# Stored data for newform 637.2.f.l, downloaded from the LMFDB on 06 December 2024.
{"Nk2": 2548, "analytic_conductor": 5.086470608755561, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 3, "char_parity": 1, "char_values": [637, 3, [248, 197], [3, 2]], "cm_discs": [], "conrey_index": 295, "dim": 16, "field_disc": 468066644398978174550016, "field_disc_factorization": [[2, 32], [3, 8], [359, 4]], "field_poly": [1, 0, 14, 0, 177, 0, 250, 0, 248, 0, 124, 0, 45, 0, 8, 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, [25, -60, 119, -80, 54, -14, 9, -2, 1]], [3, [2401, 0, 5880, 0, 11117, 0, 6668, 0, 2760, 0, 698, 0, 129, 0, 14, 0, 1]], [5, [1, 0, -12, 0, 31, 0, -14, 0, 1]]], "hecke_orbit": 12, "hecke_orbit_code": 49539939532014205, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0], [1, 1, 13, 3, 1, 3, 0], [1, 1, 91, 14, -1, 6, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "637.2.f.l", "level": 637, "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": [7, 13], "level_radical": 91, "minimal_twist": "637.2.f.l", "nf_label": "16.0.468066644398978174550016.2", "prim_orbit_index": 3, "qexp_display": "q+(1+\\beta _{4}+\\beta _{10})q^{2}+(\\beta _{8}-\\beta _{15})q^{3}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "637.2.f", "trace_display": [4, 0, 0, 0], "trace_hash": 496416794359515961, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.769", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1419.203", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "260119.941", "prec": 34}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.510", "prec": 17}, "traces": [0, 16, 4, 0, -12, 0, 0, 0, 24, -4, 0, -4, 0, 0, 0, -8, -4, 0, -56, 0, 0, 0, 28, 12, 0, -24, 0, 0, 0, 8, 28, 0, 0, 0, 0, 0, 4, -8, 0, -4, 0, 0, 0, 32, -8, 0, -4, 0, 0, 0, 36, -88, 0, -8, 0, 0, 0, -96, -48, 0, 128, 0, 0, 0, -64, 16, 0, 20, 0, 0, 0, 8, 28, 0, 76, 0, 0, 0, 28, -8, 0, 56, 0, 0, 0, 36, 8, 0, 28, 0, 0, 0, -160, 8, 0, 52, 0, 0, 0, 56, -12, 0, -80, 0, 0, 0, -4, -8, 0, -72, 0, 0, 0, -4, -64, 0, 8, 0, 0, 0, 68, 60, 0, -24, 0, 0, 0, 24, 4, 0, -112, 0, 0, 0, 24, 8, 0, 20, 0, 0, 0, -16, 152, 0, -48, 0, 0, 0, -168, 4, 0, 80, 0, 0, 0, -32, 32, 0, -84, 0, 0, 0, -116, 32, 0, -28, 0, 0, 0, -68, 152, 0, 128, 0, 0, 0, 24, 168, 0, 60, 0, 0, 0, -24, -28, 0, 4, 0, 0, 0, 200, -24, 0, -64, 0, 0, 0, -36, 4, 0, -248, 0, 0, 0, 112, 8, 0, -8, 0, 0, 0, 52, -32, 0, -24, 0, 0, 0, 32, -92, 0, 24, 0, 0, 0, -36, -240, 0, 156, 0, 0, 0, -104, -104, 0, -128, 0, 0, 0, 40, -16, 0, 80, 0, 0, 0, 112, 56, 0, -4, 0, 0, 0, 4, -124, 0, 100, 0, 0, 0, -120, -96, 0, 144, 0, 0, 0, 0, -24, 0, -4, 0, 0, 0, 80, -36, 0, 20, 0, 0, 0, -16, 24, 0, -68, 0, 0, 0, -24, 20, 0, -112, 0, 0, 0, -36, 64, 0, 360, 0, 0, 0, 112, -4, 0, -68, 0, 0, 0, 44, -48, 0, -180, 0, 0, 0, 80, 200, 0, 48, 0, 0, 0, -120, -24, 0, -136, 0, 0, 0, -160, -28, 0, 152, 0, 0, 0, 192, -224, 0, 124, 0, 0, 0, 76, 120, 0, 92, 0, 0, 0, -4, 48, 0, 152, 0, 0, 0, 24, -112, 0, -36, 0, 0, 0, -72, 40, 0, 44, 0, 0, 0, -48, -48, 0, -84, 0, 0, 0, 168, 180, 0, -328, 0, 0, 0, 140, 4, 0, -160, 0, 0, 0, 28, -56, 0, -84, 0, 0, 0, -8, -28, 0, -108, 0, 0, 0, -76, 56, 0, -40, 0, 0, 0, -104, -104, 0, -40, 0, 0, 0, -112, 176, 0, 64, 0, 0, 0, 232, -28, 0, 24, 0, 0, 0, 108, 12, 0, 48, 0, 0, 0, -124, -224, 0, -124, 0, 0, 0, 120, 24, 0, -52, 0, 0, 0, 104, 128, 0, -52, 0, 0, 0, -24, 76, 0, -88, 0, 0, 0, -60, 28, 0, -8, 0, 0, 0, 4, -148, 0, 192, 0, 0, 0, 48, -28, 0, -44, 0, 0, 0, 4, -32, 0, -160, 0, 0, 0, -68, 48, 0, 148, 0, 0, 0, -80, 208, 0, -16, 0, 0, 0, -120, -80, 0, 8, 0, 0, 0, 104, 16, 0, -12, 0, 0, 0, -196, 28, 0, 56, 0, 0, 0, -240, 32, 0, 128, 0, 0, 0, 68, 176, 0, 120, 0, 0, 0, 0, -112, 0, -12, 0, 0, 0, 168, 12, 0, -16, 0, 0, 0, 80, -80, 0, -360, 0, 0, 0, -120, 288, 0, 24, 0, 0, 0, 76, -4, 0, 124, 0, 0, 0, -104, 4, 0, -128, 0, 0, 0, -44, -184, 0, 36, 0, 0, 0, 28, 56, 0, 56, 0, 0, 0, 48, 136, 0, 32, 0, 0, 0, -240, -96, 0, 8, 0, 0, 0, 20, -156, 0, 100, 0, 0, 0, -80, 96, 0, 64, 0, 0, 0, -148, 168, 0, 88, 0, 0, 0, 24, 76, 0, 164, 0, 0, 0, -168, 148, 0, -8, 0, 0, 0, 12, 84, 0, 0, 0, 0, 0, 116, -124, 0, 32, 0, 0, 0, -68, -68, 0, 28, 0, 0, 0, 8, 92, 0, 168, 0, 0, 0, -124, -136, 0, 220, 0, 0, 0, -128, 144, 0, 488, 0, 0, 0, -40, 8, 0, -32, 0, 0, 0, -176, 156, 0, -4, 0, 0, 0, -136, 84, 0, 84, 0, 0, 0, 112, -344, 0, 24, 0, 0, 0, -20, -256, 0, 176, 0, 0, 0, 32, -88, 0, -140, 0, 0, 0, -144, -24, 0, -84, 0, 0, 0, -12, -64, 0, 136, 0, 0, 0, 124, 84, 0, -32, 0, 0, 0, -36, -40, 0, -144, 0, 0, 0, 168, 76, 0, 40, 0, 0, 0, 112, -152, 0, -192, 0, 0, 0, 44, -272, 0, -152, 0, 0, 0, -176, -48, 0, -128, 0, 0, 0, 64, -212, 0, 4, 0, 0, 0, -96, -80, 0, 132, 0, 0, 0, 100, -240, 0, -4, 0, 0, 0, 216, 136, 0, -68, 0, 0, 0, 64, -112, 0, 92, 0, 0, 0, 112, 36, 0, -56, 0, 0, 0, -4, -92, 0, 56, 0, 0, 0, -140, -196, 0, 88, 0, 0, 0, 108, -20, 0, -80, 0, 0, 0, 100, 112, 0, 0, 0, 0, 0, 216, 216, 0, -100, 0, 0, 0, 84, 632, 0, -336, 0, 0, 0, 72, -124, 0, -200, 0, 0, 0, 360, -88, 0, -16, 0, 0, 0, 220, 116, 0, -172, 0, 0, 0, 284, 192, 0, -196, 0, 0, 0, 192, -144, 0, -36, 0, 0, 0, -448, 28, 0, -148, 0, 0, 0, -80, 52, 0, 108, 0, 0, 0, -68, 176, 0, 32, 0, 0, 0, 48, 124, 0, -152, 0, 0, 0, -116, 48, 0, -148, 0, 0, 0, -192, 124, 0, -100, 0, 0, 0, 8, -48, 0, -176, 0, 0, 0, 208, -216, 0, -48, 0, 0, 0, 232, 100, 0, 96, 0, 0, 0, -200, 272, 0, 60, 0, 0, 0, -32, -116, 0, -120, 0, 0, 0, 68, 224, 0, -12, 0, 0, 0, -84, -296, 0, -52, 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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1], [-2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0], [0, -2, 0, 1, 0, 1, 0, 0, 0, 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, -1, 0, -1, 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, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 2, -2, 0], [-1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1], [0, 1, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -2, 0, 0, -1, 0, 2, -1, 0, 0, 0], [1, 0, -1, 0, 1, 0, -1, 0, 0, -1, 1, 1, 1, 0, 0, 0], [0, -1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, -2, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 1, 1, -1, 0, 0, 0], [-1, 0, -1, 0, -1, 0, 2, 0, 0, 2, -1, -2, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, -3, -2], [-1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -2, 0, -1, 0, 3, -1, 0, 0, 0, 0, 0, 1, -3], [0, 1, 0, 1, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 3, 0, 2, 0, 2, 0, 0, 0, 2, -2, -3, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, -3, -1, 4, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0], [0, 2, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 3, 0, 2, 0, 0, -4, 0, 0, 0, 0, 3, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, -3, 0, -1, 0, 0, 2, -3, 1, 0, 0, 0, 0], [-4, 0, -3, 0, -4, 0, 1, 0, 0, 1, -4, -1, 3, 0, 0, 0], [0, -6, 0, 5, 0, -1, 0, 0, -6, 0, 0, 0, 0, 5, -1, -1], [0, 0, -2, 0, 1, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 0], [0, 3, 0, -2, 0, -1, 0, 0, 3, 0, 0, 0, 0, -2, 2, -1], [0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, -5, 2, 0, -5, 0, 0, 0], [1, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, -3, 0, 0, 0, 0], [0, -4, 0, -2, 0, -1, 0, 0, -4, 0, 0, 0, 0, -2, 2, -1], [0, -1, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -1, 0, -3, 0, 5, 0, 0, 6, -3, -5, 1, 0, 0, 0], [-6, 0, 3, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, -1, 0, 1, 6, 0, 0, 0, 0, -3, 2, 1], [-1, 0, -4, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, -1, -2, 0], [0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, 0, 0, 0, 0, 0, 0, 7, -2, -6, -1, 0, 0, 0], [0, 3, 0, -1, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 0, 2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -3, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -4, 1, 0, 0, 0, 0, -2, 4, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 4, 2, -2, -1, 0, 0, 0], [0, 2, 0, -2, 0, -3, 0, 0, 2, 0, 0, 0, 0, -2, 2, -3], [-1, 0, -1, 0, -1, 0, -2, 0, 0, 3, -1, 2, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 3, -5, 3], [0, 0, 0, 4, 0, 0, 0, -5, 0, 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, 1, -4, 1, 5, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0, 0, -5, 3, 3, -1, 0, 0, 0], [0, -1, 0, -3, 0, 7, 0, 0, -1, 0, 0, 0, 0, -3, 4, 7], [12, 0, 0, 0, 0, 0, 0, 0, 0, -12, 5, 2, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -5, 6, 3], [0, 0, 0, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 3, -9, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -2, 0, -1, 0, 6, 0, 0, 6, -1, -1, 3, 0, 0, 0], [-1, 0, 7, 0, -1, 0, 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, -1], [4, 0, 1, 0, 4, 0, -1, 0, 0, 5, 4, 1, -1, 0, 0, 0], [0, -6, 0, 2, 0, -6, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -3, 0, -2, 0, 0, -1, 0, 0, 0, 0, -3, -3, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 4, 0, 0, 0, 0], [4, 0, -3, 0, 7, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 3, 0, -3, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -1, 0, -3, 0, 3, 0, 0, 5, -3, -3, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -10, -4, 0, 0, 0, 0, -3, 10, 2], [0, 2, 0, -4, 0, -1, 0, 0, 2, 0, 0, 0, 0, -4, 5, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 1, 0, 2, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 3, 0, 0, 1, 0, -3, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, -5, -1, 4], [6, 0, 0, 0, 0, 0, 0, 0, 0, -6, -1, 5, -1, 0, 0, 0], [0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, -1, 1], [0, -6, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 7, -3, -2, 0, 0, 0]]}