# Stored data for newform 507.2.j.i, downloaded from the LMFDB on 24 April 2024. {"label": "507.2.j.i", "space_label": "507.2.j", "level": 507, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029415527809531, "dim": 12, "is_polredabs": true, "nf_label": "12.0.17213603549184.1", "trace_hash": 1710708024908632785, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [28561, 0, -15886, 0, 5963, 0, -1260, 0, 195, 0, -17, 0, 1]], [5, [169, 0, 181, 0, 26, 0, 1]]], "qexp_display": "q+(-\\beta _{1}+\\beta _{8}+2\\beta _{11})q^{2}+\\beta _{7}q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "j", "char_is_real": false, "Nk2": 2028, "analytic_conductor": 4.0484153824789155, "hecke_ring_index": 1, "level_radical": 39, "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": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [507, 6, [170, 340], [6, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [3, 13], "conrey_indexes": [316, 361], "field_disc": 17213603549184, "field_disc_factorization": [[2, 12], [3, 6], [7, 8]], "field_poly": [1, 0, -6, 0, 31, 0, -28, 0, 19, 0, -5, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "10.543", "prec": 20}, {"__RealLiteral__": 0, "data": "1.552", "prec": 17}, {"__RealLiteral__": 0, "data": "803.528", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "102053.275", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 6, 0, 0], "traces": [0, 12, 0, 6, 22, 0, 0, 0, 0, -6, -2, 0, 44, 0, -20, 0, -22, -2, 0, 0, 0, 0, 18, 0, 0, -44, 0, -12, 0, 4, 2, 0, 0, 0, 0, -8, 22, 0, 0, 0, 12, 0, -10, -30, 0, 0, 0, 0, 22, -30, 0, -4, 0, -68, 0, -6, 2, 0, 0, 0, 0, 26, -4, 0, 0, 0, 36, 0, 26, 0, 0, 0, 0, 0, -30, -22, 0, -60, 0, 12, 0, -6, -6, 0, 0, 0, 0, -4, 26, 0, 4, 0, 28, 0, 0, -42, 0, 0, 0, 0, -48, 4, 0, 56, 0, -16, 0, 26, -22, 0, 0, 0, 0, -48, 0, 0, 20, 0, 32, 0, 6, 16, 0, 0, 0, 0, 10, 30, 0, -60, 0, 48, 0, 14, 64, 0, 0, 0, 0, 26, 6, 0, 56, 0, 44, 0, 30, 30, 0, 0, 0, 0, 28, -2, 0, 44, 0, 36, 0, -34, -10, 0, 0, 0, 0, 6, 38, 0, 4, 0, 132, 0, 138, 36, 0, 0, 0, 0, -100, -4, 0, 148, 0, 52, 0, -102, 4, 0, 0, 0, 0, 22, 0, 0, -260, 0, -248, 0, 18, 34, 0, 0, 0, 0, -26, 30, 0, 0, 0, -56, 0, -48, -148, 0, 0, 0, 0, 54, -110, 0, 68, 0, -60, 0, -62, 22, 0, 0, 0, 0, 196, -30, 0, -84, 0, 84, 0, 6, -34, 0, 0, 0, 0, 6, -114, 0, -12, 0, -284, 0, -96, -2, 0, 0, 0, 0, -10, 2, 0, -68, 0, -8, 0, -46, -26, 0, 0, 0, 0, -62, 2, 0, 248, 0, -180, 0, 14, -74, 0, 0, 0, 0, 0, 30, 0, -84, 0, 76, 0, 36, 132, 0, 0, 0, 0, 80, 148, 0, -264, 0, -96, 0, -38, -4, 0, 0, 0, 0, -82, 28, 0, 196, 0, 12, 0, -8, 36, 0, 0, 0, 0, -26, 28, 0, -44, 0, 376, 0, -74, 14, 0, 0, 0, 0, -50, 100, 0, -48, 0, -96, 0, 156, 0, 0, 0, 0, 0, 44, 10, 0, 204, 0, 408, 0, 16, 98, 0, 0, 0, 0, -6, -72, 0, 32, 0, -120, 0, 30, 112, 0, 0, 0, 0, -26, -134, 0, -56, 0, 20, 0, 112, -30, 0, 0, 0, 0, 18, -30, 0, 212, 0, -196, 0, 24, 38, 0, 0, 0, 0, -14, -120, 0, 128, 0, 132, 0, -16, 78, 0, 0, 0, 0, 84, -8, 0, -124, 0, 52, 0, -10, -6, 0, 0, 0, 0, -100, 28, 0, 88, 0, 132, 0, 22, -62, 0, 0, 0, 0, -30, -32, 0, 60, 0, 92, 0, 80, -214, 0, 0, 0, 0, -102, 176, 0, -292, 0, 56, 0, -136, 2, 0, 0, 0, 0, 10, 22, 0, -4, 0, -64, 0, 18, 36, 0, 0, 0, 0, 34, 206, 0, -20, 0, -328, 0, -12, -188, 0, 0, 0, 0, 46, -2, 0, -68, 0, 12, 0, 14, -38, 0, 0, 0, 0, -36, 2, 0, -308, 0, 108, 0, 66, 64, 0, 0, 0, 0, -138, 28, 0, 72, 0, -36, 0, -68, 46, 0, 0, 0, 0, -58, -138, 0, 56, 0, -200, 0, -74, 4, 0, 0, 0, 0, 114, 74, 0, -260, 0, 160, 0, 26, -304, 0, 0, 0, 0, 102, -156, 0, 8, 0, -156, 0, -94, -100, 0, 0, 0, 0, 126, -62, 0, 48, 0, 44, 0, 154, 0, 0, 0, 0, 0, -2, -130, 0, -180, 0, -436, 0, -124, 70, 0, 0, 0, 0, -18, 2, 0, 68, 0, 276, 0, -10, -6, 0, 0, 0, 0, -44, -70, 0, 524, 0, -52, 0, 40, -30, 0, 0, 0, 0, -36, 0, 0, 72, 0, -4, 0, -28, 94, 0, 0, 0, 0, 48, 128, 0, -296, 0, -4, 0, 176, 96, 0, 0, 0, 0, 0, -6, 0, -16, 0, 108, 0, 6, 110, 0, 0, 0, 0, 182, 34, 0, -60, 0, 192, 0, -30, -98, 0, 0, 0, 0, 62, -42, 0, 44, 0, 40, 0, 44, 166, 0, 0, 0, 0, -240, 92, 0, 556, 0, 392, 0, -258, 30, 0, 0, 0, 0, -180, -42, 0, -68, 0, -224, 0, 42, 72, 0, 0, 0, 0, -6, 190, 0, -68, 0, 204, 0, 304, 24, 0, 0, 0, 0, 248, 32, 0, 128, 0, 12, 0, -94, 114, 0, 0, 0, 0, 108, -6, 0, -524, 0, 20, 0, -142, 180, 0, 0, 0, 0, 96, -148, 0, -4, 0, -464, 0, -90, 66, 0, 0, 0, 0, -90, -132, 0, 360, 0, -20, 0, 122, -2, 0, 0, 0, 0, -268, -34, 0, 112, 0, -168, 0, -4, -180, 0, 0, 0, 0, 46, 138, 0, -52, 0, -104, 0, -176, 108, 0, 0, 0, 0, -160, 202, 0, -140, 0, -124, 0, -30, -2, 0, 0, 0, 0, 16, 124, 0, 404, 0, 52, 0, -90, -84, 0, 0, 0, 0, -14, 132, 0, -148, 0, 48, 0, -128, -56, 0, 0, 0, 0, 106, 24, 0, -212, 0, 0, 0, 232, -30, 0, 0, 0, 0, -6, -42, 0, 104, 0, 256, 0, 38, 168, 0, 0, 0, 0, -36, -156, 0, 264, 0, -180, 0, -98, 8, 0, 0, 0, 0, 230, -198, 0, -60, 0, 160, 0, 92, -148, 0, 0, 0, 0, 42, -132, 0, -144, 0, -16, 0, -48, 16, 0, 0, 0, 0, 38, -138, 0, -8, 0, 304, 0, 2, 138, 0, 0, 0, 0, 106, -322, 0, -188, 0, -164, 0, 200, -28, 0, 0, 0, 0, -154, 98, 0, 4, 0, 116, 0, 6, 112, 0, 0, 0, 0, 8, -106, 0, 72, 0, 28, 0, 66, -110, 0, 0, 0, 0, 46, 80, 0, -324, 0, -52, 0, -300, -28, 0, 0, 0, 0, 10, -22, 0, 444, 0, -312, 0, 188, -48, 0, 0, 0, 0, 74, 230, 0, 28, 0, -224, 0, -54, -496, 0, 0, 0, 0, 2, 220, 0, -516], "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, 13, 2, 1, 2, 0], [1, 1, 13, 3, 1, 3, 0], [1, 1, 13, 5, 1, 6, 0]], "char_orbit_index": 10, "prim_orbit_index": 5, "minimal_twist": "507.2.a.i", "char_is_minimal": false, "conrey_index": 316, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [3, 0, 0, 0, -1, 0, 0, -3, 0, -1, 0, 0], [0, 0, 1, 0, 0, 0, -3, 0, 2, 0, 3, 1], [0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 2, 0, 3, 0, -2, 3], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [4, 0, 0, -4, -2, -6, 0, -1, 0, 4, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 2, 2], [4, 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, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 3, 1], [-5, 0, 0, 5, -6, -1, 0, 0, 0, -5, 0, 0], [1, 0, 0, 0, 3, 0, 0, -1, 0, 1, 0, 0], [0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, -2], [0, 1, 1, 0, 0, 0, -3, 0, 0, 0, 0, 0], [0, 7, 2, 0, 0, 0, -8, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 1], [7, 0, 0, 0, 7, 0, 0, -7, 0, 5, 0, 0], [-1, 0, 0, 1, 4, 5, 0, -1, 0, -1, 0, 0], [0, -3, 0, 0, 0, 0, 0, 0, 3, 0, -2, 3], [-4, 0, 0, -2, 0, 3, 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, -1, 0, 0, 0, 0, 0, 0, 1, 0, -2, -2], [-2, 0, 0, 2, 1, 3, 0, 1, 0, -2, 0, 0], [1, 0, 0, 0, -2, 0, 0, -1, 0, 4, 0, 0], [0, 0, -2, 0, 0, 0, 5, 0, 3, 0, -5, -2], [0, 7, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 1, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, -7, 0, 0, -1], [-3, 0, 0, 0, -1, 0, 0, 3, 0, -4, 0, 0], [1, 0, 0, -1, 1, 0, 0, 3, 0, 1, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 8, 1], [3, 0, 0, -5, 0, -4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, -1, 0, -8, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -4, -2], [2, 0, 0, -2, 2, 0, 0, -3, 0, 2, 0, 0], [-3, 0, 0, 0, 4, 0, 0, 3, 0, 2, 0, 0], [0, 0, 3, 0, 0, 0, -4, 0, -7, 0, 4, 3], [0, -2, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, -12, -2, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 3, 0, -1, 0, -3, -1], [0, 0, 0, 0, -6, 0, 0, 0, 0, -5, 0, 0], [-2, 0, 0, 2, -1, 1, 0, -4, 0, -2, 0, 0], [0, -7, 0, 0, 0, 0, 0, 0, 7, 0, -1, -7], [0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 4, 0, 3, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2], [10, 0, 0, -10, 2, -8, 0, -5, 0, 10, 0, 0], [-1, 0, 0, 0, -3, 0, 0, 1, 0, -1, 0, 0], [0, 0, 1, 0, 0, 0, -3, 0, 1, 0, 3, 1], [0, -6, -3, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, -4, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, -8, 0, 7, 0, 8, 2], [3, 0, 0, 0, 1, 0, 0, -3, 0, -5, 0, 0], [-13, 0, 0, 13, -16, -3, 0, 9, 0, -13, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 7, 0, -7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 5, 0, -2, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, -4, 0, -4, 3], [5, 0, 0, -5, 14, 9, 0, -2, 0, 5, 0, 0], [1, 0, 0, 0, 4, 0, 0, -1, 0, -1, 0, 0], [0, 0, -5, 0, 0, 0, 11, 0, -4, 0, -11, -5], [0, -7, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0], [0, -3, -3, 0, 0, 0, -2, 0, 0, 0, 0, 0], [0, 0, -3, 0, 0, 0, 1, 0, 6, 0, -1, -3], [2, 0, 0, 0, 6, 0, 0, -2, 0, 15, 0, 0], [2, 0, 0, -2, 5, 3, 0, -6, 0, 2, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, -2, 0, -8, -1], [-3, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, -5, 0, 6, 3], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [-7, 0, 0, 0, -9, 0, 0, 7, 0, -9, 0, 0], [0, 0, -1, 0, 0, 0, -4, 0, 1, 0, 4, -1], [0, -1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0], [0, 1, -2, 0, 0, 0, -6, 0, 0, 0, 0, 0], [0, 0, -10, 0, 0, 0, -2, 0, -13, 0, 2, -10], [-1, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0], [5, 0, 0, -5, 14, 9, 0, -2, 0, 5, 0, 0], [0, 6, 0, 0, 0, 0, 0, 0, -6, 0, -4, -7], [-3, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 0, 3, 0, -5, -2], [-5, 0, 0, 5, -1, 4, 0, 2, 0, -5, 0, 0], [-10, 0, 0, 0, -5, 0, 0, 10, 0, -4, 0, 0], [0, 0, 0, 0, 0, 0, 5, 0, 7, 0, -5, 0], [0, 12, 10, 0, 0, 0, -9, 0, 0, 0, 0, 0], [0, 5, 9, 0, 0, 0, 5, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0, 2, 0, 1, 0, -2, -2], [-16, 0, 0, 0, -19, 0, 0, 16, 0, -5, 0, 0]]}