# Stored data for newform 1350.2.q.f, downloaded from the LMFDB on 19 April 2024. {"label": "1350.2.q.f", "space_label": "1350.2.q", "level": 1350, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22519097682036038, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 760076302796038320, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [20736, 0, 0, 0, -144, 0, 0, 0, 1]], [11, [3, -3, 1]]], "qexp_display": "q-\\zeta_{24}^{5}q^{2}+(-\\zeta_{24}^{2}+\\zeta_{24}^{6})q^{4}+\\cdots", "char_order": 12, "char_parity": 1, "char_degree": 4, "char_conductor": 45, "char_orbit_label": "q", "char_is_real": false, "Nk2": 5400, "analytic_conductor": 10.779804272872852, "hecke_ring_index": 1, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 24, "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": "0.798", "prec": 17}, "analytic_rank_proved": true, "char_values": [1350, 12, [1001, 1027], [2, 9]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 8, "level_primes": [2, 3, 5], "conrey_indexes": [143, 557, 1007, 1043], "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.078", "prec": 17}, {"__RealLiteral__": 0, "data": "7.399", "prec": 17}, {"__RealLiteral__": 0, "data": "4.500", "prec": 17}, {"__RealLiteral__": 0, "data": "636.651", "prec": 24}, {"__RealLiteral__": 0, "data": "27.837", "prec": 20}, {"__RealLiteral__": 0, "data": "73674.042", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c12", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 116, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, -328, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -588, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 104, 0, 0, 0, 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, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 672, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, -220, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -200, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -504, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, -216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 424, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 516, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 276, 0, 0, 0, 0, -200, 0, 0, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 504, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 336, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 300, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, -76, 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, 2, 5, 3, -1, 4, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 45, 8, -1, 6, 0], [1, 2, 45, 12, 1, 12, 0], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 17, "prim_orbit_index": 12, "minimal_twist": "450.2.p.f", "char_is_minimal": false, "conrey_index": 143, "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, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, -2, 0, 0], [0, 0, 0, 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, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, -2], [0, 0, -2, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0], [0, -3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 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, 0, 0], [0, 1, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, 0, 4], [0, 0, -2, 0, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 4, 0, 0], [0, 0, 0, -7, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [14, 0, 0, 0, -7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 0, 0, -3], [0, 0, -2, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 0, 0, 0, -5, 0], [0, 0, 0, 0, 0, 0, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, -2], [0, 0, -7, 0, 0, 0, -7, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, -4, 0, 0, 0], [0, 8, 0, 0, 0, -8, 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, 0], [0, 1, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 0, 0, -16, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -5, 0, 0, 0, 10], [0, 0, 4, 0, 0, 0, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, 0], [0, 6, 0, 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], [0, -7, 0, 0, 0, -7, 0, 0], [0, 0, 0, 12, 0, 0, 0, -12], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 8, 0, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [12, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, 0, 0, 0, 5, 0, 0], [0, 0, 0, -5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}