# Stored data for newform 2015.1.h.c, downloaded from the LMFDB on 24 April 2024.
{"label": "2015.1.h.c", "space_label": "2015.1.h", "level": 2015, "weight": 1, "hecke_orbit": 3, "hecke_orbit_code": 9007680307857375, "dim": 6, "is_polredabs": true, "nf_label": "6.6.371293.1", "trace_hash": 80979314946680159, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, 3, 6, -4, -5, 1, 1]], [3, [-1, -3, 6, 4, -5, -1, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+\\beta _{3}q^{3}+(1+\\beta _{2})q^{4}+q^{5}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 2015, "char_orbit_label": "h", "char_is_real": true, "Nk2": 2015, "analytic_conductor": 1.0056160004555, "hecke_ring_index": 1, "level_radical": 2015, "projective_image": "D13", "projective_image_type": "Dn", "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 26, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.496", "prec": 17}, "analytic_rank_proved": true, "char_values": [2015, 2, [807, 1861, 716], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [5, 13, 31], "conrey_indexes": [2014], "field_disc": 371293, "field_disc_factorization": [[13, 5]], "field_poly": [-1, -3, 6, 4, -5, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.042", "prec": 20}, {"__RealLiteral__": 0, "data": "5.614", "prec": 17}, {"__RealLiteral__": 0, "data": "-6.923", "prec": 20}, {"__RealLiteral__": 0, "data": "730.411", "prec": 24}, {"__RealLiteral__": 0, "data": "-975.771", "prec": 27}, {"__RealLiteral__": 0, "data": "104704.155", "prec": 34}], "related_objects": [], "self_twist_discs": [-2015], "cm_discs": [-2015], "rm_discs": [], "relative_dim": 6, "trace_display": [-1, 1, 6, -1], "traces": [0, 6, -1, 1, 5, 6, 2, -1, -2, 5, -1, 1, 3, -6, -2, 1, 4, 1, -3, 0, 5, 2, 2, 1, -9, 6, 1, 2, -3, 0, 2, -6, -3, -2, 2, -1, 2, 0, 0, -1, -2, 0, -9, 1, 3, 5, 2, -1, 5, 5, -1, -2, -5, 1, 4, 1, -4, 0, 0, 0, 3, 0, 1, -3, 3, -6, -4, -1, -10, -2, -2, 0, -6, 0, 0, 1, 0, 2, -2, 0, 4, 4, 0, 0, 6, 1, -11, 0, 4, 1, -3, 1, 3, -1, -2, 0, -7, -1, -3, 3, 5, -1, 9, 0, 2, 2, 2, 0, 6, 0, 2, 0, 8, 0, 0, 1, 0, -5, 0, 2, -9, 5, 0, 0, -5, 6, -6, 1, -4, -2, 1, -1, 7, 0, -2, 2, 4, 0, -4, 0, -3, 2, 0, -1, -1, 0, 0, 3, 0, 0, 2, 1, 0, 3, -9, -6, -3, 0, 0, -2, -3, 2, 8, -1, 0, -2, 0, 0, -5, 6, 2, 0, 3, 0, 0, -1, 5, 0, 2, 0, 2, 0, 2, 0, 4, 0, -2, -2, -3, -9, 0, -1, 7, -1, -2, -1, 2, 0, -7, 0, -2, 2, 11, 0, -6, 0, 0, -10, -4, 0, -9, -1, 3, 0, 0, 1, -5, 1, 0, 0, 3, -1, 0, 0, -6, 5, 0, -1, 0, 1, 2, -4, 0, 0, 3, -1, 0, 0, 4, 1, 5, 1, -3, 3, 0, 5, 0, 0, 2, 0, -1, 0, 4, -2, 2, -2, 2, 0, -4, 0, -5, 0, -2, 1, -8, 1, 0, -2, -3, 0, 4, 1, -8, -2, 0, 1, -6, 1, 0, -5, -4, 0, 4, 0, 0, 0, -2, 0, -9, 5, 0, -11, 0, -1, 6, 0, 0, -4, 0, -1, 3, 2, -11, 2, 0, 0, 6, -1, 6, 0, 1, -1, 9, 1, 0, -3, 0, -1, -4, 0, 3, 0, 4, 0, -1, -6, -2, 0, 0, -2, -4, 1, 0, 0, 0, -1, 10, 1, -1, 0, -10, -1, 0, -2, -9, -2, 0, 1, 0, 0, -2, -2, -7, 0, 0, 0, 3, -4, 0, 0, -6, 6, 0, -10, 3, 0, 0, 1, 5, 0, 0, 2, -3, 0, -4, 1, -4, 0, -5, 0, 0, -2, 11, 0, -5, 2, -2, 3, -3, 0, -2, -2, -6, 2, 0, 0, -4, -1, 0, 0, 4, 1, 4, 6, -3, 4, 0, 0, 5, 1, 0, 0, 0, 0, -7, 0, 3, 0, 0, -1, 6, 0, -2, 10, 4, 1, 0, 0, 0, 2, -11, 0, -3, 1, 2, 0, 0, 0, 0, -1, 4, 2, -2, 0, 0, 1, 0, 0, 6, 1, -3, 0, 0, -2, -2, 1, 0, 0, 2, -4, 3, 1, 5, 0, 0, -1, 0, 0, -2, -2, -2, 0, 0, -2, 0, 0, -7, 3, 2, 0, -7, 0, 2, 9, 2, -1, 6, 0, 0, 2, -3, 0, 0, 0, 0, 3, -4, 0, 0, 1, 5, 0, 0, 0, 1, -1, 9, 1, -10, 1, 9, 0, -5, 0, 0, 0, 7, 2, 0, 0, 2, -1, 0, 1, 10, 2, -11, -1, 3, 5, 2, 0, 0, 0, 9, 0, -4, 0, 0, -10, 6, 0, 2, 0, 6, 0, 9, 0, 0, 0, 2, 0, 5, 0, 2, 0, 0, 0, 3, -1, 8, -9, 0, 0, 6, 0, 0, -5, 0, 0, 0, 0, -3, 2, 0, 1, 9, -1, -3, 2, 0, 0, 4, 11, 0, -5, -2, 0, -4, 0, 0, 0, 0, -1, 5, 2, 0, 0, -2, -1, -9, 0, 4, -3, 3, 5, 4, 0, 0, 0, 0, 1, -4, 0, 11, 0, -5, -1, 0, 1, -5, -4, -2, -11, -5, 6, 2, 0, 0, 0, -6, 1, 0, -11, -2, 1, 7, -5, 0, 0, -4, 0, 0, 0, -7, -2, 0, 1, 3, 0, 1, -2, 10, 0, 0, -1, 0, 0, -4, -1, 7, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, -1, 1, 2, 2, 5, 1, 0, -2, 4, 2, -2, -1, 0, 0, 9, -2, 5, -1, -4, 0, 0, 6, 2, 0, 0, 0, 0, 0, -3, -1, -4, 0, 7, 2, 0, -2, 0, -12, 0, 0, 4, -1, 5, -1, 0, -2, 0, 0, -1, 0, -1, 11, 0, 0, 6, 0, 4, 3, 0, -2, 0, -1, 2, 3, 6, -11, 0, 1, 0, 0, -9, 0, 9, 0, 0, 0, -6, 0, 2, -1, -5, 0, 0, 1, -1, 1, 0, 4, 0, 1, 9, 0, -3, 3, 0, 0, 9, 0, -9, 0, -3, 0, -7, -6, 9, 0, 0, 0, -3, 0, -4, 0, -1, 0, -9, 0, 0, -2, 0, 0, -1, 0, -2, -2, 0, 1, 0, 2, -3, 3, 2, 0, -7, 2, -1, 0, 9, 0, 8, 0, 0, -2, 0, -1, -10, 0, 2, 3, 0, 1, 0, 1, 0, -2, 0, 0, -4, 0, 0, -2, -3, 3, 0, 0, 0, -2, -2, 0, -5, 6, 0, 0, -3, 6, 7, -3, 5, 0, 2, 0, 0, -1, 0, 0, 0, 0, 4, 0, 3, 0, 0, 0, -1, 0, -11, 3, 3, 0, 0, 1, 0, -3, 0, -1, 0, -1, -2, 2, 5, 0, 4, 1, 10, 0, 0, 0, 0, 2, 2, 5, 0, 0, 0, 0, -8, 2, -11, 0, 2, -2, 0, 9, 0, 0, -4, 0, 10, -3, 2, 0, 0, 0, 0, 0, 3, -2, 5, -1, 4, 2, 2, 0, 1, 0, 0, 0, 0, 1, -2, 0, 0, 2, 0, -2, 6, 0, 9, -2, -3, 1, 0, 0, 0, -9, -4, 0, 0, 0, 0, 2, 8, 1, -7, -1, 3, 0, 0, 0, 7, 6, 0, 0, 3, -1, 5, 0, 7, 0, -2, -1, -4, 0, 0, -1, 0, -1, -9, -2, 2, 0, 0, 0, 0, 0, 0, -9, 0, -2, -7, 0, 3, -2, 0, 0, 0, 0, -11, 0, -2, -2, 0, 0, 0, 2, 0, 0, 11, 1, 11, -2, 7, 1, 2, 0, 4, 0, 2, 1, -6, 1, 0, 2, 1, 0, 0, 0, 0, 4, 0, -1, -8, -1, -9, -10, 0, 0, 0, -1, -4, -2, -2, 0, 0, 0, 2, 0, -4, 0, -9, 0, 3, -4, -2, -1, 1, 2, 10, 0, 3, 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, -7, -5, 0, 0, 1, 0, 0, 6, 0, -5, -11, 0, 1, -10, 1, 0, -1, -6, 2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, -1, 3, -1, 0, 0, 3, 0, 0, 2, 0, -4, 0, 0, -2, 0, 11, 0, -6, 0, 8, 12, 0, 5, 0, 3, -5, 1, 0, 0, 0, 0, -10, -1, 0, 0, 0, 2, 0, -2, 0, 3, -4, 1, 4, 0, 0, 0, 2, 0, 1, 1, 11, -4, 2, -1, 4, 0, 0, -4, 0, -1, -7, 0, -4, 0, 0, 0, 3, 0, -3, 4, 0, -1, -1, 0, 0, -3, 0, -12, 0, -1, 0, 0, -2, 0, 1, 0, 4, 2, 0, 1, 0, 1, -3, 0, -2, 0, 5, 1, 0, -2, 6, 1, 7, 0, -9, 1, -3, 0, -7, 0, 0, 3, 0, -1, 0, -2, 0, 0, 2, 0, 12, 5, 0, -2, -3, 0, 0, 0, -3, 0, -2, 0, 0, -1, 2, 0, 2, 0, -8, 0, -3, 0, 4, 0, 7, -1, -1, 0, 3, 0, 0, 0, 0, -11, 0, 0, 4, 1, 2, 0, 0, -2, 4, 0, 10, 4, 2, 0, -8, 0, 3, -2, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, -3, -5, 0, -4, -1, 0, 0, 2, 0, -6, 1, 0, -2, -5, 0, 9, 0, -4, 0, 0, -1, 0, -4, -2, 0, 0, 1, 0, 1, 7, 2, -2, -12, -8, 0, 0, 6, -10, 1, -9, 0, 0, 0, 0, 2, 0, -1, 0, -2, 0, -2, 0, 0, -3, 0, 0, 0, 1, 0, 2, -2, 3, 0, 4, -2, -2, 0, 2, 1, 0, 0, 9, 3, -8, -1, -9, 0, -3, -2, -2, 0, 0, 6, 0, 0, -6, -1, 9, 1, -7, 5, -2, 0, -6, 0, 0, 11, 0, 1, -1, 0, 3, 0, 0, 0, 0, 0, 0, -5, 0, -2, 0, 0, -4, 0, -2, 0, -6, 0, 0, 4, -5, 0, 4, 0, 0, 0, -4, 0, 0, 0, 2, 4, 0, 0, 0, -1, -8, 0, -2, 0, -12, 0, -2, -4, 0, 0, 9, 0, 0, 0, 0, 0, -9, 2, 0, 0, 5, 5, -4, -12, 0, 6, 0, 0, -4, 1, 0, -11, -8, 1, 6, -1, 0, 0, 9, 0, 0, -1, -2, -3, 3, 0, 6, 0, -6, 0, 4, 0, 0, -2, 2, 0, 0, 0, 0, 1, 6, -4, 0, 0, -5, 0, 0, 0, 0, -1, 0, -1, 5, -2, 0, 0, 3, 0, -2, 0, -6, 2, 0, 0, 0, 0, -11, 0, 3, -2, 2, 2, 0, 0, -5, -5, 0, 5, -11, -1, -6, 0, 0, -2, 9, 0, 6, 0, 0, 0, 0, -1, -3, 0, 0, 0, 6, 2, 0, 1, -4, 0, 0, -2, 9, 1, 1, -4, -5, 0, 0, -1, 0, 0, 0, -1, 9, 0, 0, 2, -6, 1, 0, 0, 4, -2, 0, 1, 6, -5, 0, -3, 0, 0, -4, 1, 0, 2, 0, 0, 2, -1, 0, 3, -3, -2, -4, 0, 0, 0, 2, 0, 0, -1, 4, 0, 3, 0, 6, -11, 3, 0, 0, 0, 8, -1, 4, 0, 5, 0, 0, 0, -5, 7, 0, 0, -1, -1, 0, 0, 0, -6, 9, 0, 0, 0, -2, 0, 14, 0, 0, 0, 3, 0, 6, 0, 0, 0, 2, -1, 0, -2, 2, 0, 0, 2, -4, -1, 0, 0, 0, 1, -1, 12, 0, 0, 0, -2, -4, 0, 4, 0, 6, 1, 0, 1, 0, 0, 0, -11, -4, -1, -3, 2, 0, 0, 10, 6, -1, 7, 0, 1, 0, 2, 9, 0, -1, 0, 4, 0, 7, 0, -7, 0, 0, -1, -10, -7, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -7, 2, 0, -3, -9, 0, 0, -1, 0, -2, 0, 0, 1, 0, 0, 2, 3, 0, -7, 1, 4, 10, 0, 0, 0, -1, 2, 0, 0, 0, -6, 0, 0, -9, -2, 0, 0, 0, -2, -2, -3, 0, -9, 0, -7, 0, 0, 0, 6, 0, 2, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, -11, 3, 0, -3, -1, 0, -4, 0, -1, 0, 1, 0, 0, 4, 2, 4, 0, 3, 2, 0, 0, -6, 1, -4, 0, 0, 6, -8, 0, 0, 4, 0, 0, 7, 0, 0, -10, -4, 0, 7, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -4, 1, 1, 0, -2, 0, 5, 2, 4, 0, 3, 0, 0, 0, -3, 5, 0, 2, 0, 0, 0, 2, 0, 11, 2, 1, -3, 0, 0, -8, 0, 0, 4, -1, 0, -4, -4, 0, 1, 1, 0, 1, -6, 0, -4, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, -5, 0, -6, -2, 0, 0, 0, 2, 0, -3, 0, -1, -9, 0, -3, -2, 2, 0, -4, 0, 11, -3, 4, 0, 0, 0, 0, 0, 0, 0, -5, 0, -1, 0, 0, 2, 0, 0, -9, 0, -2, 0, 1, 1, 0, 3, -1, 0, 0, 2, -3, -2, -2, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 3, -2, -2, 6, 0, 9, 0, -6, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2, -4, 0, -4, 0, 0, 0, -3, -1, 9, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4], "projective_field": [-125, -50, 345, 240, -498, 15, -81, 180, -78, 71, -45, 17, -5, 1], "weight_parity": -1, "has_non_self_twist": 0, "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, 2015, 8, -1, 2, -2015]], "char_orbit_index": 8, "prim_orbit_index": 8, "minimal_twist": "2015.1.h.b", "char_is_minimal": true, "conrey_index": 2014, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 1, 0], [0, -1, 0, -1, 0, 0], [0, 1, -1, 1, -1, 1], [0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 1], [-1, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, -1], [0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 1, 0], [0, 0, -1, 0, 0, 0], [-1, 0, -1, 1, -1, 0], [0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [1, 0, 1, -1, 1, -1], [1, -1, 1, -1, 0, -1], [1, -1, 1, -1, 1, -1], [-1, -1, 0, -1, 0, -1], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, -1, 0], [-1, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, -1, 0, -1, 0], [-1, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, -1], [0, 0, 1, 0, 0, -1], [0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, -1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0], [-1, -1, 0, -1, 1, 0], [0, 1, 0, 0, 0, 0], [1, -1, 1, 0, 1, 0], [0, 1, -1, 1, -1, 1], [1, -1, 1, -1, 1, 0], [-1, 1, -1, 1, -1, 1], [1, 1, 1, 0, 1, 0], [1, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1], [-1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, -1, 1, -1, 1], [0, 0, 0, 0, 0, 1], [-1, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, -1, 1, 0], [0, 1, 0, 1, 0, 1], [-1, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, -1], [-2, 0, -1, 0, -1, 0], [0, 0, 0, -1, 1, 0], [0, 0, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0], [-1, 0, -1, -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, 1, 0, 0, -1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0], [0, 0, -1, 1, -1, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 0, -1, 0, 0, 0], [-2, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, -1, 0, -1, 0, 0], [0, 0, 0, 0, -1, 0], [-1, 0, -1, 1, -1, 0], [0, 0, 0, 0, -1, 0], [1, -1, 1, -1, 0, 0], [0, 0, 0, -1, 0, 0], [-1, 1, -1, 1, -1, 0], [0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, 0, 0], [0, 0, 0, -1, 0, 0], [-1, 0, -1, 1, 0, 1], [0, 1, -1, 0, 0, 1], [1, 0, 1, 0, 0, 0]]}