# Stored data for newform 300.3.l.e, downloaded from the LMFDB on 06 June 2024. {"Nk2": 2700, "analytic_conductor": 8.174407930808908, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 60, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 12, "char_orbit_label": "l", "char_order": 4, "char_parity": -1, "char_values": [300, 4, [151, 101, 277], [2, 2, 1]], "cm_discs": [-15], "conrey_index": 107, "dim": 8, "field_disc": 3317760000, "field_disc_factorization": [[2, 16], [3, 4], [5, 4]], "field_poly": [256, 0, 0, 0, 17, 0, 0, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[7, [0, 1]], [17, [921600, 0, 0, 0, 1]], [19, [-960, 0, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18015154474058028, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 16, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 15, 4, -1, 2, -15], [1, 1, 3, 2, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 2, 5, 3, -1, 4, 0], [1, 1, 12, 2, 1, 2, 0], [1, 2, 15, 5, 1, 4, 0], [1, 1, 20, 4, -1, 2, 0], [1, 2, 20, 5, 1, 4, 0], [1, 1, 60, 8, 1, 2, 0], [1, 2, 60, 12, -1, 4, 0]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": true, "is_twist_minimal": true, "label": "300.3.l.e", "level": 300, "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": [2, 3, 5], "level_radical": 30, "minimal_twist": "300.3.l.e", "nf_label": "8.0.3317760000.4", "prim_orbit_index": 12, "qexp_display": "q+\\beta _{1}q^{2}+3\\beta _{5}q^{3}+(4\\beta _{4}+\\beta _{6})q^{4}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "2.2.1.d4", "self_twist_discs": [-15], "self_twist_type": 1, "space_label": "300.3.l", "trace_display": [0, 0, 0, 0], "trace_hash": 380323329542607039, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.091", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1313.602", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "270624.991", "prec": 34}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.943", "prec": 17}, "traces": [0, 8, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, -648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -732, 0, 0, 0, 0, 0, 0, 0, 0, 0, -960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -968, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 0, 336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 976, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1372, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1188, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -892, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2856, 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, 4320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1920, 0, 0, 0, 0, 2544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4792, 0, 0, 0, 0, 1416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 616, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 616, 0, 0, 0, 0, 3528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4320, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6720, 0, 0, 0, 0, -6096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4732, 0, 0, 0, 0, 3216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1452, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8296, 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, 2744, 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, -5760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6728, 0, 0, 0, 0, 504, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4664, 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, -2264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15360, 0, 0, 0, 0, -8640, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6104, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8024, 0, 0, 0, 0, 1584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12936, 0, 0, 0, 0], "weight": 3, "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, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 4, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 3], [0, 0, 0, 0, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 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], [-5, 0, 7, 0, 0, 0, 0, 0], [0, -16, 0, -8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9], [0, 0, 0, 0, 8, 0, 16, 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, 34, 0, 0], [0, 0, 0, 0, 12, 0, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 27, 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], [-16, 0, -32, 0, 0, 0, 0, 0], [0, -5, 0, 28, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -64, 0, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-27, 0, 9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 64, 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, 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], [34, 0, 34, 0, 0, 0, 0, 0], [0, 0, 0, -14, 0, 0, 0, 0], [0, 0, 0, 0, 0, -36, 0, 21], [0, 0, 0, 0, -49, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-24, 0, -48, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -16, 0, 32], [0, 0, 0, 0, 0, 0, -27, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 48, 0, 24, 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], [118, 0, 0, 0, 0, 0, 0, 0], [0, -16, 0, -128, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -20, 0, -33, 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, -32, 0, -56], [0, 0, 0, 0, 102, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -27, 0, 36, 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], [88, 0, 56, 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, 32, 0, 64, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-81, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -154, 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], [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, 34, 0, 136, 0, 0, 0, 0], [0, 0, 0, 0, 0, 48, 0, -96], [0, 0, 0, 0, 0, 0, 14, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-99, 0, -15, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -49], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}