# Stored data for newform 1155.1.e.c, downloaded from the LMFDB on 18 April 2024.
{"label": "1155.1.e.c", "space_label": "1155.1.e", "level": 1155, "weight": 1, "hecke_orbit": 3, "hecke_orbit_code": 9007474149426307, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 2148788894153630826, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [3, 0, 1]], [29, [1, 1]]], "qexp_display": "q+(\\zeta_{12}^{2}+\\zeta_{12}^{4})q^{2}+\\zeta_{12}^{3}q^{3}+(-1+\\cdots)q^{4}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 1155, "char_orbit_label": "e", "char_is_real": true, "Nk2": 1155, "analytic_conductor": 0.5764200895911178, "hecke_ring_index": 1, "level_radical": 1155, "projective_image": "D6", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": false, "projective_field_label": "6.0.46690875.1", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.884", "prec": 17}, "analytic_rank_proved": true, "char_values": [1155, 2, [386, 232, 661, 211], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 8, "level_primes": [3, 5, 7, 11], "conrey_indexes": [1154], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.047", "prec": 20}, {"__RealLiteral__": 0, "data": "3.486", "prec": 17}, {"__RealLiteral__": 0, "data": "-1.868", "prec": 20}, {"__RealLiteral__": 0, "data": "160.374", "prec": 24}, {"__RealLiteral__": 0, "data": "-101.603", "prec": 27}, {"__RealLiteral__": 0, "data": "9259.829", "prec": 27}], "related_objects": [], "self_twist_discs": [-231], "cm_discs": [-231], "rm_discs": [], "relative_dim": 4, "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, -8, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 2, 4, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, -4, 6, 0, 0, 0, 0, -2, 8, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 0, -4, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, -2, 0, 0, 0, 0, -6, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 4, 0, 0, -8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 6, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 8, 0, 0, 0, -6, 4, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 12, -2, 0, 0, 0, 0, 4, -4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -6, 0, 0, 0, 0, 0, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 4, 4, 0, 0, 0, 0, -12, 0, 0, 0, -6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, -8, 0, 12, 0, 0, 4, -6, -8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 12, 0, 0, 0, 0, -8, 0, 8, 0, 0, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, -12, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 4, 0, 0, -12, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, -12, 0, 0, -4, 0, 0, 0, 0, 0, 0, -12, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 6, -8, 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, 4, 4, 0, 0, 0, 0, 0, 12, 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, 0, 0, -8, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 12, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -6, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, -6, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, -12, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -8, -6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 12, 0, 0, 8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 0, 0, 0, -12, 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, -12, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -12, 6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -8, 0, 0, 0, 0, 0, -6, 4, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 6, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -8, 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, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -12, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 12, 0, 0, 0, 6, -4, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 12, 0, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -4, 0, 0, 0, -4, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -8, -2, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 8, 0, 0, 0, 0], "projective_field": [21, 21, 32, 11, -3, -2, 1], "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, 231, 8, -1, 2, -231], [1, 1, 5, 2, 1, 2, 0], [1, 1, 7, 2, -1, 2, 0], [1, 1, 33, 4, 1, 2, 0], [1, 1, 35, 3, -1, 2, 0], [1, 1, 165, 4, 1, 2, 0], [1, 1, 1155, 5, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "1155.1.e.c", "char_is_minimal": true, "conrey_index": 1154, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[1, 2], [1, 4]], [[1, 3]], [[-1, 0], [-1, 2], [1, 4]], [[-1, 1]], [[-1, 1], [1, 5]], [[-1, 3]], [[-1, 2], [-1, 4]], [[-1, 0]], [[-1, 3], [-1, 5]], [[-1, 0]], [[-1, 1], [-1, 3], [-1, 5]], [[-1, 3]], [[1, 1], [-1, 5]], [[-1, 4]], [[1, 0]], [], [[-1, 2], [-1, 4]], [[-1, 1], [1, 5]], [[1, 1], [1, 3], [-1, 5]], [[1, 0]], [[-1, 2], [-1, 4]], [], [[1, 1], [-1, 5]], [[1, 2]], [[1, 1], [-1, 5]], [[-1, 3]], [[1, 1], [1, 3], [1, 5]], [[-1, 0]], [[1, 0], [1, 2]], [], [], [[-1, 3]], [], [[1, 4]], [[1, 0], [1, 2], [-1, 4]], [[1, 2], [1, 4]], [[-1, 1], [-1, 3], [-1, 3], [-1, 5]], [[1, 0]], [[1, 3], [1, 5]], [], [[1, 2], [1, 4]], [], [[1, 0], [1, 2], [-1, 4]], [[1, 1]], [], [[1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0], [1, 4]], [], [[1, 1], [1, 3], [1, 5]], [], [[1, 1], [-1, 5]], [[1, 1]], [[-1, 1], [1, 5]], [[-1, 2], [-1, 4]], [[-1, 2], [-1, 4]], [[-1, 1], [1, 5]], [[-1, 0], [1, 2], [1, 4]], [], [], [[1, 3]], [[1, 0]], [[1, 4]], [[1, 1], [-1, 5]], [[-1, 2], [-1, 4]], [], [], [[-1, 0], [-1, 2]], [], [[1, 2], [1, 4]], [[1, 3]], [[-2, 0], [-1, 2], [1, 4]], [[1, 5]], [[1, 1], [1, 1], [1, 3], [-1, 3], [-2, 5]], [[1, 3]], [[1, 2], [1, 4]], [], [[-1, 1]], [[1, 0]], [], [], [[-1, 0], [-1, 2], [1, 4]], [], [], [[-1, 3]], [[1, 2], [1, 4]], [], [[1, 3], [1, 5]], [[-1, 0]], [], [], [[-1, 1], [1, 5]], [[1, 0], [1, 2]], [], [], [[-1, 2], [-1, 4]], [[1, 0]], [[-1, 0], [-1, 2], [-1, 4]]]}