# Stored data for newform 750.2.g.f, downloaded from the LMFDB on 25 April 2024.
{"label": "750.2.g.f", "space_label": "750.2.g", "level": 750, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22518410487268078, "dim": 16, "is_polredabs": true, "trace_hash": 1023242257838291458, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [316, 1304, 592, -1328, 205, 148, -33, -4, 1]]], "qexp_display": "q-\\beta _{5}q^{2}+\\beta _{6}q^{3}+\\beta _{6}q^{4}-\\beta _{3}q^{6}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 25, "char_orbit_label": "g", "char_is_real": false, "Nk2": 3000, "analytic_conductor": 5.988780151596028, "hecke_ring_index": 15625, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [750, 5, [251, 127], [5, 2]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [151, 301, 451, 601], "field_disc": 5138595856000000000000, "field_disc_factorization": [[2, 16], [5, 12], [17921, 2]], "field_poly": [11105, 21080, 1135, -10440, 18271, 14670, -15752, -11958, 6259, 4642, -1584, -936, 262, 94, -24, -4, 1], "hecke_ring_index_factorization": [[5, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.024", "prec": 17}, {"__RealLiteral__": 0, "data": "15.039", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "746.473", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "71110.022", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c5", "trace_display": [-4, -4, 0, 8], "traces": [0, 16, -4, -4, -4, 0, -4, 8, -4, -4, 0, 2, -4, 4, -2, 0, -4, -2, 16, 0, 0, -2, -8, -6, 16, 0, 4, -4, -2, 10, 0, -18, 16, -8, -12, 0, -4, -2, -10, 4, 0, 22, -2, 4, -8, 0, -6, -2, -4, 52, 0, 28, 4, -16, -4, 0, -2, 20, 10, -20, 0, 12, 2, -2, -4, 0, 2, 18, 28, -6, 0, -28, -4, 24, -12, 0, 20, -14, -6, 20, 0, -4, 12, -36, -2, 0, -6, -20, 2, -70, 0, 12, -6, 32, -2, 0, -4, 28, -38, 12, 0, 12, -12, -6, -6, 0, -16, 68, -4, -20, 0, -2, -2, 4, -10, 0, -20, -6, 0, 64, 0, -62, -28, 22, 32, 0, 8, -2, -4, 4, 0, -38, 12, 20, -12, 0, -12, -22, -6, -30, 0, -12, -28, 8, -4, 0, -16, 12, -2, 0, 0, 12, -10, -2, 6, 0, -6, -172, 20, 4, 0, 92, -4, 34, 22, 0, 14, 28, 8, 28, 0, 0, 4, 34, 20, 0, 12, -20, 50, 30, 0, -28, 12, -28, -6, 0, 2, 16, -12, -2, 0, 32, -4, -136, 28, 0, 12, 38, 2, 0, 0, -12, 52, -60, -2, 0, -6, 24, -6, -120, 0, -8, 4, 22, -72, 0, -4, 16, 40, -16, 0, -48, 8, -16, 8, 0, 44, -42, 0, -20, 0, 6, 20, -46, 4, 0, -20, -30, -66, -60, 0, 2, -62, 16, -28, 0, -28, 10, 2, 44, 0, -8, -2, 88, 28, 0, -4, -32, 4, -6, 0, -20, 52, 54, 2, 0, 40, 50, -12, 30, 0, 12, -2, 12, 8, 0, 24, 38, 10, -18, 0, -148, 28, 74, 22, 0, 78, -64, -4, 32, 0, -12, -16, -36, 12, 0, 8, -8, -70, 36, 0, 112, 42, -58, 0, 0, -2, -92, 6, 24, 0, 32, 4, 4, 38, 0, -30, 88, 24, -10, 0, 38, -108, 80, 16, 0, -96, -20, -28, 124, 0, 22, 44, 8, -52, 0, -2, 108, -42, 4, 0, 84, 0, -80, 4, 0, -16, 68, -20, 40, 0, 4, 2, 24, 20, 0, 50, 4, 30, -30, 0, -124, 12, 28, 12, 0, 12, -22, 24, -28, 0, -58, -18, 44, -44, 0, 28, -30, -2, -20, 0, 28, 52, -6, -4, 0, 44, -6, -12, -50, 0, -38, 12, -28, 38, 0, -8, 8, 0, -120, 0, 92, -12, 18, -58, 0, -60, -164, -2, 20, 0, -22, 24, 90, -6, 0, 4, 10, 40, -20, 0, -8, -8, -12, 24, 0, 12, 116, 38, -82, 0, 12, 16, 84, 76, 0, -20, 40, 24, 50, 0, -38, -48, -16, 8, 0, 54, 70, -2, 40, 0, -176, 4, -48, 48, 0, 0, -72, -20, -12, 0, 32, -14, -66, -20, 0, 54, 58, 4, -116, 0, 48, 20, -32, 20, 0, 4, 4, 60, -50, 0, 142, 72, -108, 28, 0, -4, 8, 12, 34, 0, -8, -28, -220, 10, 0, -18, -24, 14, 40, 0, 48, 62, -56, -2, 0, 88, 28, 28, 60, 0, 32, -4, -10, 18, 0, -6, -64, -36, -16, 0, -48, 10, -96, -28, 0, 24, -24, -8, -132, 0, 20, -120, 98, -70, 0, -12, -20, -70, 114, 0, -88, 12, 32, -2, 0, -18, -122, -22, 32, 0, 60, -6, 200, 48, 0, 10, -12, -18, 126, 0, 16, 102, 24, -12, 0, -16, -2, 12, -10, 0, 202, -82, 32, -44, 0, 16, 68, -58, 24, 0, 32, -32, 38, 24, 0, -56, -112, -38, 20, 0, -22, 8, 124, -8, 0, 70, 0, -64, 40, 0, -48, -68, 18, -48, 0, -58, 148, 0, 50, 0, -218, -12, -46, 38, 0, -14, -182, -36, 0, 0, -6, -38, 110, 4, 0, -216, -120, 48, 54, 0, 32, 20, -8, -2, 0, 4, 168, -20, 22, 0, -68, 38, 64, -108, 0, -90, 138, -4, -300, 0, -184, 34, 64, 0, 0, -28, -16, 124, 90, 0, 32, -58, 42, 14, 0, -2, -40, 48, 54, 0, 54, -2, -156, -192, 0, 28, 88, -26, 4, 0, 48, -16, -196, -10, 0, 20, -20, -6, 66, 0, -48, -16, 16, 68, 0, 10, -84, 0, -16, 0, -128, 4, -90, -8, 0, 24, 236, 20, -60, 0, -30, -70, -172, -66, 0, -20, 60, 80, -50, 0, 192, 76, 2, 32, 0, 68, -12, -18, -4, 0, 182, 32, 4, 58, 0, -6, -104, 22, 110, 0, 70, -58, 124, -18, 0, 104, -36, 16, -16, 0, -48, -12, -58, 40, 0, -2, -92, -20, 28, 0, 82, -2, 0, 32, 0, 14, 100, 16, -10, 0, -2, 24, 4, 4, 0, -32, -6, 30, -230, 0, -76, -28, 10, -38, 0, 52, 18, -22, 54, 0, -98, -8, 48, 8, 0, 0, -152, 40, -16, 0, 40, 2, -122, 18, 0, 18, 80, -58, 70, 0, 72, 50, 12, -4, 0, -12, -20, 160, -18, 0, 32, 18, 144, -36, 0, -200, -182, -6, 60, 0, 48, 4, 126, -30, 0, -120, 2, 60, -120, 0, 56, -8, 92, -8, 0, -2, 114, 4, -116, 0, 92, 22, 14, -54, 0, 38, 8, -82, 220, 0, -64, -18, 104, -4, 0, -76, -58, -184, 160, 0, -188, 0, -12, -40, 0, -16, 108, 10, 74, 0, -48, 52, -16, 42, 0, 44, 78, -2, -106, 0, 2, 54, -200, 70, 0, -2, 46, -50, -20, 0, -248, -46, 12, -26, 0, -48, -92, 48, 52, 0, 82, -10, -12, 208, 0, -20, 56, 28, 70, 0, 8, -18, -122, 16, 0, -76, 24, 10, 30, 0, 60, -16, -38, -42, 0, 4, -72, 144, 4, 0, 12, 48, 28, 20, 0, 48, 28, -30, -24, 0, -172, -66, -86, -16, 0, 60, 60, -50, -216, 0, -42, -118, -72, 2, 0, 92, 68, 68, -90, 0, 162, -4, 20, -92, 0, 32, 78, 14, 170, 0, 0, 72, -236, 22, 0, -40, -156, 70, 76, 0, 132, -18, 72, -24, 0, -36, 108, 70, -12, 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, 25, 4, 1, 5, 0]], "char_orbit_index": 7, "prim_orbit_index": 4, "minimal_twist": "150.2.h.b", "char_is_minimal": false, "conrey_index": 151, "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, 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, 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], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, -1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, 0, 1, -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, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1], [-1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, 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, 0, 0], [-1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, -3, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, -2, 0, 0, -1, 0, 1, 0, -1, 1, -1, 1, 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, -1, 0, -1, 2, 0, -1, 0, 1, -1, 1, -1, 0, 0], [0, 1, 0, -1, 0, -2, 1, 0, -1, -1, 0, -1, 0, 0, 0, -1], [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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 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, 2, 1, 2, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, -2, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 1, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0], [-2, 1, 0, 2, 1, 2, -2, 0, -1, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [-1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 1, -1, 0, 0], [1, 0, 0, 0, 0, -1, 1, -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], [1, 1, 0, -1, 1, 2, -2, 0, 0, 0, 0, 0, 0, -1, 0, 1], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -2, -1, -1, 2, 0, 1, -1, 0, -1, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 1, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, -1, 1, -1, 1, 0, 0], [0, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, -2, 0, 0, 2, -1, 2, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, -1, 2, -1, -2, 0, 1, 0, 1, 0, -1, -1], [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], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0], [1, -1, -1, -1, 0, -1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 1, 0, 0, -1, -1, 0, -1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, -1, -1, -4, 3, 0, 0, -1, -1, -1, 0, 0, -2, -1], [-1, 0, 0, 1, 0, 2, -2, 0, 0, -1, -1, 0, -1, 0, 0, 0], [-1, 0, 0, 1, 0, 1, -1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1, 0, -1, 0, 0, 0, -2, 1, 1, 1, 0, 0, -1, 1, 0, 1], [2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, -1, -1, 0, 0, 0, -1, -1, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -3, 0, -2, 2, 1, 1, 0, 1, 0, 0, 0, 2, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -1, 1, -1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 1], [-1, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, -1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0], [0, 2, 0, -2, 0, -1, -1, 1, 3, -2, -2, 1, 0, 0, 1, 1], [0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 2, 1, 0, 1, 2, 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], [-1, -1, -1, 2, 0, 0, -2, 1, 0, 0, 0, -2, 1, -1, 0, 0], [-2, 1, 1, -2, 0, 1, 2, -1, -1, -1, -1, 0, -2, -1, -3, -1], [-1, 0, 0, 1, 0, 1, -1, 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], [-1, 1, 1, 0, 1, 1, -1, 1, -1, 0, 1, 0, 0, 0, 0, 0], [-2, -1, 0, 2, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [-1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1], [-6, 0, -1, -1, -1, 0, -6, 1, 1, -1, -1, 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, -1, 1, -1, 0, -2, -1, -1, 0, -1, 1, -2, -1], [0, -1, -1, 0, 0, 0, -1, -1, 0, 1, 1, 1, 0, 0, 0, 0], [1, 0, 0, 2, 1, 1, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0], [1, 0, 1, -2, 0, -2, 2, -1, -1, -1, 0, 0, 1, -1, 0, -1], [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, 2, 3, 1, 2, -2, -1, -2, 0, 0, 0, 1, 0, -2, -1], [-2, 0, 0, 0, 0, -2, -3, 0, -1, 0, 2, 1, 0, 0, 1, 1], [1, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}