# Stored data for newform 1350.2.j.f, downloaded from the LMFDB on 19 April 2024. {"label": "1350.2.j.f", "space_label": "1350.2.j", "level": 1350, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22518616645698886, "dim": 8, "is_polredabs": true, "nf_label": "8.0.303595776.1", "trace_hash": 2002889228099740303, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [4096, 0, -1088, 0, 225, 0, -17, 0, 1]], [11, [36, -18, 15, 3, 1]], [19, [-8, 1, 1]]], "qexp_display": "q+\\beta _{1}q^{2}-\\beta _{3}q^{4}-\\beta _{7}q^{7}+(\\beta _{1}+\\beta _{5}+\\cdots)q^{8}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 45, "char_orbit_label": "j", "char_is_real": false, "Nk2": 5400, "analytic_conductor": 10.779804272872852, "hecke_ring_index": 9, "level_radical": 30, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [1350, 6, [1001, 1027], [2, 3]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3, 5], "conrey_indexes": [199, 1099], "field_disc": 303595776, "field_disc_factorization": [[2, 8], [3, 4], [11, 4]], "field_poly": [81, 0, 45, 0, 16, 0, 5, 0, 1], "hecke_ring_index_factorization": [[3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.045", "prec": 17}, {"__RealLiteral__": 0, "data": "7.373", "prec": 17}, {"__RealLiteral__": 0, "data": "2.871", "prec": 17}, {"__RealLiteral__": 0, "data": "458.692", "prec": 24}, {"__RealLiteral__": 0, "data": "969.016", "prec": 24}, {"__RealLiteral__": 0, "data": "54390.987", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, -6, 0, 0, 2, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 6, 0, 4, 0, 0, 18, 0, 0, 0, 0, 0, 0, -12, 0, 0, -12, 0, 12, 0, 0, 6, 0, 0, 0, 0, 0, 0, -2, 0, 0, -6, 0, -2, 0, 0, -8, 0, 0, 0, 0, 0, 0, 48, 0, 0, -16, 0, -2, 0, 0, 8, 0, 0, 0, 0, 0, 0, 34, 0, 0, 60, 0, -136, 0, 0, 18, 0, 0, 0, 0, 0, 0, -12, 0, 0, -4, 0, 0, 0, 0, -100, 0, 0, 0, 0, 0, 0, 12, 0, 0, -24, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 12, 0, 0, 56, 0, 36, 0, 0, 38, 0, 0, 0, 0, 0, 0, 22, 0, 0, -42, 0, 40, 0, 0, -72, 0, 0, 0, 0, 0, 0, -60, 0, 0, 12, 0, 18, 0, 0, 84, 0, 0, 0, 0, 0, 0, -6, 0, 0, -72, 0, 52, 0, 0, 6, 0, 0, 0, 0, 0, 0, 24, 0, 0, -22, 0, -6, 0, 0, -16, 0, 0, 0, 0, 0, 0, -128, 0, 0, -30, 0, 52, 0, 0, 12, 0, 0, 0, 0, 0, 0, -48, 0, 0, -4, 0, -72, 0, 0, 62, 0, 0, 0, 0, 0, 0, 6, 0, 0, 36, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 36, 0, 0, 2, 0, -4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 32, 0, 0, 12, 0, 64, 0, 0, 42, 0, 0, 0, 0, 0, 0, 6, 0, 0, 24, 0, 72, 0, 0, -92, 0, 0, 0, 0, 0, 0, -32, 0, 0, 60, 0, -16, 0, 0, 2, 0, 0, 0, 0, 0, 0, -60, 0, 0, 8, 0, 16, 0, 0, -24, 0, 0, 0, 0, 0, 0, 40, 0, 0, 42, 0, 4, 0, 0, 84, 0, 0, 0, 0, 0, 0, 120, 0, 0, -34, 0, 60, 0, 0, 38, 0, 0, 0, 0, 0, 0, 30, 0, 0, -48, 0, -84, 0, 0, -68, 0, 0, 0, 0, 0, 0, -132, 0, 0, -6, 0, -18, 0, 0, -28, 0, 0, 0, 0, 0, 0, 100, 0, 0, 30, 0, -60, 0, 0, -24, 0, 0, 0, 0, 0, 0, 30, 0, 0, -24, 0, -60, 0, 0, 14, 0, 0, 0, 0, 0, 0, 4, 0, 0, 12, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 64, 0, -50, 0, 0, -4, 0, 0, 0, 0, 0, 0, -38, 0, 0, -36, 0, 36, 0, 0, -42, 0, 0, 0, 0, 0, 0, 42, 0, 0, 6, 0, -6, 0, 0, 28, 0, 0, 0, 0, 0, 0, -48, 0, 0, 48, 0, -16, 0, 0, -2, 0, 0, 0, 0, 0, 0, -66, 0, 0, -128, 0, -8, 0, 0, 26, 0, 0, 0, 0, 0, 0, 24, 0, 0, 66, 0, -88, 0, 0, 12, 0, 0, 0, 0, 0, 0, 192, 0, 0, -12, 0, -24, 0, 0, -50, 0, 0, 0, 0, 0, 0, 28, 0, 0, -84, 0, 196, 0, 0, 18, 0, 0, 0, 0, 0, 0, -36, 0, 0, 44, 0, -38, 0, 0, 64, 0, 0, 0, 0, 0, 0, -140, 0, 0, 42, 0, 46, 0, 0, 6, 0, 0, 0, 0, 0, 0, 42, 0, 0, 44, 0, -72, 0, 0, -68, 0, 0, 0, 0, 0, 0, 42, 0, 0, 84, 0, -50, 0, 0, 80, 0, 0, 0, 0, 0, 0, -168, 0, 0, -64, 0, -36, 0, 0, -118, 0, 0, 0, 0, 0, 0, -26, 0, 0, 144, 0, 40, 0, 0, 12, 0, 0, 0, 0, 0, 0, -156, 0, 0, -30, 0, -42, 0, 0, 84, 0, 0, 0, 0, 0, 0, 24, 0, 0, -24, 0, -20, 0, 0, -18, 0, 0, 0, 0, 0, 0, 96, 0, 0, -4, 0, 168, 0, 0, -44, 0, 0, 0, 0, 0, 0, -22, 0, 0, -264, 0, 76, 0, 0, -108, 0, 0, 0, 0, 0, 0, -228, 0, 0, 6, 0, 18, 0, 0, -46, 0, 0, 0, 0, 0, 0, -36, 0, 0, -168, 0, -64, 0, 0, 26, 0, 0, 0, 0, 0, 0, 186, 0, 0, -64, 0, -6, 0, 0, 260, 0, 0, 0, 0, 0, 0, -32, 0, 0, -126, 0, 4, 0, 0, 60, 0, 0, 0, 0, 0, 0, -78, 0, 0, 48, 0, 0, 0, 0, -130, 0, 0, 0, 0, 0, 0, 22, 0, 0, 6, 0, -36, 0, 0, -12, 0, 0, 0, 0, 0, 0, 96, 0, 0, 68, 0, -8, 0, 0, 48, 0, 0, 0, 0, 0, 0, 128, 0, 0, 108, 0, 52, 0, 0, -24, 0, 0, 0, 0, 0, 0, 54, 0, 0, -64, 0, 36, 0, 0, 332, 0, 0, 0, 0, 0, 0, -60, 0, 0, -108, 0, 74, 0, 0, -52, 0, 0, 0, 0, 0, 0, 24, 0, 0, 196, 0, 24, 0, 0, -34, 0, 0, 0, 0, 0, 0, -14, 0, 0, 12, 0, -28, 0, 0, -72, 0, 0, 0, 0, 0, 0, -12, 0, 0, 48, 0, -60, 0, 0, -98, 0, 0, 0, 0, 0, 0, -2, 0, 0, 144, 0, -264, 0, 0, -36, 0, 0, 0, 0, 0, 0, -168, 0, 0, 86, 0, -62, 0, 0, -64, 0, 0, 0, 0, 0, 0, 160, 0, 0, -24, 0, 30, 0, 0, -138, 0, 0, 0, 0, 0, 0, 162, 0, 0, 12, 0, -36, 0, 0, -176, 0, 0, 0, 0, 0, 0, -36, 0, 0, 120, 0, -12, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, -2, 0, 0, -144, 0, 0, 0, 0, 0, 0, -60, 0, 0, 168, 0, -8, 0, 0, 12, 0, 0, 0, 0, 0, 0, 168, 0, 0, 18, 0, 30, 0, 0, 20, 0, 0, 0, 0, 0, 0, 4, 0, 0, 90, 0, -170, 0, 0, 4, 0, 0, 0, 0, 0, 0, -120, 0, 0, -120, 0, -16, 0, 0, 92, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 46, 0, 0, 168, 0, 0, 0, 0, 0, 0, 456, 0, 0, -32, 0, 12, 0, 0, 98, 0, 0, 0, 0, 0, 0, 6, 0, 0, -168, 0, -12, 0, 0, 32, 0, 0, 0, 0, 0, 0, 42, 0, 0, 20, 0, -42, 0, 0, 136, 0, 0, 0, 0, 0, 0, 8, 0, 0, 30, 0, 48, 0, 0, 108, 0, 0, 0, 0, 0, 0, -30, 0, 0, 12, 0, 96, 0, 0, 80, 0, 0, 0, 0, 0, 0, -24, 0, 0, -126, 0, 152, 0, 0, 144, 0, 0, 0, 0, 0, 0, -288, 0, 0, -130, 0, -46, 0, 0, 100, 0, 0, 0, 0, 0, 0, -132, 0, 0, 108, 0, 148, 0, 0, -108, 0, 0, 0, 0, 0, 0, -114, 0, 0, -16, 0, 36, 0, 0, -36, 0, 0, 0, 0, 0, 0, 120, 0, 0, 108, 0, -104, 0, 0, 16, 0, 0, 0, 0, 0, 0, 96, 0, 0, -76, 0, 4, 0, 0, -132, 0, 0, 0, 0, 0, 0, -68, 0, 0, -36, 0, -164, 0, 0, -108, 0, 0, 0, 0, 0, 0, -396, 0, 0, 60, 0, 114, 0, 0, -184, 0, 0, 0, 0, 0, 0, 4, 0, 0, -180, 0, 176, 0, 0, 8, 0, 0, 0, 0, 0, 0, 12, 0, 0, -72, 0, 24, 0, 0, -424, 0, 0, 0, 0, 0, 0, 88, 0, 0, -144, 0, -62, 0, 0, 30, 0, 0, 0, 0, 0, 0, -96, 0, 0, 80, 0, 72, 0, 0, 96, 0, 0, 0, 0, 0, 0, -42, 0, 0, 72, 0, -68, 0, 0, 8, 0, 0, 0, 0, 0, 0, 60, 0, 0, 42, 0, 42, 0, 0, 64, 0, 0, 0, 0, 0, 0, 40, 0, 0, -24, 0, 248, 0, 0, 60, 0, 0, 0, 0, 0, 0, 126, 0, 0, 60, 0, 6, 0, 0, 168, 0, 0, 0, 0, 0, 0, -68, 0, 0, 120, 0, 214, 0, 0, -60, 0, 0, 0, 0, 0, 0, -252, 0, 0, -108, 0, 76, 0, 0, 32, 0, 0, 0, 0, 0, 0, 8, 0, 0, -12, 0, 48, 0, 0, 120, 0, 0, 0, 0, 0, 0, -48, 0, 0, -30, 0, 72, 0, 0, -124, 0, 0, 0, 0, 0, 0, -24, 0, 0, 192, 0, 96, 0, 0, -42, 0, 0, 0, 0, 0, 0, 48, 0, 0, 38, 0, 68, 0, 0, 104, 0, 0, 0, 0, 0, 0, 136, 0, 0, -96, 0, -128, 0, 0, -42, 0, 0, 0, 0, 0, 0, 72, 0, 0, -264, 0, -132, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 54, 0, -4, 0, 0, -36, 0, 0, 0, 0, 0, 0, -72, 0, 0, -40, 0, -14, 0, 0, 60, 0, 0, 0, 0, 0, 0, -58, 0, 0, 84, 0, -248, 0, 0, 72, 0, 0, 0, 0, 0, 0, 42, 0, 0, 50, 0, 36, 0, 0, -292, 0, 0, 0, 0, 0, 0, 60, 0, 0, 120, 0, 14, 0, 0, 60, 0, 0, 0, 0, 0, 0, 198, 0, 0, 224, 0, -48, 0, 0, 8, 0, 0, 0, 0, 0, 0, -196, 0, 0, -120, 0, -136, 0, 0, 72, 0, 0, 0, 0, 0, 0, -216, 0, 0, -30, 0, -66, 0, 0, 146, 0, 0, 0, 0, 0, 0, -12, 0, 0, -420, 0, -224, 0, 0, -30, 0, 0, 0, 0, 0, 0, 96, 0, 0, -50, 0, -14, 0, 0, -72, 0, 0, 0, 0, 0, 0, 52, 0, 0, -66, 0, -196, 0, 0, -90, 0, 0, 0, 0, 0, 0, 60, 0, 0, 8, 0, -12, 0, 0, 80, 0, 0, 0, 0, 0, 0, -12, 0, 0, -132, 0, 128, 0, 0, 32, 0, 0, 0, 0, 0, 0, 168, 0, 0, 98, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 76, 0, 0, 240, 0, 48, 0, 0, -48, 0, 0, 0, 0, 0, 0, -36, 0, 0, 36, 0, -90, 0, 0, -64, 0, 0, 0, 0, 0, 0, 128, 0, 0, -72, 0, 64, 0, 0, 50, 0, 0, 0, 0, 0, 0, 288, 0, 0, 80, 0, -8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 64, 0, 0, 102, 0, 12, 0, 0, -72, 0, 0, 0, 0, 0, 0, -480, 0, 0, 38, 0, 24, 0, 0, 68, 0, 0, 0, 0, 0, 0, -18, 0, 0, 72, 0, -224, 0, 0, 18, 0, 0, 0, 0, 0, 0, 234, 0, 0, -28, 0, 42, 0, 0, -372, 0, 0, 0, 0, 0, 0, -120, 0, 0, -60, 0, -32, 0, 0, 60, 0, 0, 0, 0, 0, 0, -144, 0, 0, 84, 0, -48, 0, 0, 150, 0, 0, 0, 0, 0, 0, -6, 0, 0, 258, 0, 10, 0, 0, -12, 0, 0, 0, 0, 0, 0, 600, 0, 0, 44, 0, 14, 0, 0, 200, 0, 0, 0, 0, 0, 0, -18, 0, 0, 72, 0, -400, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 66, 0, 0, -12, 0, 0, 0, 0, 0, 0, 96, 0, 0, 72, 0, 228, 0, 0, 16, 0, 0, 0, 0, 0, 0, 90, 0, 0, -220, 0, -4, 0, 0, 88, 0, 0, 0, 0, 0, 0, 80, 0, 0, -174, 0, 136, 0, 0, -252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66, 0, 6, 0, 0, 120, 0, 0, 0, 0, 0, 0, -64, 0, 0, 168, 0, 260, 0, 0, -4, 0, 0, 0, 0, 0, 0, -204, 0, 0, 56, 0, -26, 0, 0, -112, 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, 45, 10, 1, 6, 0], [1, 1, 9, 3, 1, 3, 0], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 10, "prim_orbit_index": 10, "minimal_twist": "90.2.e.c", "char_is_minimal": false, "conrey_index": 199, "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, 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], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 1, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 2, 2, 0, 2], [-1, 0, 1, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0, 0, 0], [0, -4, 0, 0, 1, -4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 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, 1, 2, 0, 1], [0, 1, 0, 0, 1, -1, 0, 1], [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, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -2, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 1, 4, 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, -1, 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, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, 1], [-1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 1, 0], [0, 4, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -2, 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, 2], [0, 2, 0, 0, 4, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, -1, 0, 1], [1, 0, -1, 2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -3, 1, 0, 0, 0, 0], [0, 0, 0, 0, -2, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -7, 0, 0], [0, 1, 0, 0, 1, -4, 0, 1], [0, 0, 0, 0, 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, 0, 0, 0], [0, -4, 0, 0, 3, -4, 0, 0], [-4, 0, 0, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0, -1, 0], [0, 2, 0, 0, 2, 10, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, -3, 0, 0], [0, 4, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, -8, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 1], [6, 0, 0, 0, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-16, 0, 0, 0, 0, 0, 2, 0], [0, 2, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -5, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 1, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}