# Stored data for newform 1260.2.s.e, downloaded from the LMFDB on 23 April 2024.
{"label": "1260.2.s.e", "space_label": "1260.2.s", "level": 1260, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18015635493618924, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 408517809956875576, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[11, [324, 0, 18, 0, 1]], [13, [-17, 2, 1]]], "qexp_display": "q+\\beta _{1}q^{5}+(\\beta _{1}-\\beta _{3})q^{7}+(\\beta _{2}+\\beta _{3})q^{11}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "s", "char_is_real": false, "Nk2": 5040, "analytic_conductor": 10.06115065468133, "hecke_ring_index": 3, "level_radical": 210, "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": "0.045", "prec": 17}, "analytic_rank_proved": true, "char_values": [1260, 3, [631, 281, 757, 1081], [3, 3, 3, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [361, 541], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.873", "prec": 17}, {"__RealLiteral__": 0, "data": "0.711", "prec": 17}, {"__RealLiteral__": 0, "data": "53.885", "prec": 20}, {"__RealLiteral__": 0, "data": "26.387", "prec": 20}, {"__RealLiteral__": 0, "data": "1276.650", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 0, -2, -2], "traces": [0, 4, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -2, 0, 0, 0, 24, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -12, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 8, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -22, 0, 0, 0, 24, 0, 0, 0, 0, 0, -12, 0, 38, 0, 0, 0, 14, 0, 32, 0, 0, 0, -24, 0, 26, 0, 0, 0, 0, 0, 2, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 4, 0, -28, 0, 0, 0, 12, 0, 14, 0, 0, 0, 0, 0, -28, 0, 0, 0, -36, 0, -12, 0, 0, 0, -24, 0, -28, 0, 0, 0, -4, 0, -4, 0, 0, 0, -36, 0, -16, 0, 0, 0, -24, 0, 24, 0, 0, 0, -24, 0, 4, 0, 0, 0, -12, 0, -52, 0, 0, 0, 2, 0, 36, 0, 0, 0, 12, 0, -22, 0, 0, 0, 48, 0, -4, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 2, 0, -4, 0, 0, 0, 36, 0, -64, 0, 0, 0, 12, 0, 14, 0, 0, 0, 12, 0, -12, 0, 0, 0, 24, 0, 8, 0, 0, 0, -20, 0, -14, 0, 0, 0, 24, 0, 72, 0, 0, 0, 12, 0, -34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -4, 0, 0, 0, 0, 0, -10, 0, 0, 0, -48, 0, -22, 0, 0, 0, 36, 0, -2, 0, 0, 0, -48, 0, 24, 0, 0, 0, -36, 0, 38, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, 0, -22, 0, 0, 0, -24, 0, 36, 0, 0, 0, 0, 0, 2, 0, 0, 0, -12, 0, -34, 0, 0, 0, -4, 0, -4, 0, 0, 0, 72, 0, -68, 0, 0, 0, -48, 0, -40, 0, 0, 0, -12, 0, 0, 0, 0, 0, 12, 0, -60, 0, 0, 0, 20, 0, -46, 0, 0, 0, 0, 0, -10, 0, 0, 0, -96, 0, 20, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -72, 0, 0, 0, -22, 0, 26, 0, 0, 0, -24, 0, 70, 0, 0, 0, 72, 0, -34, 0, 0, 0, 24, 0, -12, 0, 0, 0, 24, 0, 92, 0, 0, 0, 0, 0, -64, 0, 0, 0, -12, 0, 116, 0, 0, 0, 0, 0, 20, 0, 0, 0, 24, 0, -12, 0, 0, 0, 24, 0, -36, 0, 0, 0, -34, 0, -22, 0, 0, 0, -24, 0, 92, 0, 0, 0, 12, 0, -4, 0, 0, 0, -36, 0, -28, 0, 0, 0, 24, 0, -38, 0, 0, 0, -16, 0, 50, 0, 0, 0, -96, 0, -36, 0, 0, 0, 108, 0, -22, 0, 0, 0, 72, 0, 48, 0, 0, 0, 12, 0, 20, 0, 0, 0, 26, 0, 0, 0, 0, 0, 24, 0, 2, 0, 0, 0, -72, 0, 10, 0, 0, 0, 72, 0, 0, 0, 0, 0, 72, 0, 14, 0, 0, 0, -4, 0, 32, 0, 0, 0, 84, 0, -22, 0, 0, 0, -60, 0, 76, 0, 0, 0, -12, 0, -36, 0, 0, 0, -24, 0, -10, 0, 0, 0, 0, 0, -34, 0, 0, 0, 24, 0, 72, 0, 0, 0, -96, 0, 28, 0, 0, 0, -36, 0, -36, 0, 0, 0, -48, 0, 20, 0, 0, 0, -14, 0, 50, 0, 0, 0, 12, 0, -40, 0, 0, 0, 72, 0, -10, 0, 0, 0, -48, 0, -2, 0, 0, 0, -72, 0, 32, 0, 0, 0, 14, 0, -82, 0, 0, 0, 60, 0, -28, 0, 0, 0, 12, 0, -36, 0, 0, 0, 12, 0, 12, 0, 0, 0, -96, 0, 38, 0, 0, 0, -28, 0, 36, 0, 0, 0, 144, 0, 68, 0, 0, 0, 0, 0, -88, 0, 0, 0, 24, 0, 0, 0, 0, 0, 72, 0, 14, 0, 0, 0, 14, 0, 36, 0, 0, 0, -120, 0, -14, 0, 0, 0, 48, 0, 56, 0, 0, 0, -144, 0, 72, 0, 0, 0, 36, 0, 62, 0, 0, 0, -12, 0, 20, 0, 0, 0, 36, 0, -46, 0, 0, 0, 36, 0, 14, 0, 0, 0, 24, 0, -24, 0, 0, 0, 108, 0, -22, 0, 0, 0, 56, 0, 104, 0, 0, 0, 84, 0, -4, 0, 0, 0, -24, 0, 20, 0, 0, 0, -36, 0, 2, 0, 0, 0, 0, 0, -108, 0, 0, 0, 8, 0, -40, 0, 0, 0, -36, 0, -80, 0, 0, 0, 144, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, -12, 0, -88, 0, 0, 0, -16, 0, -14, 0, 0, 0, -48, 0, 44, 0, 0, 0, -72, 0, -22, 0, 0, 0, -72, 0, 12, 0, 0, 0, -120, 0, 100, 0, 0, 0, -12, 0, -14, 0, 0, 0, -36, 0, -52, 0, 0, 0, 0, 0, 44, 0, 0, 0, -60, 0, -24, 0, 0, 0, 0, 0, 34, 0, 0, 0, -2, 0, 20, 0, 0, 0, -96, 0, -28, 0, 0, 0, -12, 0, 50, 0, 0, 0, 84, 0, 24, 0, 0, 0, -60, 0, -72, 0, 0, 0, 26, 0, 86, 0, 0, 0, -120, 0, -36, 0, 0, 0, 84, 0, -34, 0, 0, 0, 216, 0, -4, 0, 0, 0, 48, 0, 140, 0, 0, 0, 36, 0, 44, 0, 0, 0, -36, 0, -36, 0, 0, 0, 36, 0, -26, 0, 0, 0, 144, 0, 12, 0, 0, 0, 0, 0, -84, 0, 0, 0, 44, 0, -124, 0, 0, 0, 72, 0, -58, 0, 0, 0, -60, 0, 72, 0, 0, 0, -24, 0, -24, 0, 0, 0, -36, 0, 38, 0, 0, 0, 8, 0, 26, 0, 0, 0, 72, 0, 36, 0, 0, 0, 0, 0, -76, 0, 0, 0, -48, 0, 24, 0, 0, 0, 48, 0, -16, 0, 0, 0, 0, 0, 22, 0, 0, 0, -60, 0, 2, 0, 0, 0, -144, 0, 2, 0, 0, 0, -24, 0, 0, 0, 0, 0, 48, 0, -28, 0, 0, 0, -28, 0, 56, 0, 0, 0, 12, 0, 80, 0, 0, 0, 72, 0, 2, 0, 0, 0, 48, 0, 2, 0, 0, 0, 48, 0, 0, 0, 0, 0, -70, 0, -94, 0, 0, 0, -24, 0, 44, 0, 0, 0, -48, 0, 8, 0, 0, 0, 12, 0, -72, 0, 0, 0, -72, 0, 36, 0, 0, 0, 32, 0, -28, 0, 0, 0, -168, 0, -58, 0, 0, 0, 0, 0, 2, 0, 0, 0, -72, 0, -24, 0, 0, 0, -36, 0, -16, 0, 0, 0, 14, 0, -140, 0, 0, 0, 24, 0, -22, 0, 0, 0, -24, 0, -56, 0, 0, 0, 120, 0, 12, 0, 0, 0, -96, 0, 80, 0, 0, 0, 24, 0, -216, 0, 0, 0, -24, 0, -84, 0, 0, 0, 0, 0, -72, 0, 0, 0, 24, 0, -12, 0, 0, 0, 72, 0, -46, 0, 0, 0, -16, 0, 108, 0, 0, 0, -96, 0, 56, 0, 0, 0, -72, 0, -144, 0, 0, 0, -96, 0, 10, 0, 0, 0, -60, 0, 116, 0, 0, 0, -14, 0, 44, 0, 0, 0, 36, 0, 0, 0, 0, 0, -96, 0, 56, 0, 0, 0, 24, 0, -12, 0, 0, 0, 0, 0, -176, 0, 0, 0, -36, 0, 26, 0, 0, 0, 72, 0, 28, 0, 0, 0, 60, 0, 32, 0, 0, 0, -36, 0, 12, 0, 0, 0, 240, 0, 68, 0, 0, 0, -4, 0, 62, 0, 0, 0, 24, 0, -64, 0, 0, 0, -24, 0, 36, 0, 0, 0, 60, 0, 0, 0, 0, 0, -36, 0, 38, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 70, 0, 0, 0, 12, 0, 10, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 44, 0, 0, 0, -4, 0, 72, 0, 0, 0, 48, 0, -72, 0, 0, 0, 0, 0, 36, 0, 0, 0, 168, 0, 0, 0, 0, 0, 12, 0, 2, 0, 0, 0, 20, 0, -140, 0, 0, 0, 108, 0, 8, 0, 0, 0, -36, 0, 116, 0, 0, 0, -72, 0, 24, 0, 0, 0, -96, 0, 36, 0, 0, 0, 44, 0, 70, 0, 0, 0, 132, 0, 32, 0, 0, 0, 24, 0, 32, 0, 0, 0, -120, 0, -36, 0, 0, 0, 12, 0, -144, 0, 0, 0, -2, 0, 86, 0, 0, 0, 72, 0, -10, 0, 0, 0, -24, 0, -40, 0, 0, 0, -252, 0, 24, 0, 0, 0, -72, 0, -196, 0, 0, 0, -12, 0, 44, 0, 0, 0, -120, 0, -52, 0, 0, 0, -12, 0, -10, 0, 0, 0, 108, 0, -36, 0, 0, 0, 48, 0, 154, 0, 0, 0, -34, 0, 36, 0, 0, 0, 0, 0, -72, 0, 0, 0, -36, 0, -154, 0, 0, 0, 36, 0, -16, 0, 0, 0, 72, 0, 38, 0, 0, 0, 2, 0, -72, 0, 0, 0, -72, 0, 62, 0, 0, 0, -72, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 104, 0, 0, 0, -22, 0, 20, 0, 0, 0, 72, 0, 14, 0, 0, 0, 84, 0, 20, 0, 0, 0, 144, 0, -24, 0, 0, 0, -24, 0, -38, 0, 0, 0, -72, 0, -100, 0, 0, 0, -96, 0, 14, 0, 0, 0, 36, 0, -100, 0, 0, 0, -96, 0, 0, 0, 0, 0, 108, 0, -70, 0, 0, 0, -4, 0, 2, 0, 0, 0, 84, 0, -108, 0, 0, 0, 168, 0, 0, 0, 0, 0, -144, 0, 24, 0, 0, 0, -72, 0, 100, 0, 0, 0, -34, 0, -4, 0, 0, 0, -72, 0, 38, 0, 0, 0, -96, 0, -10, 0, 0, 0, -156, 0, 2, 0, 0, 0, 72, 0, -92, 0, 0, 0, 2, 0, -16, 0, 0, 0, 84, 0, 116, 0, 0, 0, 36, 0, 2, 0, 0, 0, 60, 0, 72, 0, 0, 0, -144, 0, -36, 0, 0, 0, 34, 0, -36, 0, 0, 0, -72, 0, -88, 0, 0, 0, 72, 0, 238, 0, 0, 0, 84, 0, 96, 0, 0, 0, 12, 0, 62, 0, 0, 0, 20, 0, 68, 0, 0, 0, 72, 0, 38, 0, 0, 0, 96, 0, 38, 0, 0, 0, 72, 0, 24, 0, 0, 0, 120, 0, -36, 0, 0, 0, 0, 0, -40, 0, 0, 0, 36, 0, -16, 0, 0, 0, -36, 0, -22, 0, 0, 0, 0, 0, 12, 0, 0, 0, 48, 0, -34, 0, 0, 0, 120, 0, -116, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 216, 0, 0, 0, 48, 0, -10, 0, 0, 0, 84, 0, 26, 0, 0, 0, 92, 0, 108, 0, 0, 0, 0, 0, 112, 0, 0, 0, -24, 0, -96, 0, 0, 0, -72, 0, -72, 0, 0, 0, 72, 0, -28, 0, 0, 0, -10, 0, -16, 0, 0, 0, -24, 0, 62, 0, 0, 0, 24, 0, 110, 0, 0, 0, -24, 0, 48, 0, 0, 0, 96, 0, -272, 0, 0, 0, -10, 0, 212, 0, 0, 0, -96, 0, 144, 0, 0, 0, -24, 0, -36, 0, 0, 0, -12, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, -24, 0, 92, 0, 0, 0, 24, 0, 20, 0, 0, 0, -24, 0, 0, 0, 0, 0, 36, 0, 14, 0, 0, 0, 36, 0, -182, 0, 0, 0, -144, 0, -44, 0, 0, 0, -120, 0, 0, 0, 0, 0, 96, 0, 44, 0, 0, 0, -72, 0, 44, 0, 0, 0, 26, 0, 116, 0, 0, 0, 0, 0, -28, 0, 0, 0, -84, 0, -52, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 19, "prim_orbit_index": 3, "minimal_twist": "420.2.q.d", "char_is_minimal": true, "conrey_index": 361, "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], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 1, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 1], [0, 0, 0, 0], [-1, 0, 1, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, -1], [0, 0, 0, 0], [0, -7, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -2, 1], [0, 0, 0, 0], [-1, -1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [6, 0, -1, 2], [0, 0, 0, 0], [1, 1, -2, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, -1, -1, 1], [0, 0, 0, 0], [0, -1, -2, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, -2], [0, 0, 0, 0], [-1, 0, 1, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 6, 0, 0], [0, 0, 0, 0], [5, 5, -2, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -2, -2], [0, 0, 0, 0], [0, 0, 1, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-6, -6, 1, 1], [0, 0, 0, 0], [0, -4, -4, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, -2, 1], [0, 0, 0, 0], [1, 1, -1, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 3, -6], [0, 0, 0, 0], [-5, -5, 1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-6, -12, 1, -2], [0, 0, 0, 0], [0, 11, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [6, 0, 1, -2], [0, 0, 0, 0], [0, 0, -1, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 6, -2, 1], [0, 0, 0, 0], [12, 5, -2, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [7, 7, 0, 0], [0, 0, 0, 0], [8, 0, -2, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}