# Stored data for newform 2640.2.d.i, downloaded from the LMFDB on 05 December 2024. {"Nk2": 10560, "analytic_conductor": 21.080506133618023, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": 1, "char_values": [2640, 2, [991, 661, 881, 1057, 1201], [2, 2, 2, 1, 2]], "cm_discs": [], "conrey_index": 529, "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": [[7, [16, 0, 192, 0, 32, 0, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36029003210951248, "hecke_ring_generator_nbound": 7, "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": "2640.2.d.i", "level": 2640, "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, 3, 5, 11], "level_radical": 330, "minimal_twist": "165.2.c.a", "nf_label": "6.0.350464.1", "prim_orbit_index": 2, "qexp_display": "q+\\beta _{4}q^{3}+(-\\beta _{1}-\\beta _{5})q^{5}+(\\beta _{1}+3\\beta _{4}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "2640.2.d", "trace_display": [0, 0, 2, 0], "trace_hash": 2198454253404928696, "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "5.330", "prec": 17}, {"__RealLiteral__": 0, "data": "3.099", "prec": 17}, {"__RealLiteral__": 0, "data": "169.235", "prec": 24}, {"__RealLiteral__": 0, "data": "213.171", "prec": 24}, {"__RealLiteral__": 0, "data": "8139.313", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.513", "prec": 17}, "traces": [0, 6, 0, 0, 0, 2, 0, 0, 0, -6, 0, 6, 0, 0, 0, 0, 0, 0, 0, -4, 0, -16, 0, 0, 0, -2, 0, 0, 0, 16, 0, -16, 0, 0, 0, 12, 0, 0, 0, -12, 0, -16, 0, 0, 0, -2, 0, 0, 0, -22, 0, 8, 0, 0, 0, 2, 0, 0, 0, -16, 0, 4, 0, 0, 0, 28, 0, 0, 0, 24, 0, 24, 0, 0, 0, 8, 0, 0, 0, -12, 0, 6, 0, 0, 0, 44, 0, 0, 0, -4, 0, -16, 0, 0, 0, 44, 0, 0, 0, -6, 0, -80, 0, 0, 0, 4, 0, 0, 0, 12, 0, 8, 0, 0, 0, 0, 0, 0, 0, -24, 0, 6, 0, 0, 0, 26, 0, 0, 0, 16, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, -16, 0, 0, 0, 24, 0, 0, 0, -8, 0, 28, 0, 0, 0, -32, 0, 0, 0, 16, 0, 64, 0, 0, 0, 0, 0, 0, 0, -106, 0, 4, 0, 0, 0, 40, 0, 0, 0, 24, 0, -20, 0, 0, 0, -24, 0, 0, 0, 16, 0, -32, 0, 0, 0, -48, 0, 0, 0, 24, 0, -24, 0, 0, 0, -24, 0, 0, 0, -4, 0, -92, 0, 0, 0, -12, 0, 0, 0, -36, 0, -24, 0, 0, 0, 2, 0, 0, 0, -20, 0, -16, 0, 0, 0, 40, 0, 0, 0, -8, 0, 44, 0, 0, 0, 22, 0, 0, 0, -4, 0, -32, 0, 0, 0, 4, 0, 0, 0, 64, 0, -16, 0, 0, 0, -16, 0, 0, 0, 108, 0, -44, 0, 0, 0, -2, 0, 0, 0, 16, 0, 64, 0, 0, 0, -16, 0, 0, 0, -42, 0, -16, 0, 0, 0, 56, 0, 0, 0, 48, 0, 64, 0, 0, 0, -52, 0, 0, 0, 56, 0, -8, 0, 0, 0, -12, 0, 0, 0, 16, 0, -28, 0, 0, 0, -72, 0, 0, 0, -48, 0, 0, 0, 0, 0, -64, 0, 0, 0, 64, 0, -16, 0, 0, 0, 8, 0, 0, 0, -4, 0, 12, 0, 0, 0, 0, 0, 0, 0, -32, 0, 102, 0, 0, 0, 36, 0, 0, 0, 16, 0, 104, 0, 0, 0, -48, 0, 0, 0, -40, 0, -72, 0, 0, 0, 12, 0, 0, 0, -12, 0, -32, 0, 0, 0, -12, 0, 0, 0, 72, 0, -108, 0, 0, 0, 2, 0, 0, 0, 76, 0, 32, 0, 0, 0, 12, 0, 0, 0, 120, 0, -28, 0, 0, 0, -8, 0, 0, 0, -12, 0, -56, 0, 0, 0, -24, 0, 0, 0, -140, 0, 22, 0, 0, 0, -28, 0, 0, 0, 84, 0, -16, 0, 0, 0, -64, 0, 0, 0, -8, 0, -72, 0, 0, 0, -8, 0, 0, 0, -16, 0, -40, 0, 0, 0, 124, 0, 0, 0, 104, 0, -16, 0, 0, 0, -16, 0, 0, 0, -8, 0, -16, 0, 0, 0, -2, 0, 0, 0, -64, 0, -12, 0, 0, 0, -8, 0, 0, 0, 180, 0, -160, 0, 0, 0, 40, 0, 0, 0, -16, 0, 68, 0, 0, 0, 48, 0, 0, 0, 42, 0, 16, 0, 0, 0, 68, 0, 0, 0, -22, 0, -44, 0, 0, 0, -28, 0, 0, 0, -4, 0, 112, 0, 0, 0, -16, 0, 0, 0, 16, 0, 8, 0, 0, 0, 56, 0, 0, 0, -24, 0, 36, 0, 0, 0, -32, 0, 0, 0, 4, 0, -32, 0, 0, 0, -28, 0, 0, 0, -80, 0, 16, 0, 0, 0, -48, 0, 0, 0, 144, 0, 36, 0, 0, 0, 2, 0, 0, 0, 0, 0, -176, 0, 0, 0, 24, 0, 0, 0, -32, 0, -24, 0, 0, 0, 22, 0, 0, 0, 80, 0, 152, 0, 0, 0, 36, 0, 0, 0, -24, 0, -92, 0, 0, 0, -4, 0, 0, 0, -16, 0, 24, 0, 0, 0, 56, 0, 0, 0, 8, 0, 76, 0, 0, 0, -72, 0, 0, 0, -24, 0, 4, 0, 0, 0, -8, 0, 0, 0, -80, 0, 52, 0, 0, 0, -64, 0, 0, 0, -88, 0, 8, 0, 0, 0, -28, 0, 0, 0, 48, 0, 56, 0, 0, 0, -40, 0, 0, 0, 36, 0, 12, 0, 0, 0, 28, 0, 0, 0, -16, 0, 144, 0, 0, 0, 80, 0, 0, 0, -6, 0, 24, 0, 0, 0, -80, 0, 0, 0, -100, 0, -112, 0, 0, 0, 32, 0, 0, 0, -64, 0, 88, 0, 0, 0, -52, 0, 0, 0, 24, 0, 8, 0, 0, 0, -44, 0, 0, 0, -180, 0, 0, 0, 0, 0, -32, 0, 0, 0, -112, 0, 24, 0, 0, 0, 104, 0, 0, 0, 12, 0, 104, 0, 0, 0, -40, 0, 0, 0, -64, 0, 4, 0, 0, 0, -16, 0, 0, 0, -24, 0, -52, 0, 0, 0, -56, 0, 0, 0, 16, 0, 64, 0, 0, 0, 8, 0, 0, 0, -52, 0, -12, 0, 0, 0, 92, 0, 0, 0, -184, 0, -46, 0, 0, 0, -118, 0, 0, 0, 56, 0, -32, 0, 0, 0, -44, 0, 0, 0, -96, 0, 0, 0, 0, 0, 52, 0, 0, 0, -12, 0, 64, 0, 0, 0, -140, 0, 0, 0, -8, 0, 44, 0, 0, 0, 48, 0, 0, 0, -256, 0, 6, 0, 0, 0, 24, 0, 0, 0, -80, 0, 72, 0, 0, 0, 108, 0, 0, 0, 80, 0, 112, 0, 0, 0, -16, 0, 0, 0, -124, 0, 72, 0, 0, 0, -48, 0, 0, 0, 124, 0, 292, 0, 0, 0, 44, 0, 0, 0, -8, 0, 0, 0, 0, 0, -4, 0, 0, 0, -24, 0, 48, 0, 0, 0, 80, 0, 0, 0, 232, 0, -90, 0, 0, 0, -76, 0, 0, 0, 88, 0, 248, 0, 0, 0, -28, 0, 0, 0, -4, 0, -12, 0, 0, 0, 76, 0, 0, 0, -64, 0, -64, 0, 0, 0, -24, 0, 0, 0, -8, 0, -16, 0, 0, 0, 8, 0, 0, 0, -188, 0, -4, 0, 0, 0, -64, 0, 0, 0, -104, 0, 164, 0, 0, 0, -80, 0, 0, 0, 56, 0, 64, 0, 0, 0, 0, 0, 0, 0, 200, 0, 12, 0, 0, 0, 44, 0, 0, 0, -108, 0, 52, 0, 0, 0, -60, 0, 0, 0, 0, 0, -76, 0, 0, 0, -32, 0, 0, 0, -140, 0, 24, 0, 0, 0, -40, 0, 0, 0, 8, 0, 64, 0, 0, 0, -64, 0, 0, 0, -6, 0, -104, 0, 0, 0, 16, 0, 0, 0, -160, 0, -24, 0, 0, 0, 200, 0, 0, 0, 260, 0, -80, 0, 0, 0, 184, 0, 0, 0, 36, 0, 160, 0, 0, 0, -26, 0, 0, 0, -68, 0, -64, 0, 0, 0, -4, 0, 0, 0, 208, 0, 144, 0, 0, 0, -12, 0, 0, 0, 32, 0, -120, 0, 0, 0, 4, 0, 0, 0, -184, 0, -16, 0, 0, 0, 60, 0, 0, 0, -64, 0, 208, 0, 0, 0, -48, 0, 0, 0, -8, 0, -140, 0, 0, 0, -32, 0, 0, 0, -128, 0, -112, 0, 0, 0, -88, 0, 0, 0, 12, 0, -76, 0, 0, 0, -108, 0, 0, 0, 120, 0, -168, 0, 0, 0, 0, 0, 0, 0, -64, 0, 8, 0, 0, 0, 226, 0, 0, 0, 40, 0, -12, 0, 0, 0, -232, 0, 0, 0, 56, 0, -88, 0, 0, 0, 8, 0, 0, 0, 20, 0, -4, 0, 0, 0, 104, 0, 0, 0, -24, 0, 144, 0, 0, 0, 0, 0, 0, 0, 16, 0, 80, 0, 0, 0, 88, 0, 0, 0, 112, 0, -48, 0, 0, 0, -24, 0, 0, 0, -40, 0, -120, 0, 0, 0, 0, 0, 0, 0, 144, 0, -116, 0, 0, 0, -24, 0, 0, 0, -24, 0, -16, 0, 0, 0, 28, 0, 0, 0, -16, 0, -116, 0, 0, 0, -112, 0, 0, 0, -96, 0, 6, 0, 0, 0, -8, 0, 0, 0, -32, 0, 8, 0, 0, 0, 52, 0, 0, 0, 16, 0, 80, 0, 0, 0, 100, 0, 0, 0, -28, 0, 16, 0, 0, 0, -136, 0, 0, 0, 126, 0, -4, 0, 0, 0, 26, 0, 0, 0, 72, 0, 124, 0, 0, 0, 36, 0, 0, 0, 56, 0, -360, 0, 0, 0, 32, 0, 0, 0, -140, 0, -24, 0, 0, 0, -8, 0, 0, 0, -12, 0, -40, 0, 0, 0, 84, 0, 0, 0, 16, 0, 160, 0, 0, 0, -96, 0, 0, 0, -172, 0, -16, 0, 0, 0, 64, 0, 0, 0, -40, 0, 8, 0, 0, 0, -22, 0, 0, 0, -64, 0, 80, 0, 0, 0, 48, 0, 0, 0, 68, 0, -8, 0, 0, 0, 140, 0, 0, 0, 104, 0, 212, 0, 0, 0, 32, 0, 0, 0, 112, 0, 120, 0, 0, 0, 0, 0, 0, 0, 12, 0, -40, 0, 0, 0, 192, 0, 0, 0, 128, 0, 40, 0, 0, 0, -8, 0, 0, 0, 132, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 106, 0, 0, 0, -76, 0, 0, 0, 4, 0, 12, 0, 0, 0, -20, 0, 0, 0, -4, 0, 96, 0, 0, 0, -16, 0, 0, 0, 108, 0, -16, 0, 0, 0, -80, 0, 0, 0, -128, 0, -128, 0, 0, 0, -120, 0, 0, 0, 72, 0, -128, 0, 0, 0, -40, 0, 0, 0, -52, 0, -24, 0, 0, 0, 40, 0, 0, 0, 80, 0, -64, 0, 0, 0, 24, 0, 0, 0, 64, 0, -160, 0, 0, 0, -88, 0, 0, 0, 124, 0, -24, 0, 0, 0, -152, 0, 0, 0, 64, 0, -60, 0, 0, 0, -124, 0, 0, 0, 20, 0, 120, 0, 0, 0, -128, 0, 0, 0, -8, 0, -40, 0, 0, 0, -64, 0, 0, 0, 16, 0, -96, 0, 0, 0, 112, 0, 0, 0, 56, 0, 28, 0, 0, 0, 24, 0, 0, 0, -284, 0, -24, 0, 0, 0, 64, 0, 0, 0, 144, 0, -118, 0, 0, 0, -36, 0, 0, 0, 4, 0, -88, 0, 0, 0, 32, 0, 0, 0, -128, 0, -16, 0, 0, 0, -32, 0, 0, 0, 196, 0, -16, 0, 0, 0, -280, 0, 0, 0, 32, 0, -44, 0, 0, 0, -8, 0, 0, 0, 48, 0, 24, 0, 0, 0, -12, 0, 0, 0, 32, 0, 76, 0, 0, 0, -140, 0, 0, 0, 16, 0, -160, 0, 0, 0, 48, 0, 0, 0, -188, 0, -40, 0, 0, 0, 112, 0, 0, 0, -64, 0, 64, 0, 0, 0, 40, 0, 0, 0, 48, 0, -120, 0, 0, 0, -160, 0, 0, 0, -116, 0, -24, 0, 0, 0, -16, 0, 0, 0, -56, 0, -12, 0, 0, 0, 178, 0, 0, 0, 24, 0, 136, 0, 0, 0, 0, 0, 0, 0, -88, 0, 56, 0, 0, 0, 104, 0, 0, 0, -80, 0, -64, 0, 0, 0, 200, 0, 0, 0, -20, 0, 48, 0, 0, 0, 24, 0, 0, 0, 194, 0, -128, 0, 0, 0, -40, 0, 0, 0, -106, 0, 60, 0, 0, 0, -92, 0, 0, 0, -8, 0, -48, 0, 0, 0, -80, 0, 0, 0, 176, 0, 4, 0, 0, 0, -48, 0, 0, 0, 304, 0, 96, 0, 0, 0, -104, 0, 0, 0, 92, 0, -12, 0, 0, 0, 4, 0, 0, 0, 16, 0, 36, 0, 0, 0, 88, 0, 0, 0, 176, 0, -264, 0, 0, 0, 40, 0, 0, 0, 120, 0, -8, 0, 0, 0, 12, 0, 0, 0, -96, 0, -96, 0, 0, 0, 156, 0, 0, 0, -72, 0, 24, 0, 0, 0, -16, 0, 0, 0, 64, 0, -144, 0, 0, 0, 16, 0, 0, 0, 24, 0, 36, 0, 0, 0, 52, 0, 0, 0, 208, 0, 0, 0, 0, 0, 32, 0, 0, 0, 24, 0, -20, 0, 0, 0, -32, 0, 0, 0, -84, 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], [1, 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, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, -2, 1, 2], [0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 3, 0, -1, -1, 1], [0, 0, 0, 0, 0, 0], [-2, 0, -2, -1, 0, -1], [0, 0, 0, 0, 0, 0], [-3, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0], [-1, 0, -2, -1, -2, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0], [2, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-2, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [2, 1, 4, -3, -1, -1], [0, 0, 0, 0, 0, 0], [0, -2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0], [-1, 0, -1, 2, 0, 2], [0, 0, 0, 0, 0, 0], [-2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 2, 0, -2, 2, 2], [0, 0, 0, 0, 0, 0], [-5, 0, -6, 1, 0, 1], [0, 0, 0, 0, 0, 0], [1, 0, -3, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, -2, 0, -1, -4, 1], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [0, -2, 0, -1, -2, 1], [0, 0, 0, 0, 0, 0], [-4, 0, 2, -3, 0, -3], [0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, 2], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0], [6, -3, 2, 1, 7, 1], [0, 0, 0, 0, 0, 0], [0, -4, 0, 2, 4, -2], [0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [4, 0, -2, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0], [2, -2, 0, 1, -1, 1], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0], [-2, 0, -2, 1, 0, 1], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [8, 1, 2, 2, 1, -2], [0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [-2, 0, -8, 5, 0, 5], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -2, -1], [0, 0, 0, 0, 0, 0], [6, 4, -4, -3, 2, 3], [0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 4, -2], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]}