# Stored data for newform 1950.2.z.j, downloaded from the LMFDB on 16 April 2024.
{"label": "1950.2.z.j", "space_label": "1950.2.z", "level": 1950, "weight": 2, "hecke_orbit": 10, "hecke_orbit_code": 40534114666809246, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1376551498181093460, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [625, 0, -25, 0, 1]], [11, [9, -3, 1]], [17, [4096, 0, -64, 0, 1]]], "qexp_display": "q+(-\\zeta_{12}+\\zeta_{12}^{3})q^{2}+(-\\zeta_{12}+\\zeta_{12}^{3})q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 65, "char_orbit_label": "z", "char_is_real": false, "Nk2": 7800, "analytic_conductor": 15.570828394149675, "hecke_ring_index": 1, "level_radical": 390, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": [1950, 6, [1301, 1327, 301], [6, 3, 4]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 3, 5, 13], "conrey_indexes": [1699, 1849], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.559", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "81.009", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2856.556", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, 6, 0, 0, -20, 0, -2, 0, 0, -10, 0, -20, 0, 0, -2, 0, 4, 0, 0, -8, 0, -8, 0, 0, -32, 0, -2, 0, 0, 4, 0, -12, 0, 0, 12, 0, -8, 0, 0, 36, 0, -32, 0, 0, -2, 0, -10, 0, 0, 24, 0, -4, 0, 0, -4, 0, 12, 0, 0, -8, 0, -4, 0, 0, 14, 0, 10, 0, 0, 8, 0, -2, 0, 0, -10, 0, -24, 0, 0, -22, 0, -70, 0, 0, 6, 0, -4, 0, 0, 12, 0, 16, 0, 0, -10, 0, 2, 0, 0, -56, 0, 14, 0, 0, 10, 0, -16, 0, 0, 80, 0, 4, 0, 0, -4, 0, -10, 0, 0, -24, 0, -76, 0, 0, -16, 0, -16, 0, 0, 14, 0, 6, 0, 0, -4, 0, 0, 0, 0, -4, 0, 88, 0, 0, -30, 0, -10, 0, 0, 2, 0, 80, 0, 0, -24, 0, 16, 0, 0, 2, 0, 10, 0, 0, -16, 0, 6, 0, 0, 8, 0, -8, 0, 0, 8, 0, -4, 0, 0, -10, 0, -4, 0, 0, 0, 0, 72, 0, 0, 44, 0, -16, 0, 0, -16, 0, -14, 0, 0, -60, 0, 30, 0, 0, 12, 0, -4, 0, 0, 0, 0, -112, 0, 0, 10, 0, -32, 0, 0, -56, 0, -30, 0, 0, -10, 0, -24, 0, 0, 72, 0, 50, 0, 0, 4, 0, -24, 0, 0, 16, 0, -30, 0, 0, 42, 0, -2, 0, 0, -140, 0, -16, 0, 0, 6, 0, 50, 0, 0, 8, 0, -8, 0, 0, -48, 0, 8, 0, 0, -4, 0, 72, 0, 0, 4, 0, 42, 0, 0, 94, 0, 0, 0, 0, 72, 0, -14, 0, 0, -16, 0, 60, 0, 0, 20, 0, -16, 0, 0, -14, 0, -48, 0, 0, -30, 0, 4, 0, 0, 24, 0, 12, 0, 0, -4, 0, 80, 0, 0, 30, 0, -8, 0, 0, 46, 0, 10, 0, 0, -32, 0, -12, 0, 0, -12, 0, -20, 0, 0, 16, 0, -10, 0, 0, -24, 0, -44, 0, 0, 72, 0, -12, 0, 0, -20, 0, 4, 0, 0, -24, 0, 10, 0, 0, -48, 0, 12, 0, 0, -50, 0, 42, 0, 0, -2, 0, 48, 0, 0, 128, 0, 128, 0, 0, -6, 0, 6, 0, 0, 50, 0, 38, 0, 0, 32, 0, 40, 0, 0, 50, 0, -48, 0, 0, 8, 0, -14, 0, 0, -24, 0, 48, 0, 0, 4, 0, 4, 0, 0, 42, 0, -24, 0, 0, 40, 0, -28, 0, 0, 20, 0, 72, 0, 0, -14, 0, -6, 0, 0, -54, 0, 36, 0, 0, 0, 0, 20, 0, 0, -16, 0, -16, 0, 0, -8, 0, -28, 0, 0, 160, 0, -30, 0, 0, 4, 0, 160, 0, 0, -56, 0, 28, 0, 0, -4, 0, -4, 0, 0, 80, 0, -42, 0, 0, 50, 0, 4, 0, 0, -16, 0, 46, 0, 0, 10, 0, -48, 0, 0, 20, 0, 0, 0, 0, -56, 0, -12, 0, 0, -20, 0, 20, 0, 0, -38, 0, -30, 0, 0, -14, 0, -24, 0, 0, -44, 0, 16, 0, 0, -108, 0, 136, 0, 0, 16, 0, -20, 0, 0, 4, 0, 80, 0, 0, -60, 0, -14, 0, 0, -84, 0, -48, 0, 0, 12, 0, -20, 0, 0, -30, 0, -132, 0, 0, 60, 0, -2, 0, 0, 48, 0, 80, 0, 0, 0, 0, 36, 0, 0, 20, 0, -6, 0, 0, 6, 0, 4, 0, 0, -136, 0, -74, 0, 0, 44, 0, 32, 0, 0, 40, 0, 30, 0, 0, 12, 0, -60, 0, 0, -68, 0, 8, 0, 0, -14, 0, -12, 0, 0, -224, 0, -24, 0, 0, 46, 0, 4, 0, 0, 4, 0, -54, 0, 0, 40, 0, 80, 0, 0, 144, 0, 40, 0, 0, -28, 0, -12, 0, 0, 72, 0, 20, 0, 0, 32, 0, -14, 0, 0, -6, 0, -24, 0, 0, -28, 0, -44, 0, 0, 0, 0, 0, 0, 0, 20, 0, -110, 0, 0, 10, 0, -34, 0, 0, -64, 0, -8, 0, 0, -28, 0, 0, 0, 0, -6, 0, 32, 0, 0, 64, 0, 4, 0, 0, 160, 0, 16, 0, 0, -40, 0, -70, 0, 0, -4, 0, -4, 0, 0, -4, 0, 96, 0, 0, 16, 0, 16, 0, 0, 38, 0, 50, 0, 0, 4, 0, -152, 0, 0, -120, 0, 16, 0, 0, -56, 0, 10, 0, 0, -48, 0, -18, 0, 0, 4, 0, 112, 0, 0, -68, 0, -56, 0, 0, -12, 0, 0, 0, 0, 120, 0, -24, 0, 0, 36, 0, -38, 0, 0, -30, 0, 80, 0, 0, 100, 0, -44, 0, 0, 48, 0, -44, 0, 0, 16, 0, -8, 0, 0, -52, 0, 100, 0, 0, 84, 0, 16, 0, 0, -20, 0, 44, 0, 0, -28, 0, -120, 0, 0, -32, 0, -60, 0, 0, -14, 0, -30, 0, 0, -28, 0, 26, 0, 0, 60, 0, 12, 0, 0, -20, 0, -56, 0, 0, 20, 0, -12, 0, 0, -12, 0, 60, 0, 0, -2, 0, -64, 0, 0, 12, 0, -32, 0, 0, -40, 0, 0, 0, 0, 36, 0, 30, 0, 0, -32, 0, 12, 0, 0, -420, 0, 6, 0, 0, 4, 0, 20, 0, 0, 16, 0, 16, 0, 0, -16, 0, 44, 0, 0, 32, 0, -80, 0, 0, -60, 0, -28, 0, 0, -4, 0, 12, 0, 0, -60, 0, 16, 0, 0, 4, 0, -360, 0, 0, 48, 0, -14, 0, 0, -12, 0, 0, 0, 0, -48, 0, -36, 0, 0, 0, 0, 46, 0, 0, 4, 0, 36, 0, 0, 120, 0, -108, 0, 0, -50, 0, 40, 0, 0, 80, 0, -30, 0, 0, 148, 0, 8, 0, 0, 66, 0, -28, 0, 0, -12, 0, 64, 0, 0, 96, 0, -20, 0, 0, 20, 0, 32, 0, 0, -14, 0, -150, 0, 0, 30, 0, 44, 0, 0, -28, 0, -28, 0, 0, -44, 0, -42, 0, 0, -48, 0, -76, 0, 0, 2, 0, 20, 0, 0, -110, 0, 100, 0, 0, -18, 0, -70, 0, 0, 8, 0, -64, 0, 0, -8, 0, -20, 0, 0, 42, 0, -64, 0, 0, 64, 0, -6, 0, 0, 32, 0, -80, 0, 0, -50, 0, -84, 0, 0, 108, 0, 160, 0, 0, 16, 0, -8, 0, 0, 80, 0, -24, 0, 0, -16, 0, -4, 0, 0, -4, 0, -68, 0, 0, -12, 0, -24, 0, 0, -150, 0, 16, 0, 0, 16, 0, -40, 0, 0, 60, 0, -48, 0, 0, -30, 0, 4, 0, 0, -152, 0, 120, 0, 0, 36, 0, -144, 0, 0, -6, 0, -56, 0, 0, 10, 0, 8, 0, 0, 256, 0, -200, 0, 0, 12, 0, 4, 0, 0, 112, 0, -116, 0, 0, -4, 0, 188, 0, 0, -20, 0, -12, 0, 0, 0, 0, -6, 0, 0, -460, 0, 212, 0, 0, -36, 0, 36, 0, 0, -38, 0, -100, 0, 0, -28, 0, 40, 0, 0, -48, 0, 100, 0, 0, -44, 0, 40, 0, 0, -84, 0, 8, 0, 0, 120, 0, 16, 0, 0, -8, 0, 50, 0, 0, -116, 0, 10, 0, 0, -8, 0, 84, 0, 0, 16, 0, 50, 0, 0, -44, 0, 28, 0, 0, -56, 0, -28, 0, 0, -120, 0, 0, 0, 0, -24, 0, 110, 0, 0, 108, 0, -14, 0, 0, -30, 0, -60, 0, 0, -66, 0, 0, 0, 0, -4, 0, 60, 0, 0, 12, 0, 24, 0, 0, 252, 0, -24, 0, 0, 192, 0, 20, 0, 0, -12, 0, 176, 0, 0, -22, 0, -82, 0, 0, -6, 0, -2, 0, 0, -64, 0, -88, 0, 0, 40, 0, 54, 0, 0, -240, 0, -40, 0, 0, 0, 0, -30, 0, 0, 60, 0, 220, 0, 0, 8, 0, -32, 0, 0, 12, 0, 156, 0, 0, 64, 0, -46, 0, 0, -70, 0, 4, 0, 0, 20, 0, -64, 0, 0, -20, 0, -480, 0, 0, 44, 0, -16, 0, 0, 44, 0, 78, 0, 0, -24, 0, -120, 0, 0, 24, 0, -60, 0, 0, -28, 0, 12, 0, 0, 60, 0, 104, 0, 0, -10, 0, -60, 0, 0, 16, 0, 24, 0, 0, 96, 0, 32, 0, 0, 120, 0, 48, 0, 0, -14, 0, 70, 0, 0, 164, 0, 128, 0, 0, -80, 0, -48, 0, 0, -36, 0, 144, 0, 0, -22, 0, 16, 0, 0, 32, 0, 4, 0, 0, 36, 0, 36, 0, 0, -68, 0, -114, 0, 0, -24, 0, -50, 0, 0, 40, 0, -4, 0, 0, 22, 0, 50, 0, 0, 42, 0, 148, 0, 0, 8, 0, -86, 0, 0, -112, 0, 80, 0, 0, -96, 0, -12, 0, 0, 64, 0, -60, 0, 0, -10, 0, -32, 0, 0, 92, 0, 20, 0, 0, 32, 0, -96, 0, 0, 90, 0, -20, 0, 0, 6, 0, 30, 0, 0, 44, 0, 12, 0, 0, -34, 0, -100, 0, 0, -72, 0, -44, 0, 0, -42, 0, 280, 0, 0, 84, 0, 24, 0, 0, -120, 0, 2, 0, 0, 20, 0, 64, 0, 0, -48, 0, -4, 0, 0, 140, 0, -18, 0, 0, -70, 0, 64, 0, 0, 64, 0, 60, 0, 0, 64, 0, -8, 0, 0, -20, 0, -26, 0, 0, -112, 0, 6, 0, 0, 2, 0, 64, 0, 0, -6, 0, 20, 0, 0, 0, 0, -168, 0, 0, -40, 0, -50, 0, 0, -84, 0, -134, 0, 0, 76, 0, 0, 0, 0, -52, 0, 16, 0, 0, -8, 0, 16, 0, 0, 78, 0, 28, 0, 0, 80, 0, -16, 0, 0, -4, 0, -140, 0, 0, 60, 0, -50, 0, 0, -24, 0, -12, 0, 0, -24, 0, 140, 0, 0, 0, 0, 84, 0, 0, -12, 0, 16, 0, 0, -40, 0, 132, 0, 0, -4, 0, -288, 0, 0, 48, 0, -30, 0, 0, 4, 0, -48, 0, 0, 0, 0, 10, 0, 0, 24, 0, 36, 0, 0, -144, 0, 220, 0, 0, -20, 0, 2, 0, 0, 0, 0, 10, 0, 0, 8, 0, -52, 0, 0, -108, 0, -192, 0, 0, -76, 0, 12, 0, 0, 4, 0, 204, 0, 0, -48, 0, -48, 0, 0, 100, 0, -4, 0, 0, 188, 0, 20, 0, 0, 42, 0, 136, 0, 0, 28, 0, 0, 0, 0, -6, 0, -112, 0, 0, -216, 0, 40, 0, 0, -24, 0, -36, 0, 0, 36, 0, 60, 0, 0, 32, 0, 120, 0, 0, -82, 0, -28, 0, 0, 40, 0, -168, 0, 0, 6, 0, -60, 0, 0, -24, 0, -44, 0, 0, 40, 0, 54, 0, 0, 560, 0, 44, 0, 0, -36, 0, 120, 0, 0, 16, 0, -8, 0, 0, -20, 0, 0, 0, 0, -192, 0, -116, 0, 0, 10, 0, -48, 0, 0, -48, 0, -16, 0, 0, 380, 0, 16, 0, 0, 50, 0, 300, 0, 0, 16, 0, 20, 0, 0, -14, 0, -56, 0, 0, -28, 0, 8, 0, 0, 138, 0, 56, 0, 0, -56, 0, -24, 0, 0, 110, 0, 264, 0, 0, -60, 0, 80, 0, 0, 60, 0, -30, 0, 0, -60, 0, 96, 0, 0, -2, 0, 8, 0, 0, -116, 0, -4, 0, 0, 60, 0, -96, 0, 0, 80, 0, 216, 0, 0, -64, 0, 252, 0, 0, -24, 0, -112, 0, 0, -160, 0, 128, 0, 0, -70, 0, -12, 0, 0, 176, 0, 150, 0, 0, 62, 0, -8, 0, 0, 150, 0, -6, 0, 0, -2, 0, -70, 0, 0, -72, 0, 56, 0, 0, -40, 0, 40, 0, 0, 54, 0, 14, 0, 0, -84, 0, 46, 0, 0, -24, 0, 0, 0, 0, -30, 0, 70, 0, 0, -56, 0, 200, 0, 0, 8, 0, 8, 0, 0, -32, 0, -12, 0, 0, -4, 0, -8, 0, 0, 40, 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, 65, 14, 1, 6, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 13, 3, 1, 3, 0]], "char_orbit_index": 26, "prim_orbit_index": 14, "minimal_twist": "390.2.i.d", "char_is_minimal": false, "conrey_index": 1699, "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], [1, 0, 0, 0], [0, -1, 0, 1], [0, -1, 0, 1], [1, 0, -1, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 5, 0, 0], [0, 0, 0, 1], [1, 0, -1, 0], [0, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 1], [0, -3, 0, 4], [-5, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 8, 0, 0], [0, 0, 0, 1], [-5, 0, 5, 0], [0, 0, 0, 0], [-5, 0, 0, 0], [0, -3, 0, 0], [0, 4, 0, -4], [0, 0, -1, 0], [0, 0, 0, 0], [3, 0, -4, 0], [0, 0, 0, 1], [0, 5, 0, -5], [0, 0, -4, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 1, 0, 0], [0, -3, 0, 0], [-8, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, -7, 0, 7], [0, 0, 0, -5], [3, 0, -4, 0], [0, 0, 0, 0], [0, 0, -6, 0], [0, 5, 0, -5], [0, 6, 0, 0], [3, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 4, 0], [0, 0, 0, -3], [0, 1, 0, 0], [0, 0, 18, 0], [0, 0, 0, 0], [-8, 0, 0, 0], [0, 1, 0, 3], [0, 0, 0, -1], [0, 0, -1, 0], [0, 0, 0, 0], [-5, 0, 5, 0], [0, 0, 0, -5], [0, 4, 0, 0], [12, 0, -12, 0], [0, 0, 0, 0], [-2, 0, 2, 0], [0, 2, 0, -2], [0, 5, 0, -5], [-1, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, 8, 0, -8], [0, 8, 0, -8], [-4, 0, 4, 0], [0, 0, 0, 0], [-2, 0, 2, 0], [0, 1, 0, 0], [0, 0, 0, 0], [7, 0, -7, 0], [0, 0, 0, 0], [0, 0, 5, 0], [0, 0, 0, 15], [0, 1, 0, 3], [2, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 6, 0, 0], [0, 0, 0, -8], [-5, 0, 5, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 4, 0, 0], [0, -3, 0, 3], [0, 0, -11, 0], [0, 0, 0, 0], [-20, 0, 5, 0], [0, 0, 0, -4], [0, 2, 0, -2], [0, 0, 3, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, -18, 0, 0], [3, 0, 0, 0], [0, 0, 0, 0]]}