# Stored data for newform 225.4.f.a, downloaded from the LMFDB on 24 April 2024. {"label": "225.4.f.a", "space_label": "225.4.f", "level": 225, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 343664492769, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 93491807918772812, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [81, 0, 0, 0, 1]], [7, [162, 18, 1]]], "qexp_display": "q+\\zeta_{8}q^{2}+\\zeta_{8}^{2}q^{4}+(-9+9\\zeta_{8}^{2})q^{7}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 15, "char_orbit_label": "f", "char_is_real": false, "Nk2": 3600, "analytic_conductor": 13.275429751291638, "hecke_ring_index": 9, "level_radical": 15, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 8, "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": "0.628", "prec": 17}, "analytic_rank_proved": true, "char_values": [225, 4, [101, 127], [2, 1]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [3, 5], "conrey_indexes": [107, 143], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.021", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "95.736", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3113.656", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c4", "trace_display": [0, 0, 0, -36], "traces": [0, 4, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 252, 0, 0, 284, 0, 0, 0, 0, 0, -324, 0, 0, 0, 0, 0, -36, 0, 0, 784, 0, 0, 0, 0, 0, 828, 0, 0, 0, 0, 0, -576, 0, 0, 1224, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, -1944, 0, 0, -1288, 0, 0, 0, 0, 0, 1512, 0, 0, 0, 0, 0, 1512, 0, 0, -280, 0, 0, 0, 0, 0, -2268, 0, 0, 0, 0, 0, 2268, 0, 0, -4536, 0, 0, 0, 0, 0, -1008, 0, 0, 0, 0, 0, 3780, 0, 0, -3816, 0, 0, 0, 0, 0, -2556, 0, 0, 0, 0, 0, -2268, 0, 0, -508, 0, 0, 0, 0, 0, 1260, 0, 0, 0, 0, 0, -2520, 0, 0, 3528, 0, 0, 0, 0, 0, 7128, 0, 0, 0, 0, 0, 828, 0, 0, -8288, 0, 0, 0, 0, 0, -1260, 0, 0, 0, 0, 0, -9576, 0, 0, 13104, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, -2268, 0, 0, 12376, 0, 0, 0, 0, 0, -4536, 0, 0, 0, 0, 0, -4968, 0, 0, -724, 0, 0, 0, 0, 0, 13608, 0, 0, 0, 0, 0, 17892, 0, 0, 5264, 0, 0, 0, 0, 0, -7056, 0, 0, 0, 0, 0, 8820, 0, 0, 8856, 0, 0, 0, 0, 0, -13608, 0, 0, 0, 0, 0, -4536, 0, 0, -2800, 0, 0, 0, 0, 0, -17640, 0, 0, 0, 0, 0, 11016, 0, 0, 6052, 0, 0, 0, 0, 0, 11340, 0, 0, 0, 0, 0, 1512, 0, 0, -10864, 0, 0, 0, 0, 0, 15372, 0, 0, 0, 0, 0, 504, 0, 0, -40824, 0, 0, 0, 0, 0, -1512, 0, 0, 0, 0, 0, -20736, 0, 0, 10368, 0, 0, 0, 0, 0, 12096, 0, 0, 0, 0, 0, -21672, 0, 0, -1952, 0, 0, 0, 0, 0, -11016, 0, 0, 0, 0, 0, 15876, 0, 0, -26488, 0, 0, 0, 0, 0, 11160, 0, 0, 0, 0, 0, -18864, 0, 0, -5544, 0, 0, 0, 0, 0, -4860, 0, 0, 0, 0, 0, -13284, 0, 0, 7836, 0, 0, 0, 0, 0, 21924, 0, 0, 0, 0, 0, 10836, 0, 0, -42336, 0, 0, 0, 0, 0, -7128, 0, 0, 0, 0, 0, -1008, 0, 0, 17136, 0, 0, 0, 0, 0, -22428, 0, 0, 0, 0, 0, 49392, 0, 0, 34992, 0, 0, 0, 0, 0, -3780, 0, 0, 0, 0, 0, -22680, 0, 0, 51400, 0, 0, 0, 0, 0, 11592, 0, 0, 0, 0, 0, 44856, 0, 0, 280, 0, 0, 0, 0, 0, -31752, 0, 0, 0, 0, 0, 15588, 0, 0, -40824, 0, 0, 0, 0, 0, -28800, 0, 0, 0, 0, 0, -16380, 0, 0, -216, 0, 0, 0, 0, 0, -15876, 0, 0, 0, 0, 0, 11016, 0, 0, 104328, 0, 0, 0, 0, 0, 27900, 0, 0, 0, 0, 0, -27216, 0, 0, 55664, 0, 0, 0, 0, 0, 43092, 0, 0, 0, 0, 0, 1260, 0, 0, -27216, 0, 0, 0, 0, 0, 54432, 0, 0, 0, 0, 0, -34776, 0, 0, -23976, 0, 0, 0, 0, 0, 2520, 0, 0, 0, 0, 0, -13608, 0, 0, -2584, 0, 0, 0, 0, 0, -45360, 0, 0, 0, 0, 0, -17568, 0, 0, 1232, 0, 0, 0, 0, 0, -32076, 0, 0, 0, 0, 0, -49896, 0, 0, -48952, 0, 0, 0, 0, 0, 18144, 0, 0, 0, 0, 0, -34344, 0, 0, -13104, 0, 0, 0, 0, 0, 58788, 0, 0, 0, 0, 0, 77112, 0, 0, 26992, 0, 0, 0, 0, 0, -54684, 0, 0, 0, 0, 0, 12852, 0, 0, -40824, 0, 0, 0, 0, 0, 86184, 0, 0, 0, 0, 0, -1260, 0, 0, -48880, 0, 0, 0, 0, 0, -45612, 0, 0, 0, 0, 0, 19656, 0, 0, -35280, 0, 0, 0, 0, 0, 9576, 0, 0, 0, 0, 0, 54432, 0, 0, -90440, 0, 0, 0, 0, 0, -66096, 0, 0, 0, 0, 0, 5112, 0, 0, -22964, 0, 0, 0, 0, 0, -63504, 0, 0, 0, 0, 0, -40896, 0, 0, 49672, 0, 0, 0, 0, 0, -31752, 0, 0, 0, 0, 0, 57960, 0, 0, 25704, 0, 0, 0, 0, 0, -15876, 0, 0, 0, 0, 0, 97200, 0, 0, -68040, 0, 0, 0, 0, 0, 59724, 0, 0, 0, 0, 0, -35028, 0, 0, 18360, 0, 0, 0, 0, 0, 34344, 0, 0, 0, 0, 0, -4536, 0, 0, -74816, 0, 0, 0, 0, 0, -8748, 0, 0, 0, 0, 0, 2520, 0, 0, 116928, 0, 0, 0, 0, 0, 4968, 0, 0, 0, 0, 0, -57024, 0, 0, 128304, 0, 0, 0, 0, 0, 77112, 0, 0, 0, 0, 0, -81144, 0, 0, 2800, 0, 0, 0, 0, 0, -68364, 0, 0, 0, 0, 0, -95256, 0, 0, -148400, 0, 0, 0, 0, 0, 40320, 0, 0, 0, 0, 0, -6300, 0, 0, 40824, 0, 0, 0, 0, 0, 109116, 0, 0, 0, 0, 0, -2268, 0, 0, 112396, 0, 0, 0, 0, 0, 4572, 0, 0, 0, 0, 0, 15876, 0, 0, 157248, 0, 0, 0, 0, 0, -60912, 0, 0, 0, 0, 0, -7056, 0, 0, 190512, 0, 0, 0, 0, 0, -63756, 0, 0, 0, 0, 0, -46296, 0, 0, -96480, 0, 0, 0, 0, 0, -8820, 0, 0, 0, 0, 0, -31428, 0, 0, -53424, 0, 0, 0, 0, 0, 122400, 0, 0, 0, 0, 0, 117936, 0, 0, 12824, 0, 0, 0, 0, 0, -117936, 0, 0, 0, 0, 0, -29160, 0, 0, -50680, 0, 0, 0, 0, 0, 122976, 0, 0, 0, 0, 0, 77112, 0, 0, 93312, 0, 0, 0, 0, 0, -31752, 0, 0, 0, 0, 0, 131544, 0, 0, 34500, 0, 0, 0, 0, 0, -120204, 0, 0, 0, 0, 0, 11088, 0, 0, -91448, 0, 0, 0, 0, 0, -17820, 0, 0, 0, 0, 0, -17640, 0, 0, -162064, 0, 0, 0, 0, 0, -3780, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 5, 3, -1, 4, 0], [1, 1, 15, 5, 1, 4, 0]], "char_orbit_index": 6, "prim_orbit_index": 5, "minimal_twist": "225.4.f.a", "char_is_minimal": true, "conrey_index": 107, "id": 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], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-9, 0, 9, 0], [0, 0, 0, -7], [0, 0, 0, 0], [0, 0, 0, 0], [0, 9, 0, 9], [0, 0, 0, 0], [63, 0, 63, 0], [0, -9, 0, 9], [0, 0, 0, 0], [71, 0, 0, 0], [0, 14, 0, 0], [0, 0, 0, 0], [0, 0, 70, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-81, 0, 81, 0], [0, 0, 0, -34], [0, 0, 0, 0], [0, 0, 0, 0], [0, 63, 0, 63], [0, 0, 0, 0], [-9, 0, -9, 0], [0, -54, 0, 54], [0, 0, 0, 0], [196, 0, 0, 0], [0, 15, 0, 0], [0, 0, 0, 0], [0, 0, 126, 0], [0, 0, 0, 0], [0, 0, 0, 0], [207, 0, -207, 0], [0, 0, 0, 70], [0, 0, 0, 0], [0, 0, 0, 0], [0, 63, 0, 63], [0, 0, 0, 0], [-144, 0, -144, 0], [0, -9, 0, 9], [0, 0, 0, 0], [306, 0, 0, 0], [0, -168, 0, 0], [0, 0, 0, 0], [0, 0, 181, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-63, 0, 63, 0], [0, 0, 0, 106], [0, 0, 0, 0], [0, 0, 0, 0], [0, 63, 0, 63], [0, 0, 0, 0], [-486, 0, -486, 0], [0, -63, 0, 63], [0, 0, 0, 0], [-322, 0, 0, 0], [0, 196, 0, 0], [0, 0, 0, 0], [0, 0, -433, 0], [0, 0, 0, 0], [0, 0, 0, 0], [378, 0, -378, 0], [0, 0, 0, 14], [0, 0, 0, 0], [0, 0, 0, 0], [0, -198, 0, -198], [0, 0, 0, 0], [378, 0, 378, 0], [0, 207, 0, -207], [0, 0, 0, 0], [-70, 0, 0, 0], [0, -162, 0, 0], [0, 0, 0, 0], [0, 0, 488, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-567, 0, 567, 0], [0, 0, 0, -364], [0, 0, 0, 0], [0, 0, 0, 0], [0, -144, 0, -144], [0, 0, 0, 0], [567, 0, 567, 0], [0, -63, 0, 63], [0, 0, 0, 0], [-1134, 0, 0, 0], [0, 34, 0, 0], [0, 0, 0, 0], [0, 0, -1512, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-252, 0, 252, 0], [0, 0, 0, 181], [0, 0, 0, 0], [0, 0, 0, 0]]}