# Stored data for newform 1575.2.m.a, downloaded from the LMFDB on 09 June 2024.
{"Nk2": 6300, "analytic_conductor": 12.576438318351661, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 15, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 13, "char_orbit_label": "m", "char_order": 4, "char_parity": 1, "char_values": [1575, 4, [1226, 127, 451], [2, 3, 4]], "cm_discs": [], "conrey_index": 1268, "dim": 8, "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 24, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, -2, 2, 2, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 824667276839, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 3, -1, 4, 0], [1, 1, 15, 4, -1, 2, 0], [1, 1, 15, 5, 1, 4, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "1575.2.m.a", "level": 1575, "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": [3, 5, 7], "level_radical": 105, "minimal_twist": "1575.2.m.a", "nf_label": "8.0.5308416.1", "prim_orbit_index": 5, "qexp_display": "q-\\zeta_{24}^{2}q^{2}+(-1+\\zeta_{24}^{2}-\\zeta_{24}^{6}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1575.2.m", "trace_display": [-4, 0, 0, 0], "trace_hash": 480656271464250269, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.367", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "420.213", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "36568.206", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.630", "prec": 17}, "traces": [0, 8, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, -16, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 16, -36, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 24, -32, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -16, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 16, -48, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -56, -8, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 40, -40, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, -16, 16, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -112, -32, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -48, 16, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -32, 24, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, -40, 48, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 48, -20, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 72, 144, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -80, -16, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 32, 72, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 160, 48, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 112, 8, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 120, 24, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -80, 112, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -96, -4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 40, 48, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -16, 40, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 96, 48, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -96, 24, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 40, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 24, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 208, 16, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 16, -20, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, -168, -32, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -16, -56, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 192, 128, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -32, -48, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, -160, -112, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -208, -16, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -24, -80, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 96, -16, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -32, -160, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -16, -104, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 192, 80, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, -80, -144, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 96, -60, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -168, -96, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, 96, 64, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, -240, -224, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -144, -48, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -96, 32, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -144, -48, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, -80, -168, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -24, -184, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 224, 16, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 56, -192, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -128, 96, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 96, 48, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 16, -24, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 96, -248, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 168, 64, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 176, 112, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 32, -120, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 48, 64, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -16, -32, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 48, 32, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -64, 144, 0, 0, 0, 0, 0, 212, 0, 0, 0, 0, 0, 0, 0, -64, -240, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -384, 104, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 88, -112, 0, 0, 0, 0, 0, -248, 0, 0, 0, 0, 0, 0, 0, 288, 88, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 272, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -80, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 64, 144, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 256, -56, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, 0, 0, -160, 248, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -64, 80, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -272, 48, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -80, 32, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 448, 48, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -48, 160, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 216, 64, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, 176, 152, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 64, -80, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 64, 108, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, -344, -56, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 96, 184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -384, 192, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, -256, 96, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -48, 32, 0, 0, 0, 0, 0, -272, 0, 0, 0, 0, 0, 0, 0, 96, -48, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -80, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 48, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, -296, -48, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 64, 216, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, -144, 160, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -16, 192, 0, 0, 0, 0, 0, -184, 0, 0, 0, 0, 0, 0, 0, 208, -32, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, 0, 0, -32, 120, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 72, 128, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 128, -104, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 96, -40, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 304, 24, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 96, 64, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, -288, 96, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 16, -104, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 72, 108, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -312, 32, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -416, 184, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, -344, -48, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 240, 32, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 192, 80, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -96, -96, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 32, -264, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -224, 112, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 192, -96, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -416, 120, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 0, 0, -64, -176, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -368, -8, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -96, 256, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 352, -96, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 120, 224, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, -64, -276, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 40, -336, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 368, 24, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 192, -8, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, 160, -136, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -240, 32, 0, 0, 0], "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, 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, 0], [-1, 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, 0, 0, 1, 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, 2, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, -2, 0, 0, -2], [0, -1, 0, 0, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, -2, 0, 0, 2, 0], [-2, 0, 0, -2, 0, 0, 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, 0, 0, 0, 0, 0], [0, 1, 0, 0, -1, 4, 0, 1], [1, 0, 0, -1, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1], [0, -1, 0, 0, 0, -1, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 4, -4, 0, 0, 4, 0], [-4, 0, -1, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, 2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, -2, 6, 0, 2], [2, 0, 0, -2, 0, 0, 2, 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, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, 1, 0, 0, -1, 0], [-6, 0, 4, -6, 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, -2, 0, 0, 2, 4, 0, -2], [5, 0, 0, -5, 0, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 1, 0, 0, 1], [0, 2, 0, 0, 0, 2, 0, 8], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 4, -4, 0, 0, 4, 0], [-4, 0, -6, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 4, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 0, 4, -2, 0, -4], [2, 0, 0, -2, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 6, -5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 2], [0, -8, 0, 0, 0, -8, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 2, 0, 0, -2, 0], [-1, 0, 2, -1, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, -4, 12, 0, 4], [10, 0, 0, -10, 0, 0, 4, 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, 0, 0, 0, 0, 0], [0, -3, 0, 0, 1, 0, 0, 1], [0, 10, 0, 0, 0, 10, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -2, 2, 0, 0, -2, 0], [-9, 0, 6, -9, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, -2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, 0, 0, 10, -12, 0, -10], [-1, 0, 0, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}