# Stored data for newform 2340.2.c.d, downloaded from the LMFDB on 19 June 2025.
{"Nk2": 9360, "analytic_conductor": 18.68499407297961, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "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": [2340, 2, [1171, 2081, 937, 1081], [2, 2, 2, 1]], "cm_discs": [], "conrey_index": 181, "dim": 6, "field_disc": -9144576, "field_disc_factorization": [[-1, 1], [2, 8], [3, 6], [7, 2]], "field_poly": [4, 0, 36, 0, 12, 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": [[7, [144, 0, 144, 0, 24, 0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510936354621732, "hecke_ring_generator_nbound": 11, "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, 13, 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": "2340.2.c.d", "level": 2340, "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, 13], "level_radical": 390, "minimal_twist": "260.2.f.a", "nf_label": "6.0.9144576.1", "prim_orbit_index": 2, "qexp_display": "q+\\beta _{2}q^{5}+(-\\beta _{1}-\\beta _{5})q^{7}+(-2\\beta _{2}+\\cdots)q^{11}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "2340.2.c", "trace_display": [0, 0, 0, 0], "trace_hash": 688427525011867893, "trace_moments": [{"__RealLiteral__": 0, "data": "0.083", "prec": 17}, {"__RealLiteral__": 0, "data": "5.184", "prec": 17}, {"__RealLiteral__": 0, "data": "2.147", "prec": 17}, {"__RealLiteral__": 0, "data": "135.352", "prec": 24}, {"__RealLiteral__": 0, "data": "38.251", "prec": 20}, {"__RealLiteral__": 0, "data": "5201.271", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.523", "prec": 17}, "traces": [0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -6, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -6, 0, 0, 0, 12, 0, 12, 0, 0, 0, 0, 0, -12, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 24, 0, 0, 0, -60, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 48, 0, 0, 0, 24, 0, -12, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 36, 0, 0, 0, 0, 0, 24, 0, 36, 0, 0, 0, -24, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 12, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 72, 0, 0, 0, 72, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -36, 0, 0, 0, -72, 0, -102, 0, 0, 0, 0, 0, -48, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -78, 0, 0, 0, -48, 0, 120, 0, 0, 0, 0, 0, 24, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 36, 0, 0, 0, 0, 0, -36, 0, -24, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -72, 0, 0, 0, -72, 0, 48, 0, 0, 0, 0, 0, 72, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 36, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 36, 0, 0, 0, 84, 0, -72, 0, 0, 0, 0, 0, 54, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 60, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, -12, 0, 0, 0, 0, 0, -60, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, -132, 0, 0, 0, 0, 0, -144, 0, 144, 0, 0, 0, 72, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 48, 0, 0, 0, -84, 0, -96, 0, 0, 0, 0, 0, -12, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, -24, 0, 0, 0, 0, 0, -12, 0, -156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 96, 0, 0, 0, -72, 0, 108, 0, 0, 0, 0, 0, -48, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, -24, 0, 0, 0, 0, 0, 108, 0, -84, 0, 0, 0, 108, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, -54, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 132, 0, 0, 0, -72, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 24, 0, 36, 0, 0, 0, 0, 0, 144, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 108, 0, 0, 0, 0, 0, 72, 0, 66, 0, 0, 0, -36, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 36, 0, 0, 0, 24, 0, -96, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 144, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, -12, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 48, 0, -24, 0, 0, 0, -72, 0, 0, 0, 0, 0, 156, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, -48, 0, 0, 0, -48, 0, 180, 0, 0, 0, 0, 0, 72, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, -108, 0, 0, 0, 0, 0, 36, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 192, 0, 0, 0, -108, 0, 6, 0, 0, 0, 0, 0, 192, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 108, 0, 0, 0, 0, 0, -72, 0, -156, 0, 0, 0, -132, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 180, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, -24, 0, 0, 0, 24, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, -12, 0, 0, 0, 72, 0, -132, 0, 0, 0, 0, 0, 108, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -276, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, -132, 0, 0, 0, 0, 0, 24, 0, 156, 0, 0, 0, 132, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 192, 0, 0, 0, 36, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -108, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, -72, 0, 0, 0, -168, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 96, 0, 0, 0, -96, 0, 48, 0, 0, 0, 0, 0, -228, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, -108, 0, 0, 0, 0, 0, 48, 0, -24, 0, 0, 0, 72, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, -84, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 12, 0, 0, 0, 0, 0, 216, 0, 60, 0, 0, 0, -48, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 24, 0, 0, 0, 216, 0, 84, 0, 0, 0, 0, 0, -120, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 228, 0, 0, 0, 0, 0, -72, 0, -12, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 72, 0, 0, 0, 48, 0, 72, 0, 0, 0, 0, 0, 96, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, -120, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -24, 0, 0, 0, 36, 0, -18, 0, 0, 0, 0, 0, -120, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, -156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, -228, 0, 0, 0, 0, 0, -12, 0, 180, 0, 0, 0, -180, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, -216, 0, 0, 0, 0, 0, -24, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, -72, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -240, 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, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 1, -1, 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, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, 0, -1, -2, 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], [0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 1, 0], [0, 0, 0, 0, 0, 0], [0, -2, -2, 0, 0, -1], [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, 3, 4, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, -2], [0, 0, 0, 0, 0, 0], [2, 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, -4, 0, 0, -1], [0, 0, 0, 0, 0, 0], [-1, 0, 0, -2, -2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, 0, 2, -2, 0], [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, 8, 0, 0, -1], [0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, -1, 4, 0, 0, -3], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -6, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0], [0, -3, 8, 0, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-4, 0, 0, 4, -2, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 3, 4, 0, 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, 0, 0, 0, 0], [0, -6, -8, 0, 0, -2], [0, 0, 0, 0, 0, 0], [2, -2, -6, 2, -1, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 1, 0], [0, 0, 0, 0, 0, 0], [0, -2, -6, 0, 0, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]}