# Stored data for newform 495.2.c.d, downloaded from the LMFDB on 03 September 2025.
{"Nk2": 1980, "analytic_conductor": 3.952594900053379, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [495, 2, [56, 397, 46], [2, 1, 2]], "cm_discs": [], "conrey_index": 199, "dim": 6, "field_disc": -350464, "field_disc_factorization": [[-1, 1], [2, 8], [37, 2]], "field_poly": [2, -4, 4, 2, 2, -2, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [25, 0, 31, 0, 11, 0, 1]], [29, [-32, 0, 8, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510936354619887, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "495.2.c.d", "level": 495, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 5, 11], "level_radical": 165, "minimal_twist": "165.2.c.a", "nf_label": "6.0.350464.1", "prim_orbit_index": 2, "qexp_display": "q+(-\\beta _{1}-\\beta _{3}-\\beta _{5})q^{2}+(-2+\\beta _{1}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "495.2.c", "trace_display": [0, 0, -2, 0], "trace_hash": 619810401143940810, "trace_moments": [{"__RealLiteral__": 0, "data": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "5.330", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "169.235", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8139.313", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.513", "prec": 17}, "traces": [0, 6, 0, 0, -10, -2, 0, 0, 0, 0, 16, 6, 0, 0, 4, 0, 10, 0, 0, 4, -14, 0, 0, 0, 0, -2, 16, 0, 0, -16, 0, 16, 0, 0, -52, 12, 0, 0, 0, 0, -12, 16, 0, 0, -10, 0, 24, 0, 0, -22, 16, 0, 0, 0, 0, -2, -76, 0, 0, -16, 0, 4, 0, 0, -66, -28, 0, 0, 0, 0, 24, 24, 0, 0, -16, 0, -36, 0, 0, 12, 58, 0, 0, 0, 0, 44, -4, 0, 0, 4, 0, 16, 0, 0, 24, 44, 0, 0, 0, 0, -2, 80, 0, 0, -96, 0, 0, 0, 0, 12, 16, 0, 0, 0, 0, 0, 32, 0, 0, -24, 0, 6, 0, 0, 8, -26, 0, 0, 0, 0, 84, 8, 0, 0, 88, 0, 20, 0, 0, -4, 60, 0, 0, 0, 0, 24, 0, 0, 0, 8, 0, -28, 0, 0, 4, -32, 0, 0, 0, 0, 64, -64, 0, 0, -32, 0, 8, 0, 0, -106, 0, 0, 0, 0, 0, -40, 10, 0, 0, 24, 0, -20, 0, 0, -72, 24, 0, 0, 0, 0, 56, -32, 0, 0, -32, 0, -14, 0, 0, -24, -104, 0, 0, 0, 0, -24, -96, 0, 0, 4, 0, 92, 0, 0, 40, -12, 0, 0, 0, 0, -14, 24, 0, 0, 60, 0, -120, 0, 0, -20, 8, 0, 0, 0, 0, -40, 136, 0, 0, -8, 0, 44, 0, 0, -76, -22, 0, 0, 0, 0, 32, -32, 0, 0, 36, 0, 10, 0, 0, -64, 76, 0, 0, 0, 0, -16, 0, 0, 0, -108, 0, 44, 0, 0, 32, -2, 0, 0, 0, 0, -64, -64, 0, 0, -80, 0, 16, 0, 0, -42, -24, 0, 0, 0, 0, -56, -80, 0, 0, 48, 0, 64, 0, 0, 156, 52, 0, 0, 0, 0, 16, -8, 0, 0, 64, 0, 20, 0, 0, -16, -22, 0, 0, 0, 0, -72, 64, 0, 0, 48, 0, 0, 0, 0, 80, -64, 0, 0, 0, 0, -68, 16, 0, 0, 76, 0, -36, 0, 0, -4, 52, 0, 0, 0, 0, 0, 28, 0, 0, -32, 0, 102, 0, 0, 168, -36, 0, 0, 0, 0, 40, 104, 0, 0, -52, 0, -56, 0, 0, 40, -84, 0, 0, 0, 0, 12, -72, 0, 0, 12, 0, 32, 0, 0, -92, -12, 0, 0, 0, 0, -30, 108, 0, 0, -128, 0, -64, 0, 0, 76, 24, 0, 0, 0, 0, -12, 216, 0, 0, 120, 0, -28, 0, 0, 184, 8, 0, 0, 0, 0, -24, -56, 0, 0, -40, 0, -180, 0, 0, 140, -12, 0, 0, 0, 0, -28, -160, 0, 0, -84, 0, 16, 0, 0, 48, -64, 0, 0, 0, 0, 80, 72, 0, 0, 0, 0, -108, 0, 0, -16, 64, 0, 0, 0, 0, -124, -160, 0, 0, 104, 0, -16, 0, 0, -10, 16, 0, 0, 0, 0, -88, -16, 0, 0, 344, 0, -96, 0, 0, 64, 106, 0, 0, 0, 0, -8, 24, 0, 0, -180, 0, 160, 0, 0, 24, 40, 0, 0, 0, 0, -60, -68, 0, 0, 56, 0, 40, 0, 0, 42, -96, 0, 0, 0, 0, -68, -120, 0, 0, -22, 0, -44, 0, 0, -156, 28, 0, 0, 0, 0, 16, 112, 0, 0, 24, 0, -44, 0, 0, -16, -172, 0, 0, 0, 0, 56, -140, 0, 0, 24, 0, -36, 0, 0, 64, -32, 0, 0, 0, 0, 24, 32, 0, 0, 192, 0, -132, 0, 0, -80, -104, 0, 0, 0, 0, 48, -88, 0, 0, 144, 0, 36, 0, 0, 156, -2, 0, 0, 0, 0, 64, -176, 0, 0, -52, 0, -76, 0, 0, 32, 24, 0, 0, 0, 0, 22, -128, 0, 0, -80, 0, -152, 0, 0, -88, 36, 0, 0, 0, 0, -92, 92, 0, 0, 96, 0, -64, 0, 0, -16, -160, 0, 0, 0, 0, -56, 0, 0, 0, 8, 0, 76, 0, 0, 40, 72, 0, 0, 0, 0, 40, 4, 0, 0, -40, 0, 158, 0, 0, 80, 176, 0, 0, 0, 0, -64, 224, 0, 0, 88, 0, -8, 0, 0, 0, -28, 0, 0, 0, 0, 136, -56, 0, 0, -66, 0, -112, 0, 0, 36, 72, 0, 0, 0, 0, -28, 40, 0, 0, -16, 0, 144, 0, 0, 212, -80, 0, 0, 0, 0, -68, 24, 0, 0, -176, 0, 88, 0, 0, 100, 40, 0, 0, 0, 0, 32, -56, 0, 0, 64, 0, -88, 0, 0, 112, -52, 0, 0, 0, 0, -80, -8, 0, 0, 112, 0, 120, 0, 0, -180, 24, 0, 0, 0, 0, 32, 208, 0, 0, -112, 0, 24, 0, 0, 6, -104, 0, 0, 0, 0, 24, 104, 0, 0, -80, 0, 200, 0, 0, 64, 160, 0, 0, 0, 0, -16, -136, 0, 0, 24, 0, 52, 0, 0, -16, -56, 0, 0, 0, 0, -24, -64, 0, 0, 272, 0, -216, 0, 0, -52, -20, 0, 0, 0, 0, -92, -36, 0, 0, -184, 0, -46, 0, 0, -204, 118, 0, 0, 0, 0, 12, -32, 0, 0, 104, 0, -152, 0, 0, 96, -60, 0, 0, 0, 0, 52, 272, 0, 0, 12, 0, -64, 0, 0, -48, -140, 0, 0, 0, 0, 58, -44, 0, 0, -192, 0, 40, 0, 0, -256, -16, 0, 0, 0, 0, -24, -52, 0, 0, -80, 0, 72, 0, 0, 160, -108, 0, 0, 0, 0, -16, 112, 0, 0, -48, 0, 204, 0, 0, 124, -136, 0, 0, 0, 0, -48, -48, 0, 0, -124, 0, -292, 0, 0, 40, 44, 0, 0, 0, 0, 56, 0, 0, 0, -368, 0, -4, 0, 0, -24, 160, 0, 0, 0, 0, -80, -216, 0, 0, 232, 0, -90, 0, 0, -292, 76, 0, 0, 0, 0, -112, 248, 0, 0, -120, 0, 252, 0, 0, 4, 30, 0, 0, 0, 0, 76, 144, 0, 0, 64, 0, 64, 0, 0, 120, -24, 0, 0, 0, 0, -132], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0], [-2, 1, 1, 0, 0, -1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 1, 1], [0, 2, 0, 0, 3, 2], [0, 0, 0, 0, 0, 0], [3, -1, 0, 0, -2, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 3, 0], [1, -2, -3, 0, 0, 2], [0, 0, 0, 0, 0, 0], [3, -3, -2, 0, 0, 3], [0, -2, 0, -3, 1, -2], [0, 0, 0, 0, 0, 0], [2, -1, 2, 0, 0, 1], [-3, -1, 1, -1, -2, -4], [0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, -1], [0, 2, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0], [-1, 1, -2, 0, 2, 1], [5, -3, 1, 0, 0, 3], [0, 0, 0, 0, 0, 0], [0, -4, 0, -3, -3, -4], [-2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 1, 0, 0, 0, -1], [0, -4, 0, -3, -4, -4], [0, 0, 0, 0, 0, 0], [-9, 1, 1, 0, 0, -1], [2, 3, 4, 1, 1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 2, 0], [0, -1, 0, -2, -6, -1], [0, 0, 0, 0, 0, 0], [-3, 8, 4, 3, 1, 1], [2, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, 1, -1, -1], [-2, 1, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0], [4, -2, -4, 0, 0, 2], [0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0], [-5, -1, -6, 0, 0, 1], [4, -4, -2, 1, 2, 2], [0, 0, 0, 0, 0, 0], [0, -7, 0, -3, -7, -7], [0, -1, 0, 2, -4, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1], [-15, 3, -1, 0, 0, -3], [0, 0, 0, 0, 0, 0], [0, 4, 0, 2, -2, 4], [-4, 3, 2, 0, 0, -3], [0, 0, 0, 0, 0, 0], [2, -2, 0, 0, 0, 2], [0, -1, 0, -2, 4, -1], [0, 0, 0, 0, 0, 0], [-12, 2, 1, 0, 0, -2], [-6, 6, -2, 3, -3, 4], [0, 0, 0, 0, 0, 0], [0, 4, 0, 4, 0, 4], [0, 7, 0, 3, 5, 7], [0, 0, 0, 0, 0, 0], [5, 2, -1, -2, 4, 6], [4, -1, -2, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, -2, 0, 3, -3, -2], [-2, -2, -2, 0, 0, 2], [0, 0, 0, 0, 0, 0], [-8, 5, 4, 0, 0, -5], [0, 1, 0, -1, 1, 1], [0, 0, 0, 0, 0, 0], [2, 1, 2, 0, 0, -1], [10, 3, -4, 1, 6, 8], [0, 0, 0, 0, 0, 0], [0, -4, 0, -2, 2, -4], [0, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0], [8, 0, 2, 1, -5, 0], [-1, 2, 3, 0, 0, -2], [0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 3, 2], [0, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [2, 5, 8, 0, 0, -5], [0, -6, 0, -4, -4, -6], [0, 0, 0, 0, 0, 0], [6, -2, 2, 0, 0, 2], [6, 1, -4, 4, 2, 1], [0, 0, 0, 0, 0, 0], [0, -2, 0, 0, -4, -2], [0, -2, 0, 5, 2, -2], [0, 0, 0, 0, 0, 0], [0, -8, -1, -4, -6, -6]]}