# Stored data for newform 400.2.q.e, downloaded from the LMFDB on 24 April 2024.
{"label": "400.2.q.e", "space_label": "400.2.q", "level": 400, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18015498054664592, "dim": 12, "is_polredabs": true, "nf_label": "12.0.4767670494822400.1", "trace_hash": 831158270304747102, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, -18, 162, -282, 243, 20, 36, -60, 51, 6, 2, -2, 1]]], "qexp_display": "q-\\beta _{6}q^{2}-\\beta _{7}q^{3}+\\beta _{10}q^{4}+(-\\beta _{3}+\\cdots)q^{6}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 80, "char_orbit_label": "q", "char_is_real": false, "Nk2": 1600, "analytic_conductor": 3.1940160808512155, "hecke_ring_index": 4, "level_radical": 10, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "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": "0.259", "prec": 17}, "analytic_rank_proved": true, "char_values": [400, 4, [351, 101, 177], [4, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [149, 349], "field_disc": 4767670494822400, "field_disc_factorization": [[2, 22], [5, 2], [11, 2], [613, 2]], "field_poly": [64, -128, 112, -32, -32, 48, -38, 24, -8, -4, 7, -4, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.916", "prec": 20}, {"__RealLiteral__": 0, "data": "2.289", "prec": 17}, {"__RealLiteral__": 0, "data": "477.801", "prec": 24}, {"__RealLiteral__": 0, "data": "434.843", "prec": 24}, {"__RealLiteral__": 0, "data": "34930.841", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c4", "trace_display": [-2, 2, 0, -12], "traces": [0, 12, -2, 2, -2, 0, 6, -12, -2, 0, 0, -2, 6, -4, -14, 0, 2, 0, 18, 14, 0, -20, 20, -12, 14, 0, -16, -10, 10, 0, 0, -4, -2, 0, 6, 0, 2, 8, -28, 0, 0, 0, -10, 0, 44, 0, -10, 0, 58, -4, 0, 10, 0, 16, -10, 0, 6, 16, -4, -20, 0, 4, -22, 0, -38, 0, 32, -50, -50, 0, 0, 0, 54, -40, -10, 0, 60, 8, 48, -12, 0, -8, 12, -2, -34, 0, 6, 64, -56, 0, 0, 0, -50, -44, -32, 0, -34, 0, 30, -12, 0, 16, 14, 48, 8, 0, -54, -46, 6, 40, 0, -12, -30, 0, 96, 0, -52, 8, -90, 0, 0, 0, 46, -10, 34, 0, -56, 0, 54, -76, 0, -56, -24, 28, -8, 0, 14, 4, -70, 22, 0, -24, -36, 0, 10, 0, 12, 46, -18, 48, 0, 0, 8, 52, -74, 0, 16, -32, 114, 20, 0, 56, -28, -2, -60, 0, 68, -56, -86, 0, 0, 72, -2, 36, -52, 0, 32, 0, 46, 46, 0, -16, 20, 36, 2, 0, -74, 90, 16, 40, 0, 84, -30, 0, 100, 0, -50, 32, -90, 0, 0, 0, -2, 8, 38, 0, 44, 0, 112, -20, 0, 22, 82, -56, 30, 0, 78, 16, -54, -78, 0, 4, -30, 0, 30, 0, 56, -24, -24, 8, 0, 0, 68, 32, -36, 0, 46, 16, 114, -64, 0, -40, -90, -68, -82, 0, 56, 80, -82, 0, 0, -74, -72, 52, 18, 0, -78, 0, -46, 4, 0, 8, 22, 92, 84, 0, -46, -86, 56, -60, 0, -124, -46, 0, 34, 0, -158, 36, -80, 0, 0, 0, -32, -86, 92, 0, -12, 0, 134, -24, 0, -28, -28, -20, 22, 0, 10, -104, -16, 32, 0, -12, -34, 0, -72, 0, 122, 62, -106, 0, 0, 0, 40, -32, -78, 0, 58, -60, 102, 160, 0, -36, 92, -14, -52, 0, -68, -84, -112, 0, 0, 50, 4, -36, -8, 0, -18, 0, 76, 54, 0, 48, 90, -96, -38, 0, -48, 90, 44, -20, 0, 88, -24, 0, 18, 0, -10, -48, -84, 0, 0, 0, 94, 36, -20, 0, -70, 0, 54, 28, 0, 76, -26, 100, 20, 0, -8, 16, -22, -10, 0, 60, -50, 0, -50, 0, 58, -100, -4, -4, 0, 0, 46, 4, -42, 0, 94, 0, 76, -164, 0, 8, 44, -40, -50, 0, 48, 196, -106, 0, 0, -94, 76, -68, -116, 0, -40, 0, 78, -178, 0, 24, -18, -64, 54, 0, 20, -100, 78, -4, 0, -84, 66, 0, 56, 0, -14, -120, -120, 0, 0, 0, 16, 6, 74, 0, 28, 0, 82, 32, 0, -38, 64, 0, 86, 0, -28, -4, -12, 142, 0, -12, -46, 0, -60, 0, 16, 136, 44, 48, 0, 0, -38, -28, 70, 0, 10, 84, 12, 84, 0, -24, -148, 196, -42, 0, 36, -212, -22, 0, 0, 24, 56, 24, 100, 0, -38, 0, 24, 80, 0, -116, 6, -168, -24, 0, -106, 122, -6, 44, 0, 124, -74, 0, 4, 0, -14, -56, 88, 0, 0, 0, -8, 130, 22, 0, -30, 0, 28, 92, 0, 116, 2, -124, 86, 0, -20, -48, -24, -134, 0, -164, 70, 0, -10, 0, -4, -158, -54, -84, 0, 0, -34, -72, -56, 0, 80, -60, -24, -56, 0, 48, 16, 12, 64, 0, -52, 180, -20, 0, 0, -56, -60, 88, -34, 0, 10, 0, 20, -14, 0, -72, 124, 20, -64, 0, -10, -98, 46, -60, 0, -52, -82, 0, -108, 0, -24, 104, -60, 0, 0, 0, 24, -52, 6, 0, 10, 0, -104, 112, 0, -104, -46, -28, 10, 0, 50, 120, 108, -8, 0, 164, -22, 0, -56, 0, 104, 234, 26, -156, 0, 0, -90, 76, -76, 0, -50, 36, -44, 32, 0, 48, 30, 56, -28, 0, 20, -296, -8, 0, 0, 76, 20, -4, 78, 0, 128, 0, -72, 78, 0, 172, -64, -40, 152, 0, 64, 176, 8, -140, 0, -4, -46, 0, 32, 0, 76, 24, -44, 0, 0, 0, -122, -2, 58, 0, 96, 0, 54, 120, 0, 122, 152, 204, -74, 0, 116, -40, 14, 76, 0, 88, 0, 0, 104, 0, -48, -164, -14, -88, 0, 0, 6, 56, -10, 0, 4, 68, -26, -100, 0, 32, -138, -66, 54, 0, -118, 136, -60, 0, 0, -68, 34, -108, 112, 0, -78, 0, 30, -176, 0, 20, -32, 132, -54, 0, 42, -188, -36, 32, 0, -224, 136, 0, -96, 0, 2, 4, 98, 0, 0, 0, -122, 28, -58, 0, -110, 0, -118, 112, 0, -104, -46, -56, -32, 0, -172, 64, 10, 150, 0, -96, 174, 0, 130, 0, -126, 152, 62, 44, 0, 0, 74, -8, -112, 0, -52, 84, -58, 248, 0, -140, 116, 18, 44, 0, -172, -336, 186, 0, 0, 112, -120, 96, -118, 0, -86, 0, -40, 56, 0, -44, -78, -24, -60, 0, 136, 154, -100, 80, 0, 216, -72, 0, -108, 0, -42, -16, -4, 0, 0, 0, 200, 84, -130, 0, -160, 0, -118, -128, 0, 68, -76, -140, -28, 0, -18, 140, -68, -118, 0, -92, -66, 0, 30, 0, -38, -148, 32, 156, 0, 0, -122, -8, 98, 0, -120, 36, -128, -140, 0, -104, 126, -78, 56, 0, 104, 224, 38, 0, 0, -98, 124, 184, 128, 0, 94, 0, -152, -96, 0, 4, -78, 80, -20, 0, -22, -112, 14, -52, 0, -8, 12, 0, -90, 0, 212, 68, 158, 0, 0, 0, 52, -56, -150, 0, 140, 0, -156, -112, 0, -62, 160, -128, 18, 0, 36, 8, -98, 176, 0, 132, -106, 0, 198, 0, -102, 84, 262, -140, 0, 0, -58, -84, 64, 0, -36, -96, -50, 36, 0, -36, -148, 28, 100, 0, 212, -136, 194, 0, 0, 122, 60, -160, 34, 0, 62, 0, -80, -54, 0, 132, -102, -140, -68, 0, 60, 112, -108, 4, 0, 212, 158, 0, -8, 0, 144, -4, 170, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 80, 17, 1, 4, 0]], "char_orbit_index": 17, "prim_orbit_index": 17, "minimal_twist": "400.2.l.f", "char_is_minimal": false, "conrey_index": 149, "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, 0, 0, 0, 0], [1, 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, -1, 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, 0, -1, -1, -2, -1, 0, 0, -1, 1, -1], [-1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 2, 3, 1, -1, -1, 0, -1, 0], [-1, -1, 0, -1, -2, -2, 0, 0, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 1, 0, 2, 2, -1, 1, 1, -1, 0], [0, 2, -2, 0, 1, 2, -1, 0, -1, 0, 0, 0], [0, 0, 1, 0, 1, 1, 1, -2, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 2, 2, 0, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, -1, -1, 0, 1, 0, 0, 0, -2], [1, -1, 0, 1, 0, -1, 0, 0, -1, 1, 1, 0], [1, 1, -1, -1, 1, -1, -1, -1, 0, -1, 0, 1], [1, 2, -1, -1, 0, 2, 0, 0, -2, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 2, 1, 4, 3, 0, 0, 2, -2, 0], [1, -1, -1, 0, 0, -1, -2, 1, 0, -2, 1, 0], [-1, -2, 3, 1, -2, 0, 4, -1, 2, 2, -2, -1], [1, 0, -1, 2, 1, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, -2, -1, -2, -1, 0, -1, -2, 1, -2], [-2, -1, 1, -2, -2, -2, 2, 0, 1, -1, -1, -1], [1, -1, -1, -1, 1, -3, -1, 1, 0, -1, 0, 1], [0, -2, 3, 0, -3, -3, -1, 0, 2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 1], [1, 2, -1, 0, 2, 0, -1, 2, -1, 1, -1, 1], [-1, -2, 1, -1, -2, -5, 0, 0, 2, -2, 2, 0], [1, 1, 3, 1, 0, 3, 3, -1, 0, 1, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -3, -5, -3, -1, 0, -1, 2, -1], [1, -2, 1, 0, -3, -2, 1, 0, 2, 2, 2, 0], [-3, 1, -1, 2, 1, 1, 1, 1, 1, 2, -2, -2], [-1, 0, -1, 0, -1, -4, 1, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 3, 4, 5, 2, -2, 0, 0, 0, 2], [0, -2, 2, 0, 0, 0, 2, 2, 1, 0, -1, 0], [0, -1, -1, 0, 0, 0, 2, 0, 1, 1, 1, 2], [5, 1, -1, -1, 2, 1, -2, -1, -1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, -3, -2, -3, -2, 3, 1, -3, 1, 1], [0, 0, 2, -1, 1, 0, -1, -1, 2, -2, 0, 1], [6, 1, 0, 1, 1, 3, -2, 1, -2, 0, 0, 0], [0, 0, -3, -1, 4, 0, -4, 0, -2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 3, -3, 2, 4, 4, -2, 0, -3, 1, 1, 1], [-1, 3, -3, -1, 1, 1, 1, 1, -1, 1, -1, -1], [1, 2, 0, -2, -2, 1, 0, 0, -2, 0, 0, -2], [-2, 0, -2, -3, -2, -6, -2, 2, 1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, -1, -3, -5, -1, -1, 0, 1, 0, 1], [0, -1, 0, 3, -2, 0, 0, -2, 3, 3, -1, -2], [0, 2, -2, -2, 1, 4, -3, 2, -1, -2, 3, 2], [0, 1, 1, -2, 4, 2, 0, -2, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 1, 1, 0, 1, 0, 2, 0, 0, 0], [-1, -1, 1, 3, 2, 1, 0, -1, -1, -1, -1, 3], [3, 0, 1, 1, 2, 0, -2, 2, -2, 2, 0, -2], [-3, -2, 1, 4, -2, 2, 3, 0, 1, 3, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, 1, 2, -2, -2, -2, -2, 0, 2], [-5, 1, 0, -1, 0, 4, 0, -1, 1, -1, 1, 0], [-5, -1, -1, -1, -1, 3, -1, 3, 1, -1, 0, -1], [3, -2, 4, 2, 2, 1, 4, 2, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, -1, 1, 0, -1, -1, 0, 0, -2, 1], [3, 3, -1, -1, -1, -1, -1, -1, 0, -1, 2, -1], [-3, -1, 1, 2, -2, 0, 0, 2, 1, 1, -1, 2], [0, 2, 2, 2, 4, 4, 0, -2, -1, -2, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, -2, 2, 1, 2, -1, 4, -2, 0, 1, 2], [4, -2, 0, -1, 3, -2, -3, 0, -2, 2, -2, 0], [3, 1, -1, 1, -2, 1, 0, 1, 0, 1, -2, 1], [-2, 2, -4, 3, -1, 0, -7, 2, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 2, 1, -2, 0, 0, 2, -1, -1, -1, 2], [2, -2, 2, -2, 1, 2, 0, -2, -2, -2, 0, -2], [-2, -1, -3, -2, -4, -4, -6, 1, -1, -3, 3, 0], [-1, -1, 1, -1, 1, 1, 1, 1, 0, 1, -2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 3, 1, 1, -3, 1, -3, 0, -1, -2, 1], [5, 2, 1, -2, -1, 0, -1, -1, -4, -4, 2, -1], [-4, -1, 2, 1, -2, -5, -3, -1, 0, 0, 2, -2], [-1, -1, -2, 1, -2, 3, 2, -2, -1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 2, 2, 0, 0, 2, -2, 0], [-4, 0, -2, 0, 2, 2, 2, -2, 1, 2, -1, 4], [-2, 0, 1, -1, 2, 3, 0, 2, 0, 0, 0, 0], [-3, -1, -3, -3, 0, -1, -4, -1, -2, -3, 4, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 2, 2, 6, -1, 0, 1, 3, -1, -1], [-1, 2, -3, 5, 4, 8, 6, -2, -2, 2, -2, 2], [4, 0, 0, -2, -2, -8, -1, 0, -2, 2, 2, -2], [-1, -1, 2, -3, -6, -4, 2, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}