192, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 64, 0, 0, 0, 16, 0, -224, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -136, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -152, 0, 24, 0, -56, 0, 0, 0, 216, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -240, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 140, 0, 0, 0, 72, 0, -56, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 152, 0, 240, 0, 0, 0, -48, 0, 48, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 204, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 276, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, -96, 0, -80, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -184, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, -180, 0, -104, 0, -136, 0, 4, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -216, 0, 72, 0, -28, 0, 88, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, -96, 0, 0, 0, 192, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 220, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 56, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 184, 0, 0, 0, 40, 0, -240, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -96, 0, -120, 0, 0, 0, 84, 0, 40, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, -372, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380, 0, 24, 0, -168, 0, -204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 300, 0, -24, 0, -24, 0, 148, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, -144, 0, -144, 0, -48, 0, 432, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152, 0, -104, 0, -108, 0, 0, 0, -216, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 300, 0, -140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, -120, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 48, 0, 0, 0, 32, 0, 168, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 16, 0, -264, 0, 0, 0, 92, 0, -168, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 320, 0, 348, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, -56, 0, -24, 0, 136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -356, 0, 208, 0, 312, 0, -48, 0, 12, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 48, 0, -240, 0, -224, 0, -100, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, -312, 0, 164, 0, 0, 0, -168, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 60, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 168, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -400, 0, 0, 0, 0, 0, 180, 0, 0, 0, -72, 0, 16, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 312, 0, 72, 0, 0, 0, -396, 0, -152, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, -152, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 24, 0, -16, 0, 168, 0, -80, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 224, 0, 120, 0, -336, 0, -232, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 32, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, -112, 0, 336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 40, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 12, 0, 0, 0, 112, 0, 64, 0, 0, 0, 0, 0, 0, 0, 544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 168, 0, 0, 0, -108, 0, 216, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0, 0, 312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, -220, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 136, 0, 144, 0, 168, 0, -436, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -348, 0, -232, 0, 312, 0, -264, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 120, 0, -256, 0, -84, 0, -12, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 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, 56, 8, -1, 2, 0], [1, 1, 280, 14, 1, 2, 0], [1, 1, 20, 4, -1, 2, 0]], "char_orbit_index": 14, "prim_orbit_index": 14, "minimal_twist": "2240.2.n.a", "char_is_minimal": true, "conrey_index": 1119, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, -4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 2, 1, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 0, 0, -1, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 4, 0, 0, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, -1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, 0, -2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [8, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, -8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 4, -4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 3, 3, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, -2, -2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 0, 0, -4, -4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}