# Stored data for newform 1150.2.b.j, downloaded from the LMFDB on 23 April 2024.
{"label": "1150.2.b.j", "space_label": "1150.2.b", "level": 1150, "weight": 2, "hecke_orbit": 10, "hecke_orbit_code": 40532465399366782, "dim": 6, "is_polredabs": true, "nf_label": "6.0.77580864.1", "trace_hash": 845860524607268782, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [144, 0, 105, 0, 19, 0, 1]], [7, [4096, 0, 825, 0, 51, 0, 1]], [11, [144, -39, -3, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+\\beta _{1}q^{3}-q^{4}-\\beta _{3}q^{6}+(\\beta _{1}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "b", "char_is_real": true, "Nk2": 4600, "analytic_conductor": 9.182796232447243, "hecke_ring_index": 1, "level_radical": 230, "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": "0.512", "prec": 17}, "analytic_rank_proved": true, "char_values": [1150, 2, [277, 51], [1, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 5, 23], "conrey_indexes": [599], "field_disc": -77580864, "field_disc_factorization": [[-1, 1], [2, 6], [3, 2], [367, 2]], "field_poly": [144, 0, 105, 0, 19, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.521", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "169.385", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7825.266", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 6, 0, 0, -6, 0, 2, 0, 0, -20, 0, 6, 0, 0, -6, 0, 6, 0, 0, -6, 0, -44, 0, 0, -2, 0, -2, 0, 0, 8, 0, -10, 0, 0, 14, 0, 20, 0, 0, -28, 0, 2, 0, 0, -6, 0, -6, 0, 0, -60, 0, -42, 0, 0, 28, 0, 6, 0, 0, -28, 0, 2, 0, 0, -6, 0, -18, 0, 0, 2, 0, 22, 0, 0, 4, 0, 6, 0, 0, 8, 0, 14, 0, 0, 44, 0, 48, 0, 0, -36, 0, 2, 0, 0, 28, 0, 2, 0, 0, -114, 0, -8, 0, 0, 2, 0, -36, 0, 0, 30, 0, 16, 0, 0, 44, 0, -8, 0, 0, -32, 0, 108, 0, 0, 10, 0, 16, 0, 0, -16, 0, 0, 0, 0, -16, 0, -14, 0, 0, 12, 0, 48, 0, 0, -20, 0, -16, 0, 0, 18, 0, -18, 0, 0, 48, 0, 28, 0, 0, 12, 0, -6, 0, 0, -2, 0, 16, 0, 0, 16, 0, 16, 0, 0, -72, 0, 6, 0, 0, 12, 0, -6, 0, 0, 6, 0, -32, 0, 0, 170, 0, 12, 0, 0, 66, 0, 60, 0, 0, 56, 0, 40, 0, 0, 42, 0, 54, 0, 0, 48, 0, 24, 0, 0, -28, 0, -28, 0, 0, -52, 0, -24, 0, 0, -6, 0, -36, 0, 0, 20, 0, -306, 0, 0, 68, 0, 28, 0, 0, 24, 0, -60, 0, 0, -2, 0, -54, 0, 0, 12, 0, -70, 0, 0, -36, 0, 6, 0, 0, 104, 0, -84, 0, 0, 18, 0, 102, 0, 0, -48, 0, 14, 0, 0, 18, 0, -2, 0, 0, -28, 0, -24, 0, 0, -22, 0, -96, 0, 0, 32, 0, -134, 0, 0, 0, 0, -4, 0, 0, -2, 0, 48, 0, 0, -6, 0, -18, 0, 0, 2, 0, 32, 0, 0, -56, 0, -8, 0, 0, 48, 0, 216, 0, 0, -14, 0, 2, 0, 0, 20, 0, 44, 0, 0, -56, 0, -44, 0, 0, 12, 0, 84, 0, 0, -48, 0, -58, 0, 0, -60, 0, 34, 0, 0, -84, 0, 36, 0, 0, -160, 0, -12, 0, 0, -2, 0, -2, 0, 0, 30, 0, -36, 0, 0, -6, 0, -28, 0, 0, 78, 0, 52, 0, 0, -2, 0, 16, 0, 0, 90, 0, 14, 0, 0, 46, 0, 114, 0, 0, -14, 0, 112, 0, 0, 8, 0, -100, 0, 0, -130, 0, -144, 0, 0, 20, 0, -2, 0, 0, 24, 0, 26, 0, 0, 36, 0, -30, 0, 0, 6, 0, 92, 0, 0, 14, 0, -30, 0, 0, 98, 0, 294, 0, 0, -16, 0, -8, 0, 0, -86, 0, -126, 0, 0, 28, 0, -44, 0, 0, 18, 0, -24, 0, 0, 8, 0, -40, 0, 0, 184, 0, -56, 0, 0, -112, 0, 32, 0, 0, 16, 0, -64, 0, 0, -108, 0, -52, 0, 0, -64, 0, 36, 0, 0, -2, 0, -10, 0, 0, 80, 0, -96, 0, 0, -16, 0, -6, 0, 0, 96, 0, -8, 0, 0, 8, 0, 16, 0, 0, 114, 0, 52, 0, 0, 0, 0, -62, 0, 0, -6, 0, 36, 0, 0, -144, 0, 16, 0, 0, -228, 0, 44, 0, 0, 14, 0, 170, 0, 0, -166, 0, -100, 0, 0, 4, 0, -12, 0, 0, 16, 0, -96, 0, 0, -48, 0, 88, 0, 0, 12, 0, 86, 0, 0, -148, 0, 20, 0, 0, 236, 0, 116, 0, 0, 16, 0, -36, 0, 0, 14, 0, 114, 0, 0, -6, 0, -18, 0, 0, -34, 0, -46, 0, 0, 18, 0, 72, 0, 0, -156, 0, 132, 0, 0, 2, 0, -48, 0, 0, -74, 0, 28, 0, 0, -28, 0, 2, 0, 0, 8, 0, 28, 0, 0, 18, 0, -12, 0, 0, -102, 0, -12, 0, 0, 6, 0, 32, 0, 0, 12, 0, -82, 0, 0, 56, 0, 2, 0, 0, -56, 0, 178, 0, 0, -16, 0, 52, 0, 0, 152, 0, 318, 0, 0, 2, 0, -16, 0, 0, -72, 0, -216, 0, 0, -16, 0, -36, 0, 0, -12, 0, -84, 0, 0, -50, 0, 72, 0, 0, -228, 0, -26, 0, 0, -6, 0, -84, 0, 0, -14, 0, -272, 0, 0, -54, 0, -12, 0, 0, 142, 0, 0, 0, 0, 6, 0, 122, 0, 0, 28, 0, -112, 0, 0, 40, 0, -6, 0, 0, 48, 0, 170, 0, 0, 32, 0, 16, 0, 0, 148, 0, 4, 0, 0, -60, 0, -170, 0, 0, -18, 0, 42, 0, 0, -12, 0, 0, 0, 0, -52, 0, -60, 0, 0, -160, 0, -66, 0, 0, -148, 0, 42, 0, 0, -60, 0, 132, 0, 0, 150, 0, -36, 0, 0, 110, 0, -56, 0, 0, -8, 0, -60, 0, 0, -40, 0, -58, 0, 0, -94, 0, -76, 0, 0, -144, 0, -42, 0, 0, 202, 0, -20, 0, 0, -54, 0, -64, 0, 0, -4, 0, -116, 0, 0, 44, 0, -48, 0, 0, -116, 0, -14, 0, 0, -24, 0, -216, 0, 0, -196, 0, 4, 0, 0, 152, 0, 28, 0, 0, -236, 0, 150, 0, 0, 28, 0, 110, 0, 0, 384, 0, -136, 0, 0, 6, 0, 52, 0, 0, 12, 0, 12, 0, 0, 24, 0, -42, 0, 0, -144, 0, 168, 0, 0, 144, 0, 6, 0, 0, 44, 0, 84, 0, 0, 36, 0, 106, 0, 0, 84, 0, -196, 0, 0, -44, 0, -20, 0, 0, -56, 0, -302, 0, 0, 306, 0, 176, 0, 0, 124, 0, 6, 0, 0, -20, 0, -68, 0, 0, 80, 0, -14, 0, 0, -28, 0, 48, 0, 0, -128, 0, -12, 0, 0, 120, 0, -24, 0, 0, -270, 0, -108, 0, 0, 60, 0, 44, 0, 0, -54, 0, 162, 0, 0, 140, 0, 2, 0, 0, 192, 0, -104, 0, 0, 54, 0, -56, 0, 0, 48, 0, 114, 0, 0, -68, 0, -12, 0, 0, -136, 0, -246, 0, 0, 70, 0, 102, 0, 0, -8, 0, 160, 0, 0, 60, 0, 36, 0, 0, -24, 0, 160, 0, 0, -6, 0, -170, 0, 0, 394, 0, -140, 0, 0, 216, 0, -104, 0, 0, -14, 0, 54, 0, 0, 84, 0, 0, 0, 0, -40, 0, -120, 0, 0, -52, 0, -18, 0, 0, -24, 0, -148, 0, 0, -102, 0, 36, 0, 0, 66, 0, 270, 0, 0, 96, 0, 48, 0, 0, -60, 0, 28, 0, 0, -14, 0, 136, 0, 0, -176, 0, 82, 0, 0, -6, 0, -18, 0, 0, -148, 0, 136, 0, 0, 2, 0, 8, 0, 0, 74, 0, -48, 0, 0, 108, 0, 28, 0, 0, -28, 0, -64, 0, 0, 24, 0, 64, 0, 0, -82, 0, -204, 0, 0, -148, 0, 22, 0, 0, 72, 0, -194, 0, 0, 96, 0, 228, 0, 0, 0, 0, 30, 0, 0, 52, 0, -32, 0, 0, 152, 0, -224, 0, 0, 134, 0, -36, 0, 0, -40, 0, 304, 0, 0, 14, 0, 0, 0, 0, 180, 0, -4, 0, 0, 4, 0, -64, 0, 0, 112, 0, 58, 0, 0, -148, 0, 2, 0, 0, 84, 0, 144, 0, 0, -48, 0, 184, 0, 0, 22, 0, -20, 0, 0, 48, 0, 6, 0, 0, -36, 0, 312, 0, 0, 18, 0, -108, 0, 0, 158, 0, 70, 0, 0, -66, 0, -2, 0, 0, 108, 0, -20, 0, 0, -32, 0, -48, 0, 0, -84, 0, 148, 0, 0, 306, 0, 56, 0, 0, 0, 0, -64, 0, 0, 8, 0, -44, 0, 0, -180, 0, -40, 0, 0, 114, 0, -48, 0, 0, 48, 0, -490, 0, 0, -216, 0, -100, 0, 0, -78, 0, 148, 0, 0, -8, 0, 14, 0, 0, -232, 0, 156, 0, 0, -2, 0, -2, 0, 0, -402, 0, 44, 0, 0, 176, 0, -20, 0, 0, -200, 0, 232, 0, 0, -44, 0, 18, 0, 0, 192, 0, -240, 0, 0, -8, 0, 56, 0, 0, 112, 0, -72, 0, 0, 44, 0, 36, 0, 0, -68, 0, 392, 0, 0, 36, 0, -12, 0, 0, 146, 0, 36, 0, 0, -84, 0, 82, 0, 0, 54, 0, -284, 0, 0, -28, 0, 48, 0, 0, 284, 0, -168, 0, 0, 58, 0, 102, 0, 0, -76, 0, 228, 0, 0, -50, 0, 60, 0, 0, 232, 0, -252, 0, 0, -34, 0, -104, 0, 0, -70, 0, -20, 0, 0, 100, 0, 84, 0, 0, 144, 0, -120, 0, 0, -36, 0, 10, 0, 0, -152, 0, 168, 0, 0, 192, 0, 160, 0, 0, -214, 0, -228, 0, 0, 12, 0, 112, 0, 0, 16, 0, 104, 0, 0, 82, 0, 2, 0, 0, 210, 0, 28, 0, 0, 2, 0, 92, 0, 0, -12, 0, -88, 0, 0, -312, 0, -30, 0, 0, 36, 0, -174, 0, 0, 36, 0, 46, 0, 0, 24, 0, -210, 0, 0, 12, 0, 6, 0, 0, 36, 0, 8, 0, 0, 28, 0, -276, 0, 0, 12, 0, 90, 0, 0, -108, 0, -78, 0, 0, 6, 0, -90, 0, 0, -52, 0, 66, 0, 0, -324, 0, -40, 0, 0, -48, 0, 2, 0, 0, -148, 0, -16, 0, 0, -16, 0, -52, 0, 0, -136, 0, 60, 0, 0, 184, 0, -90, 0, 0, 134, 0, 176, 0, 0, -14, 0, 204, 0, 0, -52, 0, 158, 0, 0, -92, 0, -46, 0, 0, -58, 0, 66, 0, 0, -114, 0, -160, 0, 0, -148, 0, -32, 0, 0, -72, 0, 14, 0, 0, -210, 0, 16, 0, 0, -112, 0, -204, 0, 0, 4, 0, -48, 0, 0, 24, 0, -8, 0, 0, -148, 0, 46, 0, 0, 100, 0, 160, 0, 0, 8, 0, -416, 0, 0, -48, 0, 130, 0, 0, 180, 0, 88, 0, 0, 144, 0, 96, 0, 0, -266, 0, 176, 0, 0, -212, 0, -20, 0, 0, -680, 0, -78, 0, 0, 2, 0, -120, 0, 0, -324, 0, -168, 0, 0, -22, 0, -24, 0, 0, -16, 0, -8, 0, 0, -26, 0, -48, 0, 0, 48, 0, -48, 0, 0, -120, 0, -36, 0, 0, 26, 0, 106, 0, 0, 30, 0, 106, 0, 0, 102, 0, 112, 0, 0, 12, 0, -6, 0, 0, 132, 0, -180, 0, 0, -92, 0, -12, 0, 0, 128, 0, 52, 0, 0, -110, 0, -14, 0, 0, 112, 0, 88, 0, 0, 30, 0, -134, 0, 0, -108, 0, -106, 0, 0, 166, 0, -98, 0, 0, 64, 0, 366, 0, 0, -294, 0, 62, 0, 0, 8, 0, 48, 0, 0, 0, 0, 16, 0, 0, -36, 0, 18, 0, 0, 8, 0, -20, 0, 0, -184, 0, -236, 0, 0, 28, 0, 86, 0, 0, 16, 0, -420, 0, 0, 126, 0, -352, 0, 0, -160, 0, 6, 0, 0, 100, 0, -28, 0, 0, 272, 0, 352, 0, 0, 44, 0, -132, 0, 0, 104, 0, -112, 0, 0, 84, 0, -18, 0, 0, -148, 0, 176, 0, 0, 24, 0, -36, 0, 0, -126, 0, 318, 0, 0, -274, 0, -8, 0, 0, 144, 0, -92, 0, 0, 40, 0, -24, 0, 0, -144, 0, 78, 0, 0, -22, 0, -184, 0, 0, 198, 0, 102, 0, 0, 56, 0, -2, 0, 0, -150, 0, 156, 0, 0, 42, 0, 112, 0, 0, 116, 0, -20, 0, 0, -32, 0, 6, 0, 0, 16, 0, 246, 0, 0, -300, 0, -16, 0, 0, 100, 0, 84, 0, 0, 64, 0, -144, 0, 0, -208, 0, -94, 0, 0, 4, 0, 108, 0, 0, 20, 0, -60, 0, 0, 52, 0, -120, 0, 0, 30, 0, 60, 0, 0, -10, 0, 64, 0, 0, -132, 0, 24, 0, 0, -36, 0, 6, 0, 0, 120, 0, 124, 0, 0, -516, 0, 2, 0, 0, 176, 0, -196, 0, 0, 10, 0, -140, 0, 0, -18, 0, 156, 0, 0, -108, 0, -80, 0, 0, -36, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "230.2.a.d", "char_is_minimal": false, "conrey_index": 599, "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], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 1, 1, 0, -1, 0], [0, 0, -1, 0, 0, 0], [-4, 0, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0], [2, 0, 0, 1, 0, -2], [0, -1, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0], [-1, 0, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, -2, 0, 0, 0], [0, -1, -4, 0, -1, 0], [-1, 0, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0], [-9, 0, 0, -2, 0, 3], [0, 1, 2, 0, 2, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 1], [0, -2, -5, 0, 1, 0], [0, -1, -1, 0, 1, 0], [2, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, 0, -1], [0, 0, 1, 0, 0, 0], [0, 3, 3, 0, -3, 0], [2, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0], [4, 0, 0, 1, 0, -1], [0, 0, 0, 0, 2, 0], [0, -1, -1, 0, 1, 0], [-5, 0, 0, -2, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 2], [0, -2, -9, 0, -3, 0], [0, 0, -8, 0, 0, 0], [-2, 0, 0, -1, 0, 2], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, -2, -6, 0, -2, 0], [0, 1, 0, 0, 0, 0], [-11, 0, 0, -1, 0, 2], [0, 0, 0, 0, 0, 0], [-7, 0, 0, 1, 0, 1], [0, -1, -1, 0, -1, 0], [0, 0, 6, 0, 0, 0], [5, 0, 0, 2, 0, 1], [0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 1], [0, -2, -9, 0, -3, 0], [0, 2, 2, 0, 0, 0], [-4, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, 0, 1, 0, -4], [0, 1, -1, 0, 1, 0], [0, -8, -5, 0, 1, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-3, 0, 0, -3, 0, -3], [0, 0, 4, 0, 4, 0], [0, -1, 2, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0], [4, 0, 0, 1, 0, 0], [0, 1, 4, 0, 1, 0], [0, 2, 4, 0, 2, 0], [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 1], [0, 8, -5, 0, 1, 0], [0, -2, -5, 0, 1, 0], [4, 0, 0, 4, 0, -4], [0, 0, 0, 0, 0, 0], [4, 0, 0, 4, 0, -1], [0, 1, 0, 0, -2, 0], [0, 0, -2, 0, 2, 0], [9, 0, 0, 2, 0, -3], [0, 0, 0, 0, 0, 0], [8, 0, 0, 0, 0, 0], [0, 4, 14, 0, 2, 0], [0, -1, -2, 0, -2, 0], [-4, 0, 0, 4, 0, -2], [0, 0, 0, 0, 0, 0], [-2, 0, 0, -5, 0, 2], [0, 0, -1, 0, 0, 0], [0, 0, 5, 0, -1, 0], [6, 0, 0, 2, 0, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 3, -10, 0, 0, 0], [0, -1, -11, 0, -2, 0], [-21, 0, 0, -3, 0, 3], [0, 0, 0, 0, 0, 0]]}