# Stored data for newform 690.2.i.c, downloaded from the LMFDB on 18 April 2024. {"label": "690.2.i.c", "space_label": "690.2.i", "level": 690, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007749044110002, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 1050810565698960492, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [144, 0, 0, 0, 1]]], "qexp_display": "q-\\zeta_{24}^{5}q^{2}+(-1+\\zeta_{24}+\\zeta_{24}^{3})q^{3}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 15, "char_orbit_label": "i", "char_is_real": false, "Nk2": 2760, "analytic_conductor": 5.509677739468347, "hecke_ring_index": 16, "level_radical": 690, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 24, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.641", "prec": 17}, "analytic_rank_proved": true, "char_values": [690, 4, [461, 277, 511], [2, 1, 4]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 3, 5, 23], "conrey_indexes": [47, 323], "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.458", "prec": 17}, {"__RealLiteral__": 0, "data": "1.449", "prec": 17}, {"__RealLiteral__": 0, "data": "378.282", "prec": 24}, {"__RealLiteral__": 0, "data": "313.633", "prec": 24}, {"__RealLiteral__": 0, "data": "28701.966", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c4", "trace_display": [0, -8, 0, 0], "traces": [0, 8, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, 8, -8, 0, -8, -8, 0, 16, 0, 0, 0, 32, 0, 0, 8, 0, -8, 0, 0, 16, 0, 0, 32, 0, 0, -8, 0, 0, 0, -8, 0, 0, -16, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 64, 0, 0, 32, 0, 8, -32, 0, 0, 0, 0, -64, -48, 0, 0, 48, 0, -16, 24, 0, -8, 0, 0, 8, 0, 0, 56, 48, 0, 0, 72, 0, -32, 32, 0, -8, -96, 0, 0, 0, 0, 8, 16, 0, 0, 0, 0, 0, -48, 0, 0, -48, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, 8, -8, 0, 0, -168, 0, 48, 0, 0, 0, -48, 0, 0, 16, 0, -32, -48, 0, 40, 0, 0, -8, 0, 0, -16, -24, 0, 0, -48, 0, -40, 0, 0, -8, 32, 0, 0, 0, 0, -16, -48, 0, 0, 8, 0, -32, -32, 0, -64, -16, 0, 0, 0, 0, 0, 16, 0, 0, 96, 0, 8, -32, 0, -32, 64, 0, 32, 0, 0, 0, 0, 0, 0, 24, 0, -8, -24, 0, 48, 40, 0, 32, 0, 0, 96, -16, 0, 0, 96, 0, 16, 8, 0, -48, 32, 0, -24, 0, 0, 40, 96, 0, 0, 0, 0, 0, -80, 0, 0, -32, 0, 0, 0, 0, 0, -32, 0, 0, 32, 0, -16, 144, 0, 8, -112, 0, -88, 0, 0, -96, -48, 0, 0, -56, 0, 0, -32, 0, 0, 8, 0, 16, 0, 0, 128, 40, 0, 0, 24, 0, 32, -48, 0, 0, 0, 0, 96, 0, 0, -8, -56, 0, 0, 0, 0, 16, -16, 0, 24, -64, 0, -16, 0, 0, -32, -24, 0, 0, 96, 0, -160, -16, 0, 8, 192, 0, -16, 0, 0, 0, -64, 0, 0, 48, 0, -8, 16, 0, 96, 16, 0, 48, 0, 0, 48, 0, 0, 0, 88, 0, -32, 48, 0, -64, -32, 0, 0, 0, 0, 0, 96, 0, 0, -72, 0, 0, 0, 0, 0, -80, 0, -32, 0, 0, 16, -32, 0, 0, -48, 0, -144, 8, 0, 8, 104, 0, 168, 0, 0, 32, 80, 0, 0, -48, 0, 0, 80, 0, -56, -16, 0, 0, 0, 0, 96, 16, 0, 0, -192, 0, 16, 16, 0, -64, 0, 0, 40, 0, 0, 128, 88, 0, 0, -8, 0, 48, -96, 0, -64, -96, 0, 0, 0, 0, -96, 48, 0, 0, -16, 0, -32, 0, 0, -48, -32, 0, 32, 0, 0, 48, 96, 0, 0, 32, 0, 8, 176, 0, 112, 32, 0, -24, 0, 0, 40, 144, 0, 0, -48, 0, 16, 0, 0, 16, -384, 0, -32, 0, 0, 0, 32, 0, 0, -8, 0, 0, 32, 0, -48, 80, 0, 8, 0, 0, 96, 8, 0, 0, 96, 0, -96, -56, 0, -16, 96, 0, 0, 0, 0, 8, 96, 0, 0, 40, 0, -48, -144, 0, 0, 0, 0, 16, 0, 0, 64, -112, 0, 0, -32, 0, 8, -48, 0, -72, -192, 0, 0, 0, 0, -32, 64, 0, 0, 48, 0, -32, -80, 0, 0, 64, 0, -32, 0, 0, -32, 48, 0, 0, 0, 0, -8, -16, 0, 40, 32, 0, -64, 0, 0, 96, 64, 0, 0, 32, 0, 8, -48, 0, 0, 32, 0, 0, 0, 0, 0, -32, 0, 0, -104, 0, 0, -24, 0, -48, 192, 0, 16, 0, 0, 8, 72, 0, 0, -64, 0, -16, 192, 0, -64, -16, 0, -40, 0, 0, -48, 0, 0, 0, 0, 0, -80, -8, 0, 0, -208, 0, -48, 0, 0, 32, 0, 0, 0, 80, 0, 0, -32, 0, -96, 0, 0, 48, 0, 0, -40, -56, 0, 0, -184, 0, 0, -48, 0, 0, 176, 0, -32, 0, 0, 48, -40, 0, 0, 8, 0, -48, -144, 0, -96, 144, 0, -32, 0, 0, -192, 32, 0, 0, 80, 0, -24, 96, 0, 64, 96, 0, 144, 0, 0, 0, 32, 0, 0, -96, 0, 0, 24, 0, -8, -8, 0, 32, 0, 0, 48, 0, 0, 0, -24, 0, -64, 16, 0, -8, -224, 0, 0, 0, 0, 64, 0, 0, 0, -96, 0, -40, 48, 0, 32, -144, 0, 8, 0, 0, 16, 32, 0, 0, -256, 0, 56, -112, 0, 0, -192, 0, 112, 0, 0, 168, 96, 0, 0, -48, 0, -32, -64, 0, -40, -8, 0, 48, 0, 0, 96, 144, 0, 0, 192, 0, -32, 0, 0, 112, -240, 0, -112, 0, 0, 0, -144, 0, 0, 24, 0, 48, -192, 0, -72, -64, 0, -8, 0, 0, 48, 24, 0, 0, 0, 0, 96, -176, 0, -16, 192, 0, -160, 0, 0, -80, 208, 0, 0, 40, 0, -32, -64, 0, -144, 80, 0, 48, 0, 0, -128, 64, 0, 0, 0, 0, 16, -16, 0, -56, -96, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 96, 96, 0, 32, 192, 0, 16, 0, 0, 112, -8, 0, 0, 64, 0, 0, 64, 0, 48, 120, 0, -32, 0, 0, -16, 0, 0, 0, -288, 0, 24, -56, 0, 0, 48, 0, 64, 0, 0, 0, -48, 0, 0, -32, 0, 296, 96, 0, 48, 288, 0, 16, 0, 0, 48, -8, 0, 0, -64, 0, 80, 96, 0, -112, -128, 0, 0, 0, 0, 256, 80, 0, 0, 192, 0, 8, 32, 0, -8, 432, 0, -192, 0, 0, -32, 48, 0, 0, 48, 0, 0, 64, 0, -16, 64, 0, 0, 0, 0, 128, 80, 0, 0, -96, 0, 48, -32, 0, 0, 0, 0, -56, 0, 0, 32, 176, 0, 0, -64, 0, 48, -48, 0, -240, -128, 0, -16, 0, 0, -112, -144, 0, 0, 32, 0, -256, -32, 0, -8, -56, 0, -96, 0, 0, 0, 0, 0, 0, -48, 0, 88, -288, 0, -192, 32, 0, 32, 0, 0, 32, -104, 0, 0, 0, 0, -96, -48, 0, 128, -32, 0, 32, 0, 0, 16, 24, 0, 0, -56], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "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]], "char_orbit_index": 9, "prim_orbit_index": 5, "minimal_twist": "690.2.i.c", "char_is_minimal": true, "conrey_index": 47, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [-1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, -1, 1, 0], [-1, -1, 0, 0, 0, 1, 0, 0], [0, 0, -2, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, -2, 0, -1, 0, -2, 0, 0], [-1, 0, 0, -1, 0, 0, 0, 1], [0, -4, 0, 0, 0, 4, 0, 0], [1, 0, 0, 1, 0, 1, 0, 0], [-1, 0, 0, 1, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 2, 0], [-1, -2, 1, 1, 1, 0, -1, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 0, 3, 0], [2, 1, 0, -2, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [0, 1, 0, 0, -1, 1, 0, 0], [0, 0, 2, 0, -2, 0, 0, -2], [4, 0, 0, 4, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, -1, 0, 0], [1, 0, 2, 0, 0, 0, 0, 2], [0, -1, 0, 0, 2, 1, 0, 0], [-1, 0, 0, -1, 0, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2], [0, -4, 0, 0, 0, -4, -2, 0], [2, -1, -1, 0, 0, 1, -1, -1], [0, 0, -2, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 1, 0, 0], [4, 8, 0, -4, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 3], [0, -6, 0, 0, -2, 0, 2, 0], [-1, 2, 0, 0, 0, -2, 0, 0], [0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0], [0, -1, 2, -2, 0, -1, 2, 2], [-1, 0, 1, 1, 0, 0, 0, 0], [0, -6, 0, 0, 0, 6, 0, 0], [0, 0, 2, 0, 2, 0, -2, 0], [-2, 0, 0, 2, 0, 0, 0, 4], [0, -4, 0, 0, 0, -4, 0, 0], [0, 1, -2, -4, -1, 1, 0, 2], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, -2, 2, 0], [1, -1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0, 0], [0, 0, 0, 0, -2, -1, -2, 0], [0, 0, 3, 0, 6, 0, 0, -3], [1, 0, -2, 1, 0, 0, 0, 0], [0, 6, 0, 0, 3, 0, 3, 0], [0, 1, 0, 5, 0, 1, 0, 0], [8, 0, -4, 0, 0, 0, 0, -4], [0, 0, 0, 0, -2, 0, 0, 0], [0, 0, 2, 0, -1, 0, 1, 0], [4, 0, 0, -4, 0, 0, 0, -2], [0, 1, 0, 0, 0, 1, 4, 0], [1, 0, 0, 1, 1, -2, 1, -1], [-4, 0, -2, 0, 0, 0, 0, 2], [0, 0, 0, 0, -2, 0, 2, 0], [0, 0, 0, 0, 4, 0, 4, 2], [0, 0, 0, 1, 0, 0, 0, 0], [0, -2, 0, 0, 3, 6, 1, 0], [-8, 4, 0, 0, 0, -4, 0, 0], [-6, 0, 4, -6, 0, 0, 0, 0], [0, 0, 0, 0, -3, 0, -3, 0], [0, 1, 0, -1, 0, 1, 0, 0], [6, 0, 2, 0, 0, 0, 0, 2], [0, 3, 0, 0, -6, -3, 0, 0], [-2, 0, 0, -2, 0, 1, 0, 0], [3, 0, 0, -3, 0, 0, 0, -4], [0, 0, 0, 0, 0, 0, -2, 0], [-1, 1, -4, 1, 2, 0, -2, 0], [0, 0, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 8, 0, -8, 0], [1, 2, 0, -1, -2, 0, -2, 2], [0, 0, -1, 2, 0, 0, 0, -1], [0, -1, 0, 0, 0, 1, -1, 0], [7, 4, 0, 0, 0, -4, 0, 0], [6, 0, 0, 6, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0, -2, -2], [9, 0, 6, -9, 0, 0, 0, 0], [0, -2, 0, 0, -4, 2, 0, 0], [-4, 0, -2, -4, -2, 8, 2, 0], [4, 0, 0, -4, 0, 0, 0, 0], [0, 4, 0, 0, 0, 4, -2, 0], [-1, 4, 1, 1, -2, 0, 2, 0], [-12, 0, 2, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, -2, 0, -2, -4], [0, 0, 2, -2, 0, 0, 0, 2], [0, -3, 0, 0, 0, 3, 2, 0], [1, 1, 0, 0, 0, -1, 0, 0], [2, 0, 2, 2, 0, 0, 0, 0], [0, -5, 0, 0, 0, 0, 0, 0], [0, -4, 0, 16, 0, -4, 0, 0], [0, 0, 2, -1, 0, 0, 0, -2]]}