# Stored data for newform 450.3.g.c, downloaded from the LMFDB on 25 April 2024. {"label": "450.3.g.c", "space_label": "450.3.g", "level": 450, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9007611621933506, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1412942037310454856, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [18, -6, 1]], [11, [12, 1]], [17, [288, -24, 1]]], "qexp_display": "q+(-1-i)q^{2}+2iq^{4}+(3+3i)q^{7}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "g", "char_is_real": false, "Nk2": 4050, "analytic_conductor": 12.26161189621336, "hecke_ring_index": 1, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.248", "prec": 17}, "analytic_rank_proved": true, "char_values": [450, 4, [101, 127], [4, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [307, 343], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "1.962", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.358", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "90.886", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.3.c4", "trace_display": [-2, 0, 0, 6], "traces": [0, 2, -2, 0, 0, 0, 0, 6, 4, 0, 0, -24, 0, 24, 0, 0, -8, 24, 0, 0, 0, 0, 24, 6, 0, 0, -48, 0, -12, 0, 0, -16, 8, 0, 0, 0, 0, 96, 40, 0, 0, 96, 0, 54, 0, 0, -12, 54, 0, 0, 0, 0, 48, -24, 0, 0, 24, 0, 60, 0, 0, 64, 16, 0, 0, 0, 0, 6, -48, 0, 0, 96, 0, 24, 0, 0, -80, -72, 0, 0, 0, 0, -96, 186, 0, 0, -108, 0, -48, 0, 0, 144, 12, 0, 0, 0, 0, -24, -62, 0, 0, 156, 0, -186, 0, 0, 48, 54, 0, 0, 0, 0, -24, -144, 0, 0, -120, 0, 120, 0, 0, 46, -64, 0, 0, 0, 0, -234, -16, 0, 0, -264, 0, -120, 0, 0, 96, -336, 0, 0, 0, 0, -96, -288, 0, 0, -48, 0, -192, 0, 0, -496, 80, 0, 0, 0, 0, -144, 80, 0, 0, 36, 0, -186, 0, 0, -372, -6, 0, 0, 0, 0, 108, 336, 0, 0, 96, 0, -60, 0, 0, 284, -144, 0, 0, 0, 0, -288, -108, 0, 0, -384, 0, 264, 0, 0, 124, 264, 0, 0, 0, 0, -156, -180, 0, 0, 372, 0, -96, 0, 0, -56, -48, 0, 0, 0, 0, -48, 320, 0, 0, 576, 0, 234, 0, 0, 288, -186, 0, 0, 0, 0, 120, -504, 0, 0, -240, 0, 144, 0, 0, 64, -46, 0, 0, 0, 0, 480, -32, 0, 0, -504, 0, -72, 0, 0, 32, 384, 0, 0, 0, 0, 264, 666, 0, 0, 240, 0, -12, 0, 0, -176, -96, 0, 0, 0, 0, 576, -200, 0, 0, 576, 0, 234, 0, 0, 576, 288, 0, 0, 0, 0, 48, 336, 0, 0, 384, 0, 0, 0, 0, 324, 496, 0, 0, 0, 0, 486, 144, 0, 0, -1104, 0, -96, 0, 0, -160, -456, 0, 0, 0, 0, -36, -480, 0, 0, 372, 0, 192, 0, 0, -296, 372, 0, 0, 0, 0, -384, -238, 0, 0, 192, 0, 480, 0, 0, -672, 234, 0, 0, 0, 0, -96, 576, 0, 0, 120, 0, 600, 0, 0, -78, -284, 0, 0, 0, 0, 426, -24, 0, 0, -144, 0, -336, 0, 0, 216, 720, 0, 0, 0, 0, 384, 246, 0, 0, -528, 0, 48, 0, 0, 144, -124, 0, 0, 0, 0, 216, 320, 0, 0, 36, 0, -192, 0, 0, 360, -1152, 0, 0, 0, 0, -372, -360, 0, 0, 192, 0, -480, 0, 0, -1216, 56, 0, 0, 0, 0, 192, -108, 0, 0, -624, 0, 504, 0, 0, -640, 120, 0, 0, 0, 0, -576, 426, 0, 0, -468, 0, 48, 0, 0, -1152, -288, 0, 0, 0, 0, -864, -740, 0, 0, -444, 0, -426, 0, 0, 1008, -6, 0, 0, 0, 0, 240, -648, 0, 0, -288, 0, -720, 0, 0, 2304, -64, 0, 0, 0, 0, -1254, 128, 0, 0, 1176, 0, -720, 0, 0, 64, 288, 0, 0, 0, 0, 504, -1254, 0, 0, 144, 0, 468, 0, 0, 144, -32, 0, 0, 0, 0, -648, 576, 0, 0, 1116, 0, -246, 0, 0, -1332, -192, 0, 0, 0, 0, -240, 1152, 0, 0, 24, 0, -960, 0, 0, 1084, 176, 0, 0, 0, 0, -294, 672, 0, 0, -1200, 0, -240, 0, 0, 400, -576, 0, 0, 0, 0, -576, -954, 0, 0, -468, 0, 192, 0, 0, 1384, -576, 0, 0, 0, 0, 336, -2, 0, 0, 1116, 0, 288, 0, 0, -672, -426, 0, 0, 0, 0, -384, -624, 0, 0, 0, 0, -144, 0, 0, -1216, -324, 0, 0, 0, 0, -534, -160, 0, 0, 1296, 0, -456, 0, 0, -288, -696, 0, 0, 0, 0, 1104, 180, 0, 0, 192, 0, 288, 0, 0, -1616, 160, 0, 0, 0, 0, -744, -720, 0, 0, 1536, 0, 954, 0, 0, 960, 1254, 0, 0, 0, 0, -372, -24, 0, 0, -384, 0, 324, 0, 0, 704, 296, 0, 0, 0, 0, 180, 12, 0, 0, -768, 0, 1464, 0, 0, 476, -216, 0, 0, 0, 0, -192, 1866, 0, 0, -960, 0, -216, 0, 0, -136, 672, 0, 0, 0, 0, 1152, -260, 0, 0, -384, 0, -1920, 0, 0, -1152, 468, 0, 0, 0, 0, -120, -48, 0, 0, -1200, 0, 240, 0, 0, -1116, 78, 0, 0, 0, 0, 1926, 288, 0, 0, 1296, 0, 144, 0, 0, 48, -72, 0, 0, 0, 0, 144, 486, 0, 0, 672, 0, 576, 0, 0, 2144, -216, 0, 0, 0, 0, 816, 40, 0, 0, -2724, 0, -960, 0, 0, -492, 1440, 0, 0, 0, 0, 528, -264, 0, 0, -96, 0, 0, 0, 0, -1152, -144, 0, 0, 0, 0, 186, -528, 0, 0, -864, 0, 768, 0, 0, -640, -456, 0, 0, 0, 0, -36, -288, 0, 0, 384, 0, 312, 0, 0, 824, -360, 0, 0, 0, 0, 1080, 160, 0, 0, -1344, 0, 1434, 0, 0, 720, -246, 0, 0, 0, 0, -192, 744, 0, 0, 960, 0, 1080, 0, 0, -118, 1216, 0, 0, 0, 0, 138, 96, 0, 0, 576, 0, 744, 0, 0, 216, 1104, 0, 0, 0, 0, 624, 246, 0, 0, -1008, 0, 96, 0, 0, 144, 640, 0, 0, 0, 0, 2256, 80, 0, 0, -1824, 0, 1914, 0, 0, -852, -966, 0, 0, 0, 0, 468, -1080, 0, 0, -96, 0, -960, 0, 0, -576, 1152, 0, 0, 0, 0, -2154, 372, 0, 0, 2256, 0, -2232, 0, 0, 1480, -792, 0, 0, 0, 0, 444, 1152, 0, 0, 852, 0, -240, 0, 0, 1240, -1008, 0, 0, 0, 0, -984, 36, 0, 0, 1476, 0, 288, 0, 0, 1296, 474, 0, 0, 0, 0, 288, 1296, 0, 0, 1440, 0, 480, 0, 0, -1794, -2304, 0, 0, 0, 0, -1254, 92, 0, 0, 1416, 0, 600, 0, 0, -256, 1224, 0, 0, 0, 0, -1176, -1254, 0, 0, 1440, 0, -960, 0, 0, -2336, -64, 0, 0, 0, 0, 216, 920, 0, 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, 5, 3, -1, 4, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "50.3.c.a", "char_is_minimal": true, "conrey_index": 307, "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], [1, 0], [-1, -1], [0, 0], [0, 2], [0, 0], [0, 0], [3, 3], [2, -2], [0, 0], [0, 0], [-12, 0], [0, 0], [12, -12], [0, -6], [0, 0], [-4, 0], [12, 12], [0, 0], [0, 20], [0, 0], [0, 0], [12, 12], [3, -3], [0, 0], [0, 0], [-24, 0], [0, 0], [-6, 6], [0, 30], [0, 0], [-8, 0], [4, 4], [0, 0], [0, -24], [0, 0], [0, 0], [48, 48], [20, -20], [0, 0], [0, 0], [48, 0], [0, 0], [27, -27], [0, -24], [0, 0], [-6, 0], [27, 27], [0, 0], [0, -31], [0, 0], [0, 0], [24, 24], [-12, 12], [0, 0], [0, 0], [12, 0], [0, 0], [30, -30], [0, 60], [0, 0], [32, 0], [8, 8], [0, 0], [0, -8], [0, 0], [0, 0], [3, 3], [-24, 24], [0, 0], [0, 0], [48, 0], [0, 0], [12, -12], [0, -96], [0, 0], [-40, 0], [-36, -36], [0, 0], [0, 40], [0, 0], [0, 0], [-48, -48], [93, -93], [0, 0], [0, 0], [-54, 0], [0, 0], [-24, 24], [0, -30], [0, 0], [72, 0], [6, 6], [0, 0], [0, -54], [0, 0], [0, 0], [-12, -12], [-31, 31], [0, 0], [0, 0]]}