# Stored data for newform 300.3.c.a, downloaded from the LMFDB on 25 April 2024. {"label": "300.3.c.a", "space_label": "300.3.c", "level": 300, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 137489285420, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1276290743143530127, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [108, 0, 1]], [13, [18, 1]]], "qexp_display": "q+(-1-\\zeta_{6})q^{2}+\\zeta_{6}q^{3}+(-2+2\\zeta_{6})q^{4}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 4, "char_orbit_label": "c", "char_is_real": true, "Nk2": 2700, "analytic_conductor": 8.174407930808908, "hecke_ring_index": 2, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [300, 2, [151, 101, 277], [1, 2, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [151], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.916", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.703", "prec": 20}, {"__RealLiteral__": 0, "data": "1.390", "prec": 17}, {"__RealLiteral__": 0, "data": "140.230", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c2", "trace_display": [-2, 0, 0, 0], "traces": [0, 2, -2, 0, -4, 0, 6, 0, 16, -6, 0, 0, -12, -36, 36, 0, -16, -20, 6, 0, 0, -36, -36, 0, 0, 0, 36, 0, -72, -72, 0, 0, -32, 36, 20, 0, 12, -108, -48, 0, 0, 36, 36, 0, 72, 0, 24, 0, 48, -118, 0, 0, 72, 52, -18, 0, 0, 48, 72, 0, 0, -148, 24, 0, 128, 0, -36, 0, 40, -24, 0, 0, -48, -72, 108, 0, 96, 216, -108, 0, 0, 18, -36, 0, 72, 0, 72, 0, 0, -36, 0, 0, -48, -24, 0, 0, -96, 144, 118, 0, 0, 72, -60, 0, -288, 0, -52, 0, 36, -52, 0, 0, 288, 20, -48, 0, 144, 108, 108, 0, 0, 26, 148, 0, -48, 0, -108, 0, -128, -72, 0, 0, -72, 288, 144, 0, -160, -220, 24, 0, 0, 0, 360, 0, 48, 0, 72, 0, 216, 576, 0, 0, 0, 60, -216, 0, 216, -468, -312, 0, 0, -144, -18, 0, -72, 0, -312, 0, -288, 310, 0, 0, -144, -292, -216, 0, -288, -108, 36, 0, 0, 524, -648, 0, 0, 0, 24, 0, 0, 108, 0, 0, 0, -360, -144, 0, 236, 308, 108, 0, 0, -144, -72, 0, 120, 0, 36, 0, 288, -288, 0, 0, -104, -360, -648, 0, 0, -144, 52, 0, 0, 360, -324, 0, -576, 0, -20, 0, -96, 676, 0, 0, -576, 364, -108, 0, -216, 312, -360, 0, 0, -212, -26, 0, 296, 0, 108, 0, 0, 312, 0, 0, 216, 144, 756, 0, -256, -28, 72, 0, 0, 216, 468, 0, 288, 0, -288, 0, -288, -216, 0, 0, 160, 648, 220, 0, 48, -540, 648, 0, 0, -468, 0, 0, -720, 0, 648, 0, 96, -378, 0, 0, 144, 116, -354, 0, -864, -108, -576, 0, 0, -432, 648, 0, -384, 0, -60, 0, -432, -36, 0, 0, 0, -936, 468, 0, 624, -500, 156, 0, 0, 648, 144, 0, -36, 0, 432, 0, 288, 0, 0, 0, 624, 324, 456, 0, 288, 936, -310, 0, 0, 144, 144, 0, 0, 0, 292, 0, 432, -868, 0, 0, 576, 316, 108, 0, 72, 360, 252, 0, 0, 338, -524, 0, 1296, 0, -444, 0, 192, -108, 0, 0, 48, 540, 360, 0, 0, 1296, -108, 0, 0, -756, -648, 0, 384, 0, 360, 0, -288, -576, 0, 0, -944, -468, -308, 0, -216, 612, 648, 0, 0, -900, 144, 0, -144, 0, -1296, 0, 0, -100, 0, 0, -72, -648, -72, 0, 576, -648, 288, 0, 0, -572, 840, 0, 416, 0, 360, 0, 1296, -648, 0, 0, -144, 72, 144, 0, 104, 192, -216, 0, 0, 354, -360, 0, 648, 0, 324, 0, 0, 108, 0, 0, -40, -648, -744, 0, 384, -576, -676, 0, 0, -576, 648, 0, 576, 0, -364, 0, -216, -864, 0, 0, 0, 432, -312, 0, 720, -156, 1224, 0, 0, 1944, 212, 0, -52, 0, 54, 0, -1184, -432, 0, 0, -216, 720, 864, 0, 192, -2160, -312, 0, 0, -456, -1116, 0, 0, 0, -144, 0, -1512, -504, 0, 0, 1024, -144, 28, 0, 144, 0, -1944, 0, 0, 108, -216, 0, -936, 0, 648, 0, -288, 962, 0, 0, -576, -648, -108, 0, 0, -252, 216, 0, 0, -1300, -1128, 0, 320, 0, -648, 0, 440, 444, 0, 0, -192, 1872, 540, 0, -1296, -1148, -72, 0, 0, -360, 468, 0, 0, 0, -288, 0, 0, 396, 0, 0, -1296, 648, 648, 0, -384, 1008, 378, 0, 0, 1872, 432, 0, -576, 0, -116, 0, 708, 192, 0, 0, 864, -1996, 108, 0, -1152, -648, -432, 0, 0, -1228, 432, 0, -1296, 0, 216, 0, 768, 1296, 0, 0, -120, -828, -936, 0, 1728, -116, 36, 0, 0, 72, -936, 0, -864, 0, 936, 0, 936, 1080, 0, 0, 0, -840, 500, 0, -312, 2124, 1296, 0, 0, 1620, -648, 0, 288, 0, 480, 0, 144, 648, 0, 0, -864, 1900, -156, 0, -288, 216, 0, 0, 0, -484, 1296, 0, 0, 0, -324, 0, -912, -324, 0, 0, 576, -648, -936, 0, -620, 1612, 60, 0, 0, 744, -144, 0, -288, 0, -360, 0, 576, -936, 0, 0, 584, -648, -1944, 0, 0, -360, 868, 0, 0, 1512, 324, 0, 0, 0, -316, 0, 216, -620, 0, 0, -288, -96, -360, 0, -504, -1224, -1584, 0, 0, -216, -338, 0, -1048, 0, 78, 0, 0, -54, 0, 0, 888, -2412, 756, 0, -384, 864, 108, 0, 0, -864, 936, 0, -192, 0, -540, 0, -720, 3888, 0, 0, 0, 1116, -1296, 0, -216, -1692, 1128, 0, 0, -2916, 756, 0, 1296, 0, -192, 0, -768, 2564, 0, 0, 720, 844, -216, 0, 1152, 1944, 576, 0, 0, 2160, -240, 0, 944, 0, 468, 0, -616, -648, 0, 0, 0, 2664, -612, 0, -1296, 188, 864, 0, 0, 108, 900, 0, 288, 0, -432, 0, 576, -540, 0, 0, 2592, 1128, 1944, 0, -480, 576, 100, 0, 0, 2376, -660, 0, 0, 0, 648, 0, 144, 1436, 0, 0, -2304, 1180, 648, 0, 576, 72, -2556, 0, 0, 910, 572, 0, -1680, 0, 0, 0, -416, 288, 0, 0, 720, 1332, -2664, 0, 0, 364, 648, 0, 0, -648, 432, 0, 288, 0, -72, 0, 288, -1872, 0, 0, -416, -432, -192, 0, 432, 1548, -2712, 0, 0, -3204, -354, 0, -720, 0, -744, 0, 0, -4536, 0, 0, -648, 0, 1728, 0, 2304, 432, -108, 0, 0, -520, -648, 0, 160, 0, 648, 0, 1488, -216, 0, 0, -384, -1872, 576, 0, -1352, -2808, 180, 0, 0, 936, 576, 0, -1296, 0, 1404, 0, 1152, 108, 0, 0, -728, 936, 1992, 0, 864, -1872, 864, 0, 0, 0, -1404, 0, 864, 0, -432, 0, -624, 1296, 0, 0, 0, -3100, 156, 0, -2448, -1296, 504, 0, 0, 1826, -1944, 0, 424, 0, -432, 0, 208, -480, 0, 0, -108, -3888, -900, 0, 1184, 412, 432, 0, 0, 156, -252, 0, 0, 0, -720, 0, -1728, -288, 0, 0, -384, -1296, 2160, 0, -624, 396, 1536, 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, 4, 2, -1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "60.3.f.a", "char_is_minimal": true, "conrey_index": 151, "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, 1], [-2, 2], [0, 0], [3, -1], [0, 6], [8, 0], [-3, 0], [0, 0], [0, -6], [-6, -2], [-18, 0], [18, -6], [0, 0], [-8, -8], [-10, 0], [3, 3], [0, -8], [0, 0], [-18, 0], [-18, 6], [0, 4], [0, 8], [0, 0], [18, 18], [0, -3], [-36, -12], [-36, 0], [0, 0], [0, 4], [-16, 16], [18, 0], [10, 10], [0, 0], [6, -6], [-54, 0], [-24, 8], [0, -18], [0, 0], [18, 0], [18, 18], [0, 12], [36, 12], [0, 0], [12, -4], [0, 0], [24, -8], [-59, 0], [0, 0], [0, -10], [36, -36], [26, 0], [-9, 3], [0, 0], [0, 48], [24, 0], [36, 36], [0, 18], [0, 0], [-74, 0], [12, -4], [0, -18], [64, 0], [0, 0], [-18, -18], [0, 24], [20, -20], [-12, 0], [0, 0], [0, 60], [-24, 0], [-36, 0], [54, 54], [0, 0], [48, 16], [108, 0], [-54, 18], [0, -52], [0, 0], [9, 0], [-18, -18], [0, -52], [36, -36], [0, 0], [36, -12], [0, -36], [0, -48], [-18, 0], [0, 0], [0, -108], [-24, -8], [-12, 0], [0, 0], [0, 0], [-48, -16], [72, 0], [59, 59], [0, 18], [0, 0]]}