# Stored data for newform 270.2.c.c, downloaded from the LMFDB on 09 September 2024.
{"Nk2": 1080, "analytic_conductor": 2.1559608545745705, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "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": [270, 2, [191, 217], [2, 1]], "cm_discs": [], "conrey_index": 109, "dim": 4, "field_disc": 5776, "field_disc_factorization": [[2, 4], [19, 2]], "field_poly": [25, 0, -9, 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, [19, 0, 1]], [11, [-19, 0, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007336727249166, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 15, 4, -1, 2, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "270.2.c.c", "level": 270, "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], "level_radical": 30, "minimal_twist": "270.2.c.c", "nf_label": "4.0.5776.1", "prim_orbit_index": 2, "qexp_display": "q-\\beta _{2}q^{2}-q^{4}+\\beta _{1}q^{5}+(1+2\\beta _{3})q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "270.2.c", "trace_display": [0, 0, 0, 0], "trace_hash": 856261413242472456, "trace_moments": [{"__RealLiteral__": 0, "data": "0.041", "prec": 17}, {"__RealLiteral__": 0, "data": "3.785", "prec": 17}, {"__RealLiteral__": 0, "data": "0.783", "prec": 17}, {"__RealLiteral__": 0, "data": "123.890", "prec": 24}, {"__RealLiteral__": 0, "data": "17.710", "prec": 20}, {"__RealLiteral__": 0, "data": "4966.843", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.763", "prec": 17}, "traces": [0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, -24, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 28, 0, 0, -16, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -8, 0, 0, -48, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, -16, 0, 0, -4, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, -12, 0, 0, -40, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 32, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 76, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -20, 0, 0, 52, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 32, 0, 0, 8, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 48, 0, 0, 12, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 24, 0, 0, -60, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, -72, 0, 0, 88, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -56, 0, 0, 16, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 4, 0, 0, 152, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -20, 0, 0, 72, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, -152, 0, 0, -24, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 72, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -76, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 8, 0, 0, 16, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, -32, 0, 0, -20, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 64, 0, 0, 12, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 40, 0, 0, -36, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, -152, 0, 0, -16, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 56, 0, 0, -152, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 28, 0, 0, -120, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 76, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 76, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 160, 0, 0, -16, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 64, 0, 0, -152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -168, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, -52, 0, 0, 44, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -76, 0, 0, -128, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, 20, 0, 0, 68, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 96, 0, 0, -152, 0, 0, 0, 0, 0, 114, 0, 0, 0, 0, 0, -88, 0, 0, 20, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, -52, 0, 0, 76, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, -80, 0, 0, -108, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 104, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152, 0, 0, -32, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, -8, 0, 0, -64, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 140, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -16, 0, 0, -36, 0, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, -32, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, -56, 0, 0, -152, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, -152, 0, 0, 168, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, -116, 0, 0, -24, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 60, 0, 0, -80, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 48, 0, 0, -76, 0, 0, 0, 0, 0, -190, 0, 0, 0, 0, 0, -48, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, -156, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 288, 0, 0, 84, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 56, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, -16, 0, 0, 152, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -212, 0, 0, 0, 0, 0, 0, 0, 0, -28], "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], [1, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [1, 0, 0, 2], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 2, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, -1, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, -4, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [-1, 0, 0, -2], [0, 0, -2, 0], [0, 0, 0, 0], [5, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [7, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [0, -1, 10, 0], [0, 0, 0, 0], [-2, 0, 0, -4], [0, 0, 6, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, -4, 2, 0], [0, 0, 0, 0], [2, 0, 0, 4], [0, -2, 1, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [-12, 0, 0, 0], [0, 1, -5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -3, 0], [0, 0, 0, 0], [10, 0, 0, 1], [0, -2, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 2, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 0, -7, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 4], [0, 0, 4, 0], [0, 0, 0, 0], [10, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, -2], [0, -4, 2, 0], [0, 0, 0, 0], [6, 0, 0, 0], [0, 0, 19, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [2, 0, 0, 4], [0, 0, -5, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 4, -2, 0], [0, 0, 0, 0], [1, 0, 0, 2], [0, 4, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, -6, 0, 0], [0, 0, 0, 0], [-1, 0, 0, -2], [0, 0, 12, 0], [0, 0, 0, 0], [-5, 0, 0, -1]]}