# Stored data for newform 1360.2.e.d, downloaded from the LMFDB on 10 February 2025. {"Nk2": 5440, "analytic_conductor": 10.859654674894132, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 2, "char_parity": 1, "char_values": [1360, 2, [511, 341, 817, 241], [2, 2, 1, 2]], "cm_discs": [], "conrey_index": 1089, "dim": 8, "field_disc": 619810816, "field_disc_factorization": [[2, 12], [389, 2]], "field_poly": [1, 2, 2, -8, 14, -2, 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": [[3, [4, 0, 100, 0, 76, 0, 16, 0, 1]], [7, [196, 0, 548, 0, 292, 0, 36, 0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13511073793574224, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "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": "1360.2.e.d", "level": 1360, "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": [2, 5, 17], "level_radical": 170, "minimal_twist": "85.2.b.a", "nf_label": "8.0.619810816.2", "prim_orbit_index": 2, "qexp_display": "q+(-\\beta _{2}-\\beta _{3}+\\beta _{4}-\\beta _{5}+\\beta _{6})q^{3}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1360.2.e", "trace_display": [0, 0, -2, 0], "trace_hash": 955194900113301755, "trace_moments": [{"__RealLiteral__": 0, "data": "0.111", "prec": 17}, {"__RealLiteral__": 0, "data": "7.325", "prec": 17}, {"__RealLiteral__": 0, "data": "0.948", "prec": 17}, {"__RealLiteral__": 0, "data": "294.005", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "18708.358", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.511", "prec": 17}, "traces": [0, 8, 0, 0, 0, -2, 0, 0, 0, -8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 24, 0, 0, 0, -12, 0, 0, 0, 8, 0, 24, 0, 0, 0, 0, 0, 0, 0, -44, 0, -12, 0, 0, 0, -22, 0, 0, 0, -16, 0, 8, 0, 0, 0, 8, 0, 0, 0, -16, 0, 12, 0, 0, 0, 20, 0, 0, 0, -8, 0, 20, 0, 0, 0, -4, 0, 0, 0, -24, 0, -8, 0, 0, 0, -2, 0, 0, 0, -48, 0, -36, 0, 0, 0, -4, 0, 0, 0, -24, 0, 24, 0, 0, 0, 52, 0, 0, 0, 4, 0, -40, 0, 0, 0, 48, 0, 0, 0, -20, 0, -24, 0, 0, 0, 22, 0, 0, 0, -68, 0, 48, 0, 0, 0, -56, 0, 0, 0, -12, 0, -44, 0, 0, 0, 4, 0, 0, 0, 72, 0, 8, 0, 0, 0, -8, 0, 0, 0, 64, 0, 32, 0, 0, 0, -32, 0, 0, 0, -80, 0, 40, 0, 0, 0, 68, 0, 0, 0, 48, 0, -8, 0, 0, 0, 60, 0, 0, 0, -40, 0, -8, 0, 0, 0, 24, 0, 0, 0, -40, 0, -20, 0, 0, 0, 28, 0, 0, 0, 72, 0, -48, 0, 0, 0, -12, 0, 0, 0, 8, 0, -12, 0, 0, 0, 44, 0, 0, 0, 56, 0, 12, 0, 0, 0, 20, 0, 0, 0, 16, 0, -44, 0, 0, 0, -78, 0, 0, 0, 100, 0, -48, 0, 0, 0, 12, 0, 0, 0, 32, 0, 56, 0, 0, 0, 92, 0, 0, 0, 36, 0, -88, 0, 0, 0, -8, 0, 0, 0, 36, 0, -16, 0, 0, 0, -120, 0, 0, 0, -8, 0, -72, 0, 0, 0, 4, 0, 0, 0, -28, 0, 68, 0, 0, 0, 12, 0, 0, 0, -28, 0, 36, 0, 0, 0, -8, 0, 0, 0, 0, 0, -16, 0, 0, 0, 32, 0, 0, 0, -36, 0, 24, 0, 0, 0, 68, 0, 0, 0, 152, 0, -88, 0, 0, 0, -24, 0, 0, 0, -32, 0, 16, 0, 0, 0, -8, 0, 0, 0, 128, 0, 8, 0, 0, 0, -116, 0, 0, 0, 12, 0, -24, 0, 0, 0, -120, 0, 0, 0, -176, 0, 100, 0, 0, 0, -20, 0, 0, 0, 40, 0, 8, 0, 0, 0, -56, 0, 0, 0, -16, 0, -48, 0, 0, 0, -46, 0, 0, 0, 32, 0, 124, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -64, 0, -56, 0, 0, 0, -120, 0, 0, 0, -44, 0, 80, 0, 0, 0, 64, 0, 0, 0, 92, 0, 80, 0, 0, 0, 40, 0, 0, 0, -20, 0, 80, 0, 0, 0, -28, 0, 0, 0, -28, 0, -64, 0, 0, 0, 32, 0, 0, 0, -40, 0, -72, 0, 0, 0, 28, 0, 0, 0, 72, 0, 120, 0, 0, 0, 8, 0, 0, 0, 56, 0, 56, 0, 0, 0, -24, 0, 0, 0, -72, 0, 72, 0, 0, 0, 48, 0, 0, 0, -88, 0, -200, 0, 0, 0, -8, 0, 0, 0, 72, 0, 16, 0, 0, 0, -24, 0, 0, 0, -128, 0, -96, 0, 0, 0, -28, 0, 0, 0, 44, 0, 96, 0, 0, 0, -8, 0, 0, 0, -16, 0, -4, 0, 0, 0, 20, 0, 0, 0, 8, 0, 56, 0, 0, 0, -84, 0, 0, 0, 32, 0, -12, 0, 0, 0, -120, 0, 0, 0, -32, 0, -128, 0, 0, 0, -8, 0, 0, 0, 24, 0, 132, 0, 0, 0, -46, 0, 0, 0, 80, 0, -184, 0, 0, 0, -124, 0, 0, 0, 108, 0, 112, 0, 0, 0, -88, 0, 0, 0, 24, 0, -40, 0, 0, 0, -20, 0, 0, 0, 64, 0, -20, 0, 0, 0, -32, 0, 0, 0, -8, 0, 148, 0, 0, 0, 72, 0, 0, 0, 120, 0, -32, 0, 0, 0, 8, 0, 0, 0, -156, 0, -104, 0, 0, 0, 48, 0, 0, 0, 48, 0, -104, 0, 0, 0, 92, 0, 0, 0, 8, 0, -124, 0, 0, 0, -144, 0, 0, 0, -32, 0, 8, 0, 0, 0, 24, 0, 0, 0, -152, 0, 116, 0, 0, 0, -136, 0, 0, 0, 60, 0, 148, 0, 0, 0, 64, 0, 0, 0, 112, 0, 36, 0, 0, 0, 192, 0, 0, 0, 0, 0, 56, 0, 0, 0, 40, 0, 0, 0, 168, 0, 204, 0, 0, 0, 44, 0, 0, 0, 44, 0, 136, 0, 0, 0, 22, 0, 0, 0, -96, 0, -68, 0, 0, 0, 20, 0, 0, 0, 136, 0, -56, 0, 0, 0, 68, 0, 0, 0, -36, 0, -136, 0, 0, 0, 8, 0, 0, 0, -12, 0, -104, 0, 0, 0, -20, 0, 0, 0, 80, 0, 28, 0, 0, 0, 56, 0, 0, 0, -108, 0, 68, 0, 0, 0, 0, 0, 0, 0, 16, 0, -8, 0, 0, 0, 16, 0, 0, 0, -44, 0, -72, 0, 0, 0, 122, 0, 0, 0, 96, 0, -104, 0, 0, 0, -28, 0, 0, 0, -40, 0, 40, 0, 0, 0, -44, 0, 0, 0, -144, 0, -168, 0, 0, 0, 120, 0, 0, 0, -104, 0, -244, 0, 0, 0, 0, 0, 0, 0, -100, 0, -144, 0, 0, 0, 16, 0, 0, 0, 136, 0, -16, 0, 0, 0, 20, 0, 0, 0, -112, 0, 44, 0, 0, 0, -60, 0, 0, 0, 40, 0, -268, 0, 0, 0, 0, 0, 0, 0, 108, 0, -200, 0, 0, 0, -20, 0, 0, 0, -184, 0, 80, 0, 0, 0, 52, 0, 0, 0, 160, 0, 80, 0, 0, 0, -76, 0, 0, 0, -76, 0, 64, 0, 0, 0, -36, 0, 0, 0, -32, 0, -128, 0, 0, 0, 196, 0, 0, 0, -20, 0, 44, 0, 0, 0, -84, 0, 0, 0, 28, 0, -20, 0, 0, 0, 144, 0, 0, 0, 168, 0, -136, 0, 0, 0, 16, 0, 0, 0, -80, 0, -72, 0, 0, 0, 120, 0, 0, 0, -160, 0, -184, 0, 0, 0, 68, 0, 0, 0, -216, 0, 120, 0, 0, 0, -32, 0, 0, 0, -96, 0, 128, 0, 0, 0, -56, 0, 0, 0, -264, 0, -4, 0, 0, 0, -72, 0, 0, 0, -8, 0, 56, 0, 0, 0, -88, 0, 0, 0, 120, 0, 32, 0, 0, 0, 56, 0, 0, 0, 152, 0, -28, 0, 0, 0, 136, 0, 0, 0, 176, 0, 60, 0, 0, 0, -76, 0, 0, 0, 120, 0, 152, 0, 0, 0, 28, 0, 0, 0, -80, 0, 124, 0, 0, 0, 112, 0, 0, 0, -52, 0, -16, 0, 0, 0, 122, 0, 0, 0, -124, 0, 216, 0, 0, 0, 8, 0, 0, 0, -12, 0, -40, 0, 0, 0, -16, 0, 0, 0, 156, 0, -40, 0, 0, 0, 120, 0, 0, 0, -40, 0, 48, 0, 0, 0, 108, 0, 0, 0, -200, 0, -72, 0, 0, 0, 32, 0, 0, 0, -276, 0, 240, 0, 0, 0, 100, 0, 0, 0, 88, 0, 208, 0, 0, 0, -72, 0, 0, 0, -16, 0, 52, 0, 0, 0, 68, 0, 0, 0, 120, 0, 176, 0, 0, 0, -40, 0, 0, 0, -192, 0, 56, 0, 0, 0, -76, 0, 0, 0, -232, 0, -104, 0, 0, 0, -280, 0, 0, 0, -48, 0, -4, 0, 0, 0, -16, 0, 0, 0, -112, 0, 344, 0, 0, 0, -124, 0, 0, 0, 72, 0, -208, 0, 0, 0, 8, 0, 0, 0, 16, 0, -96, 0, 0, 0, -20, 0, 0, 0, -288, 0, 208, 0, 0, 0, 76, 0, 0, 0, 80, 0, -16, 0, 0, 0, -48, 0, 0, 0, 260, 0, 40, 0, 0, 0, -76, 0, 0, 0, -36, 0, 192, 0, 0, 0, 172, 0, 0, 0, -128, 0, 260, 0, 0, 0, -144, 0, 0, 0, 276, 0, -60, 0, 0, 0, 112, 0, 0, 0, 160, 0, -288, 0, 0, 0, -132, 0, 0, 0, 40, 0, -128, 0, 0, 0, 72, 0, 0, 0, -120, 0, -72, 0, 0, 0, 236, 0, 0, 0, 72, 0, -76, 0, 0, 0, 0, 0, 0, 0, -88, 0, 64, 0, 0, 0, -76, 0, 0, 0, -284, 0, 116, 0, 0, 0, -136, 0, 0, 0, 108, 0, 92, 0, 0, 0, -128, 0, 0, 0, 40, 0, -28, 0, 0, 0, 88, 0, 0, 0, -40, 0, -216, 0, 0, 0, -8, 0, 0, 0, 216, 0, 152, 0, 0, 0, 76, 0, 0, 0, 52, 0, 144, 0, 0, 0, 2, 0, 0, 0, -56, 0, 80, 0, 0, 0, -56, 0, 0, 0, 264, 0, 184, 0, 0, 0, 104, 0, 0, 0, 232, 0, -80, 0, 0, 0, 24, 0, 0, 0, -8, 0, 152, 0, 0, 0, -68, 0, 0, 0, 12, 0, 116, 0, 0, 0, -16, 0, 0, 0, -88, 0, -160, 0, 0, 0, 72, 0, 0, 0, -80, 0, 184, 0, 0, 0, 120, 0, 0, 0, -36, 0, 56, 0, 0, 0, 68, 0, 0, 0, -56, 0, 216, 0, 0, 0, -8, 0, 0, 0, -184, 0, -132, 0, 0, 0, -80, 0, 0, 0, 192, 0, -64, 0, 0, 0, -136, 0, 0, 0, 4, 0, 180, 0, 0, 0, -108, 0, 0, 0, -316, 0, -208, 0, 0, 0, -116, 0, 0, 0, 88, 0, 36, 0, 0, 0, 12, 0, 0, 0, -136, 0, -120, 0, 0, 0, 72, 0, 0, 0, 192, 0, 136, 0, 0, 0, -152, 0, 0, 0, 20, 0, -120, 0, 0, 0, 4, 0, 0, 0, -256, 0, -24, 0, 0, 0, -76, 0, 0, 0, -240, 0, -56, 0, 0, 0, 4, 0, 0, 0, 272, 0, 40, 0, 0, 0, 40, 0, 0, 0, -8, 0, -32, 0, 0, 0, 148, 0, 0, 0, -284, 0, 112, 0, 0, 0, -236, 0, 0, 0, 168, 0, -12, 0, 0, 0, -48, 0, 0, 0, 152, 0, -112, 0, 0, 0, -268, 0, 0, 0, -124, 0, -176, 0, 0, 0, 116, 0, 0, 0, 8, 0, -288, 0, 0, 0, 192, 0, 0, 0, 88, 0, -16, 0, 0, 0, -272, 0, 0, 0, 80, 0, -72, 0, 0, 0, 88, 0, 0, 0, -344, 0, -116, 0, 0, 0, -248, 0, 0, 0, -72, 0, -88, 0, 0, 0, 120, 0, 0, 0, 152, 0, 68, 0, 0, 0, 88, 0, 0, 0, 128, 0, -36, 0, 0, 0, -16, 0, 0, 0, 184, 0, 124, 0, 0, 0, 48, 0, 0, 0, 256, 0, 168, 0, 0, 0, 32, 0, 0, 0, -48, 0, -164, 0, 0, 0, 0, 0, 0, 0, -44, 0, 64, 0, 0, 0, -34, 0, 0, 0, 112, 0, -168, 0, 0, 0, -112, 0, 0, 0, 16, 0, -40, 0, 0, 0, -88, 0, 0, 0, -48, 0, 28, 0, 0, 0, 184, 0, 0, 0, -176, 0, 308, 0, 0, 0, 20, 0, 0, 0, 80, 0, -104, 0, 0, 0, -160, 0, 0, 0, -100, 0, -136, 0, 0, 0, 284, 0, 0, 0, 80, 0, -288, 0, 0, 0, -120, 0, 0, 0, 264, 0, 32, 0, 0, 0, -96, 0, 0, 0, -104, 0, 344, 0, 0, 0, 24, 0, 0, 0, 44, 0, -260, 0, 0, 0, 16, 0, 0, 0, -60, 0, -220, 0, 0, 0, -184, 0, 0, 0, 32, 0, -20, 0, 0, 0, 224, 0, 0, 0, 32, 0, 108, 0, 0, 0, -208, 0, 0, 0, 40, 0, -180, 0, 0, 0, -84, 0, 0, 0, 332, 0, -128, 0, 0, 0, 4, 0, 0, 0, -168, 0, -80, 0, 0, 0, 76, 0, 0, 0, 8, 0, -240, 0, 0, 0, 4, 0, 0, 0, 212, 0, -144, 0, 0, 0, -68, 0, 0, 0, -92, 0, -80, 0, 0, 0, 200, 0, 0, 0, -104, 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, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -1, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -2, -1, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, -3, 3, -3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -2, 2, 1, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -2, -2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 2, 3, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -1, -1, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -2, -1, 0, 0, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 2, 1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -2, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, -1, 2, -3, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 1, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 2, 1, 1, 1, -3, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -2, -2, 2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, -3, 1, -1, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, -1, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -4, -1, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, -1, -2, 2, -2, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, -3, 3, -3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 0, -1, -5, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, -2, 4, -4, 3, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 2, 2, -2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 3, -3, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -5, -3, 3, -3, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -3, 6, 3, -2, -3, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 2, -3, 3, -3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, -3, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, -2, 1, -2, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, -2, 3, -3, 3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 1, 3, -7, 3, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 6, -1, 1, -1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, -1, 0, -5, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 1, -5, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 3, -3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, -2, 4, -4, 4, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 4, 3, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 5, 5, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -6, 1, -1, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 8, -6, 4, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, -4, 4, -4, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 1, -2, 3, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0]]}