# Stored data for newform 120.2.m.b, downloaded from the LMFDB on 23 April 2024.
{"label": "120.2.m.b", "space_label": "120.2.m", "level": 120, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504424294645880, "dim": 16, "is_polredabs": true, "trace_hash": 1492037384224629698, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [56, 0, -16, 0, 1]]], "qexp_display": "q-\\beta _{3}q^{2}-\\beta _{13}q^{3}-\\beta _{11}q^{4}+\\beta _{7}q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 120, "char_orbit_label": "m", "char_is_real": true, "Nk2": 480, "analytic_conductor": 0.9582048242553646, "hecke_ring_index": 8192, "level_radical": 30, "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": "0.886", "prec": 17}, "analytic_rank_proved": true, "char_values": [120, 2, [31, 61, 41, 97], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 8, "level_primes": [2, 3, 5], "conrey_indexes": [59], "field_disc": 43252570821266243584, "field_disc_factorization": [[2, 54], [7, 4]], "field_poly": [4, 0, 64, 0, 352, 0, 880, 0, 1092, 0, 672, 0, 192, 0, 24, 0, 1], "hecke_ring_index_factorization": [[2, 13]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.067", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2564.716", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "960453.272", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 16, 0, 0, 0, 0, 0, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, -32, 16, 0, 0, 0, 0, 16, 0, 0, 0, -32, 0, -32, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 32, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, -64, 0, 0, 0, 0, 32, 64, 0, 0, 0, 0, -48, 0, 0, 32, 0, 0, 0, 0, 0, -16, -64, 0, 0, 0, 0, 64, 0, 0, 64, -64, 0, 0, 0, 0, -32, -96, 0, 0, 0, 0, 0, 0, 0, -32, -32, 0, 0, 0, 0, -64, -16, 0, 0, 64, 0, -96, 0, 0, 0, 32, 0, 0, 0, 0, 0, -64, 0, 0, 96, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 32, 0, 0, 0, 64, 0, -128, 0, 0, 0, 64, 0, 0, 0, 0, 0, 128, 0, 0, 48, 0, -32, 0, 0, 64, 0, 0, 0, 0, 0, 96, 0, 0, 0, 64, 0, 96, 0, 0, 0, -32, 0, 0, 0, 0, -96, 64, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, -96, 160, 0, 0, -64, 0, 96, 0, 0, -128, -64, 0, 0, 0, 0, 48, -96, 0, 0, 0, 0, 0, 0, 0, -64, 32, 0, 0, 0, 0, -64, 32, 0, 0, -192, 0, -160, 0, 0, 32, 112, 0, 0, 0, 0, 0, -256, 0, 0, -192, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 112, 0, 0, 0, 160, 0, -32, 0, 0, 0, 64, 0, 0, 0, 0, 0, 192, 0, 0, -144, 0, -64, 0, 0, -32, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 128, 192, 0, 0, 0, 0, 96, 0, 0, 128, 0, 0, 0, 0, 0, -128, -160, 0, 0, -128, 0, 256, 0, 0, 32, -64, 0, 0, 0, 0, 64, -96, 0, 0, 0, 0, 0, 0, 0, -64, 128, 0, 0, 0, 0, -96, -112, 0, 0, -256, 0, -96, 0, 0, 64, 96, 0, 0, 0, 0, 0, -64, 0, 0, 288, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 160, 0, 0, 0, -32, 0, -192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, -160, 0, 32, 0, 0, -32, 0, 0, 0, 0, 0, 96, 0, 0, 0, 192, 0, 192, 0, 0, 0, -224, 0, 0, 0, 0, -160, 192, 0, 0, 0, 0, -80, 0, 0, 64, 0, 0, 0, 0, 0, -128, 256, 0, 0, -64, 0, 128, 0, 0, -160, -64, 0, 0, 0, 0, -64, -288, 0, 0, 0, 0, 0, 0, 0, -32, -160, 0, 0, 0, 0, -128, -128, 0, 0, 128, 0, -224, 0, 0, 0, 16, 0, 0, 0, 0, 0, -256, 0, 0, -96, 0, 0, 0, 0, -64, -96, 0, 0, 0, 0, 32, 0, 0, 0, 160, 0, -224, 0, 0, 0, 192, 0, 0, 0, 0, 0, 192, 0, 0, 304, 0, -64, 0, 0, 128, 0, 0, 0, 0, 0, 64, 0, 0, 0, 128, 0, 128, 0, 0, 0, -64, 0, 0, 0, 0, 160, 192, 0, 0, 0, 0, -64, 0, 0, 32, 0, 0, 0, 0, 0, -128, -160, 0, 0, 64, 0, 128, 0, 0, 384, -128, 0, 0, 0, 0, -64, -160, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, -96, 352, 0, 0, 64, 0, -256, 0, 0, -128, 192, 0, 0, 0, 0, 0, -256, 0, 0, 96, 0, 0, 0, 0, -128, -112, 0, 0, 0, 0, 96, 0, 0, 0, 160, 0, -192, 0, 0, 0, 128, 0, 0, 0, 0, 0, -64, 0, 0, 192, 0, 192, 0, 0, 224, 0, 0, 0, 0, 0, 128, 0, 0, 0, -64, 0, 256, 0, 0, 0, -32, 0, 0, 0, 0, -224, 128, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 32, -160, 0, 0, -64, 0, 192, 0, 0, -224, -256, 0, 0, 0, 0, -64, -224, 0, 0, 0, 0, 0, 0, 0, -128, -256, 0, 0, 0, 0, -128, 0, 0, 0, -128, 0, -64, 0, 0, -16, 64, 0, 0, 0, 0, 0, 128, 0, 0, -480, 0, 0, 0, 0, -64, 160, 0, 0, 0, 0, 144, 0, 0, 0, -320, 0, -224, 0, 0, 0, 64, 0, 0, 0, 0, 0, 320, 0, 0, -160, 0, -96, 0, 0, 224, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 320, 0, 0, 0, -320, 0, 0, 0, 0, 288, 64, 0, 0, 0, 0, 128, 0, 0, 32, 0, 0, 0, 0, 0, -48, -96, 0, 0, -320, 0, 0, 0, 0, 320, -64, 0, 0, 0, 0, 192, -64, 0, 0, 0, 0, 0, 0, 0, -96, 288, 0, 0, 0, 0, -128, -144, 0, 0, 192, 0, 32, 0, 0, 0, 96, 0, 0, 0, 0, 0, -192, 0, 0, 288, 0, 0, 0, 0, -192, 320, 0, 0, 0, 0, 64, 0, 0, 0, 64, 0, -64, 0, 0, 0, 384, 0, 0, 0, 0, 0, 192, 0, 0, -128, 0, 256, 0, 0, -96, 0, 0, 0, 0, 0, 32, 0, 0, 0, -64, 0, 32, 0, 0, 0, -64, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, -256, 0, 0, 192, 0, 0, 0, 0, 0, -96, 96, 0, 0, 128, 0, 256, 0, 0, -448, 64, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, -96, -192, 0, 0, 0, 0, 0, 112, 0, 0, -192, 0, -160, 0, 0, -64, 256, 0, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, -64, -128, 0, 0, 0, 0, 64, 0, 0, 0, 128, 0, -160, 0, 0, 0, -32], "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, 3, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 15, 4, -1, 2, 0], [1, 1, 24, 6, 1, 2, 0], [1, 1, 40, 5, -1, 2, 0], [1, 1, 120, 13, 1, 2, 0]], "char_orbit_index": 13, "prim_orbit_index": 13, "minimal_twist": "120.2.m.b", "char_is_minimal": true, "conrey_index": 59, "id": null, "nf_label": 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, 0, 0, 0, 0], [1, 0, 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], [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, -1, 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, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0], [-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, -1, 0], [0, -1, 0, 0, 1, -1, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, -1, 0, 0, -1, 0, 1, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 2, 1, -1, 1, 1, -1, 0, 0, -1, 1], [0, 1, 1, 1, 1, 1, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -1, -1, -1, 2, 0, -1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [0, 0, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 1], [-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0], [0, -1, 1, -1, -1, -1, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 1, -1, 1, 1, -1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 1, 1, 1, 1, 0, -1, -1, 0, 1, -1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 1, 1, 1, 1], [0, 1, -1, -1, -3, -1, 0, 1, 1, -1, 0, 2, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -1, -1, -1, 2, 1, 1], [0, 0, 0, 0, 0, 0, -2, -1, 1, 0, -2, 0, 1, 1, 2, 0], [0, 0, 1, 1, 2, 2, 0, -1, -1, 0, 1, -1, 0, 0, 0, 0], [1, -1, 0, 0, 1, 0, 1, 0, 0, 2, -1, -1, 0, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, -2, 0, 0], [0, 0, 2, -2, 0, 0, 0, 0, 0, -1, 1, 1, 1, -1, -1, -1], [-2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0], [0, -1, -2, 2, -1, 1, 0, 0, 0, -1, 0, 0, -1, 1, 0, 0], [-2, -1, -1, -1, 1, -1, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, 1, 0, 0, -1, 1], [0, 0, 2, 2, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0], [0, 0, 1, 1, 0, 0, 0, -1, -1, 1, -2, -2, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 2, 1, -1, 0, 2, -2, -1, -1, 0, 0], [0, 0, 0, 0, -2, 2, 0, 0, 0, -2, 1, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 3, -3, 1, 0, -1, -2, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -1, -1, -2, -2], [0, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, -2, 1, 1, 2, 1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0], [0, 1, -3, -2, 1, -1, 0, 2, 0, 1, 0, 0, 1, -1, 0, 0], [2, 1, 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2], [0, 0, -3, -3, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0], [2, 1, -1, -1, 1, 0, 0, 1, 1, 2, 2, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, -1, 1, -4, -2, 0, 0, 0, 1, -1], [0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0], [0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 1, -2, 2, -1, -1], [0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, 1, 1, 1, 2, -2], [0, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0], [0, 0, -3, -2, -2, 0, 1, 1, 1, -1, 0, 1, 2, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 3, -3, 0, 0], [0, 0, -3, -3, 0, 0, 2, 0, 0, 1, 1, -1, 0, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0], [0, 0, 1, -1, 2, -2, 0, 0, 0, 2, -1, -1, -3, 3, 0, 0], [4, -1, 1, 1, -1, -1, 0, -1, -1, -1, -2, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, -2, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, -2, -2, 0, -2], [0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 2, 3, -3, 0, 2, 0, 1, 1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0], [0, -3, -1, -1, 1, -1, 0, 1, 1, 1, -2, -2, 0, 0, 0, 0], [2, 1, 1, -1, -1, 1, 0, 0, 0, 0, 2, -2, 2, -1, 1, 1], [4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4, 0, 0, 0, 0, -3, 3, 1, -1, -1, -1, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 3, 3, 0, 0, 0, 0], [0, 2, 2, -2, -2, 2, 0, 0, 0, -2, 2, 2, -2, 2, 0, 0], [-3, 0, 0, 0, -2, 2, 0, 0, 0, -2, 3, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, -1, 1, -2, 0, 2, -3, -3, 0, -2], [0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [2, 1, -1, -1, -1, 1, 0, 1, 1, -2, 5, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, -1, 1, 1, -2, 0, 0, 0, 1, -1], [0, -2, 2, 2, -2, 0, 0, -2, -2, -1, -1, 0, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 4], [0, -2, 0, 0, 2, -2, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0], [-1, 1, 4, 1, 1, 1, -1, -1, -1, 1, -1, 0, 3, -2, 1, -1], [-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1, 0, 0], [0, 0, 3, 3, 0, 0, 2, 0, 0, 1, 1, -1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, -2, 0, 0, -2, 0, -1, 1, 0, 0, 0, 0], [4, 2, 2, 2, 2, 2, 0, -2, -2, 0, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 2, 2], [0, 0, 2, -1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0], [4, -1, 0, 0, -1, 1, 0, 0, 0, -1, -3, 3, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 2, 2, -2, 2]]}