# Stored data for newform 350.4.c.a, downloaded from the LMFDB on 15 June 2026. {"Nk2": 5600, "analytic_conductor": 20.650668502009214, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [350, 2, [127, 101], [1, 2]], "cm_discs": [], "conrey_index": 99, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[3, [100, 0, 1]], [11, [-9, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 137506062686, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 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": "350.4.c.a", "level": 350, "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, 5, 7], "level_radical": 70, "minimal_twist": "350.4.a.j", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+2 i q^{2}+10 i q^{3}-4 q^{4}-20 q^{6}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "350.4.c", "trace_display": [0, 0, 0, 0], "trace_hash": 1836295395335149515, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.998", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "16.342", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "168.425", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 2, 0, 0, -8, 0, -40, 0, 0, -146, 0, 18, 0, 0, 28, 0, 32, 0, 0, 20, 0, 140, 0, 0, 160, 0, 208, 0, 0, -378, 0, -464, 0, 0, 384, 0, 584, 0, 0, 1040, 0, -876, 0, 0, -72, 0, -300, 0, 0, -98, 0, 1920, 0, 0, 1840, 0, -112, 0, 0, 1344, 0, 412, 0, 0, -128, 0, -360, 0, 0, -1500, 0, -942, 0, 0, 1220, 0, -80, 0, 0, -1486, 0, 5258, 0, 0, -560, 0, -1412, 0, 0, -360, 0, -728, 0, 0, -1944, 0, -640, 0, 0, -1314, 0, -1452, 0, 0, -832, 0, 1416, 0, 0, 1382, 0, 6100, 0, 0, -400, 0, 1512, 0, 0, -1344, 0, -2500, 0, 0, 1856, 0, -2044, 0, 0, -7060, 0, -2232, 0, 0, 2396, 0, -1536, 0, 0, -1348, 0, -9720, 0, 0, -2336, 0, -2456, 0, 0, 2562, 0, 1906, 0, 0, 252, 0, -4160, 0, 0, 7080, 0, 1050, 0, 0, 3504, 0, -3984, 0, 0, -1014, 0, -1460, 0, 0, 7560, 0, 288, 0, 0, 1296, 0, -5828, 0, 0, 1200, 0, 9280, 0, 0, -6440, 0, -1752, 0, 0, -736, 0, 392, 0, 0, -652, 0, 11980, 0, 0, -7680, 0, 7192, 0, 0, 180, 0, -11912, 0, 0, 3504, 0, -7360, 0, 0, -12280, 0, -9984, 0, 0, 448, 0, 6084, 0, 0, 1172, 0, 1260, 0, 0, -15184, 0, -5376, 0, 0, 10752, 0, -1340, 0, 0, -1648, 0, 17520, 0, 0, -19920, 0, 2760, 0, 0, 4124, 0, 512, 0, 0, -4270, 0, 27594, 0, 0, 1440, 0, 280, 0, 0, 3528, 0, -680, 0, 0, -5592, 0, 6000, 0, 0, 33872, 0, 13362, 0, 0, 3768, 0, 1872, 0, 0, -8606, 0, -3680, 0, 0, 1960, 0, -4880, 0, 0, 7800, 0, 4942, 0, 0, 320, 0, -28032, 0, 0, 35960, 0, 12072, 0, 0, 2600, 0, 5944, 0, 0, -3402, 0, 17520, 0, 0, -21032, 0, -3728, 0, 0, 6804, 0, -20162, 0, 0, -720, 0, 2240, 0, 0, 30420, 0, -4176, 0, 0, 5648, 0, 3336, 0, 0, -20740, 0, -47840, 0, 0, -26880, 0, 1440, 0, 0, -15114, 0, -13518, 0, 0, 2912, 0, -8240, 0, 0, 63948, 0, -4956, 0, 0, 3456, 0, 7776, 0, 0, -8854, 0, 20620, 0, 0, 2560, 0, 2404, 0, 0, 1398, 0, 14400, 0, 0, -8052, 0, 5256, 0, 0, 1400, 0, 11202, 0, 0, 5808, 0, -5292, 0, 0, -9340, 0, -27960, 0, 0, 21900, 0, 3328, 0, 0, -72, 0, 10990, 0, 0, -5664, 0, 18840, 0, 0, 9360, 0, 5400, 0, 0, -6496, 0, -5528, 0, 0, -29896, 0, 7154, 0, 0, -24400, 0, 12472, 0, 0, -24750, 0, -7884, 0, 0, -24, 0, 1600, 0, 0, -88320, 0, 11400, 0, 0, -6048, 0, -5172, 0, 0, -8386, 0, 13000, 0, 0, 29720, 0, 5376, 0, 0, 408, 0, -31720, 0, 0, 10000, 0, -55480, 0, 0, -18640, 0, 7794, 0, 0, 2080, 0, -7424, 0, 0, -16264, 0, -3600, 0, 0, 8176, 0, -2700, 0, 0, -11880, 0, 8596, 0, 0, -14304, 0, 28240, 0, 0, 16680, 0, 34044, 0, 0, 8928, 0, 23676, 0, 0, 13084, 0, -98112, 0, 0, 7200, 0, -9584, 0, 0, -882, 0, -6746, 0, 0, 6144, 0, 14560, 0, 0, -30076, 0, -3780, 0, 0, 18824, 0, 5392, 0, 0, 36712, 0, 17280, 0, 0, 38880, 0, 904, 0, 0, 28998, 0, -18914, 0, 0, -12264, 0, 9344, 0, 0, 12020, 0, 13944, 0, 0, 9824, 0, -17280, 0, 0, -4640, 0, -40260, 0, 0, 16560, 0, -10248, 0, 0, -6750, 0, -54896, 0, 0, -7624, 0, 29040, 0, 0, -26460, 0, 50544, 0, 0, -26416, 0, -1008, 0, 0, 21776, 0, 69000, 0, 0, 16640, 0, -36584, 0, 0, -58560, 0, 56998, 0, 0, -17796, 0, -28320, 0, 0, 68766, 0, 11634, 0, 0, -4200, 0, 3840, 0, 0, 12096, 0, -32480, 0, 0, -27640, 0, -14016, 0, 0, -4104, 0, 28444, 0, 0, 15936, 0, -89060, 0, 0, 62360, 0, 3708, 0, 0, 31112, 0, 4056, 0, 0, 2576, 0, -120, 0, 0, 5840, 0, -1372, 0, 0, -36816, 0, -1244, 0, 0, 4068, 0, -30240, 0, 0, -25860, 0, 15564, 0, 0, -1152, 0, 37728, 0, 0, -15004, 0, 108478, 0, 0, 26880, 0, -5184, 0, 0, 41628, 0, -25172, 0, 0, 23312, 0, 50000, 0, 0, -135434, 0, 67776, 0, 0, -46648, 0, -4800, 0, 0, -5914, 0, 10400, 0, 0, -37120, 0, 9508, 0, 0, -12264, 0, -40472, 0, 0, -39312, 0, 25760, 0, 0, -13500, 0, -26784, 0, 0, 7008, 0, -18432, 0, 0, -44860, 0, -71520, 0, 0, 103076, 0, 2944, 0, 0, -8760, 0, -8478, 0, 0, -1568, 0, 44640, 0, 0, 118380, 0, -21294, 0, 0, -30520, 0, 2608, 0, 0, 93312, 0, 26280, 0, 0, -47920, 0, -48256, 0, 0, 56058, 0, 16156, 0, 0, 10980, 0, 30720, 0, 0, 53144, 0, -71148, 0, 0, -28768, 0, 18816, 0, 0, 45128, 0, 94120, 0, 0, 26960, 0, -720, 0, 0, 588, 0, 22664, 0, 0, 47648, 0, 141912, 0, 0, 4520, 0, 45750, 0, 0, 5768, 0, -14016, 0, 0, -16276, 0, -61320, 0, 0, 29440, 0, -60416, 0, 0, -13374, 0, -62296, 0, 0, -3000, 0, 49120, 0, 0, -86400, 0, 32544, 0, 0, 39936, 0, -19920, 0, 0, -14434, 0, 47322, 0, 0, -51240, 0, -1792, 0, 0, 87696, 0, -67968, 0, 0, -24336, 0, -38120, 0, 0, 105996, 0, 81630, 0, 0, 43340, 0, -4688, 0, 0, 10778, 0, -132080, 0, 0, -5040, 0, -24512, 0, 0, -87324, 0, -980, 0, 0, -39240, 0, 60736, 0, 0, -182920, 0, -16896, 0, 0, 21504, 0, -12708, 0, 0, 63856, 0, -88980, 0, 0, -103368, 0, -43008, 0, 0, 19572, 0, 48066, 0, 0, 5360, 0, -21000, 0, 0, 19200, 0, -23508, 0, 0, 61604, 0, 6592, 0, 0, -3240, 0, -100886, 0, 0, -70080, 0, -72576, 0, 0, -52950, 0, -85010, 0, 0, -13188, 0, 79680, 0, 0, -280600, 0], "weight": 4, "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], [1, 0], [0, 2], [0, 10], [-4, 0], [0, 0], [-20, 0], [0, -7], [0, -8], [-73, 0], [0, 0], [9, 0], [0, -40], [0, -52], [14, 0], [0, 0], [16, 0], [0, -96], [0, -146], [10, 0], [0, 0], [70, 0], [0, 18], [0, 75], [80, 0], [0, 0], [104, 0], [0, -460], [0, 28], [-189, 0], [0, 0], [-232, 0], [0, 32], [0, 90], [192, 0], [0, 0], [292, 0], [0, -305], [0, 20], [520, 0], [0, 0], [-438, 0], [0, 140], [0, 353], [-36, 0], [0, 0], [-150, 0], [0, 486], [0, 160], [-49, 0], [0, 0], [960, 0], [0, 208], [0, -354], [920, 0], [0, 0], [-56, 0], [0, 100], [0, -378], [672, 0], [0, 0], [206, 0], [0, -464], [0, 511], [-64, 0], [0, 0], [-180, 0], [0, -599], [0, 384], [-750, 0], [0, 0], [-471, 0], [0, 584], [0, 614], [610, 0], [0, 0], [-40, 0], [0, -63], [0, 1040], [-743, 0], [0, 0], [2629, 0], [0, -876], [0, 996], [-280, 0], [0, 0], [-706, 0], [0, -1890], [0, -72], [-180, 0], [0, 0], [-364, 0], [0, -300], [0, -2320], [-972, 0], [0, 0], [-320, 0], [0, 184], [0, -98], [-657, 0], [0, 0]]}