# Stored data for newform 675.2.f.g, downloaded from the LMFDB on 14 December 2025.
{"Nk2": 2700, "analytic_conductor": 5.389902136436426, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 15, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 4, "char_parity": 1, "char_values": [675, 4, [326, 352], [2, 1]], "cm_discs": [], "conrey_index": 107, "dim": 8, "field_disc": 33973862400, "field_disc_factorization": [[2, 24], [3, 4], [5, 2]], "field_poly": [100, 0, 0, 0, 44, 0, 0, 0, 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, [100, 0, 0, 0, 44, 0, 0, 0, 1]], [7, [1, -4, 8, 4, 1]], [29, [2250, 0, -96, 0, 1]]], "hecke_orbit": 7, "hecke_orbit_code": 27021941395161763, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 5, 3, -1, 4, 0], [1, 1, 15, 5, 1, 4, 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": "675.2.f.g", "level": 675, "level_is_powerful": true, "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], "level_radical": 15, "minimal_twist": "135.2.f.b", "nf_label": "8.0.33973862400.8", "prim_orbit_index": 5, "qexp_display": "q+\\beta _{1}q^{2}+(2\\beta _{2}+\\beta _{4}+\\beta _{5})q^{4}+(-1+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "675.2.f", "trace_display": [0, 0, 0, -8], "trace_hash": 1062876238425039776, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.532", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "367.174", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "26054.081", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.628", "prec": 17}, "traces": [0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -40, 0, 0, 16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -8, 0, 0, -32, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 72, 0, 0, -8, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -8, 0, 0, 48, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, -48, 0, 0, -8, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -8, 0, 0, 64, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 24, 0, 0, -96, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 104, 0, 0, -104, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -56, 0, 0, 16, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -96, 0, 0, -8, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -56, 0, 0, 64, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 16, 0, 0, 40, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 88, 0, 0, 160, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -32, 0, 0, -104, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 8, 0, 0, -160, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 104, 0, 0, 40, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 40, 0, 0, 80, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 48, 0, 0, 64, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -192, 0, 0, 136, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -24, 0, 0, -224, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -72, 0, 0, 80, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -80, 0, 0, -192, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 56, 0, 0, 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 104, 0, 0, -192, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, -24, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 184, 0, 0, 144, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, -80, 0, 0, 208, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 168, 0, 0, -8, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, -96, 0, 0, 256, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, -112, 0, 0, -56, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -128, 0, 0, -128, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 96, 0, 0, 40, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 96, 0, 0, -104, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 104, 0, 0, -272, 0, 0, 0, 0, 0, -176, 0, 0, 0, 0, 0, -40, 0, 0, -224, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 64, 0, 0, 48, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -16, 0, 0, -104, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -56, 0, 0, -48, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, -224, 0, 0, -104, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, -104, 0, 0, 224, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 112, 0, 0, -32, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -48, 0, 0, 16, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 24, 0, 0, 184, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, -56, 0, 0, 64, 0, 0, 0, 0, 0, -232, 0, 0, 0, 0, 0, 16, 0, 0, 184, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 72, 0, 0, 64, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 240, 0, 0, -112, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, -16, 0, 0, -192, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -48, 0, 0, -80, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 64, 0, 0, -240, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, -48, 0, 0, 152, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 160, 0, 0, -240, 0, 0, 0, 0, 0, -280, 0, 0, 0, 0, 0, 208, 0, 0, 136, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -200, 0, 0, 352, 0, 0, 0, 0, 0, -272, 0, 0, 0, 0, 0, -288, 0, 0, 208, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 56, 0, 0, -144, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, -144, 0, 0, 48, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -88, 0, 0, 80, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, -120, 0, 0, 216, 0, 0, 0, 0, 0, 232, 0, 0, 0, 0, 0, 144, 0, 0, 16, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 24, 0, 0, -296, 0, 0, 0, 0, 0, 40, 0, 0, 0], "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, 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, 2, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 2, 0, 0, 1, 1], [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, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, -1, 0, 0], [0, -2, 0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 2, -2, 0, 0], [0, 0, 0, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 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, 2, 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, 1, 0, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, -5, 0, 0, -4, 0, 0], [0, 2, 0, -2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 3, -3, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -2, 0, -3, 0, 0, 0], [0, 0, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 3, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, -2, 0, 0], [0, -1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 1, -1, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, -2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 2, 0, 0, 0], [0, 0, 0, -3, 0, 0, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, -5, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 9, 0, 0, 2, 0, 0], [0, 1, 0, -1, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 0, 0, 0, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, -5, 0, -1, 0, 0, 0], [0, 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, -3, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 3, 0, 0], [0, 5, 0, -5, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, -3, 3, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-11, 0, 11, 0, 8, 0, 0, 0], [0, 0, 0, -1, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, -3, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, -6, 0, 0, 2, 0, 0], [0, -3, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, -1, 0, 0], [0, -4, 0, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 16, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 4, 0, -5, 0, 0, 0], [0, 0, 0, -2, 0, 0, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}