# Stored data for newform 69.4.c.a, downloaded from the LMFDB on 23 April 2024. {"label": "69.4.c.a", "space_label": "69.4.c", "level": 69, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 137506062405, "dim": 2, "is_polredabs": true, "nf_label": "2.0.23.1", "trace_hash": 204824035985644657, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [23, 0, 1]]], "qexp_display": "q-\\beta q^{2}+(2-\\beta )q^{3}-15q^{4}+(-23+\\cdots)q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 69, "char_orbit_label": "c", "char_is_real": true, "Nk2": 1104, "analytic_conductor": 4.071131790396103, "hecke_ring_index": 2, "level_radical": 69, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.762", "prec": 17}, "analytic_rank_proved": true, "char_values": [69, 2, [47, 28], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [3, 23], "conrey_indexes": [68], "field_disc": -23, "field_disc_factorization": [[-1, 1], [23, 1]], "field_poly": [6, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.776", "prec": 17}, {"__RealLiteral__": 0, "data": "0.127", "prec": 17}, {"__RealLiteral__": 0, "data": "20.676", "prec": 20}, {"__RealLiteral__": 0, "data": "3.125", "prec": 17}, {"__RealLiteral__": 0, "data": "271.105", "prec": 24}], "related_objects": [], "self_twist_discs": [-23], "cm_discs": [-23], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.1.d2", "trace_display": [0, 4, 0, 0], "traces": [0, 2, 0, 4, -30, 0, -46, 0, 0, -38, 0, 0, -60, 148, 0, 0, 82, 0, -184, 0, 0, 0, 0, 0, 322, -250, 0, -260, 0, 0, 0, 688, 0, 0, 0, 0, 570, 0, 0, 296, 0, 0, 0, 0, 0, 0, -1058, 0, 164, 686, 0, 0, -2220, 0, 506, 0, 0, 0, -1288, 0, 0, 0, 0, 0, 1346, 0, 0, 0, 0, -1058, 0, 0, 1288, 2452, 0, -500, 0, 0, -3404, 0, 0, -14, -2944, 0, 0, 0, 0, -1288, 0, 0, 0, 0, 0, 1376, 6164, 0, 690, 0, 0, 0, 3750, 0, 0, 0, 0, 0, 0, 0, 3900, 0, 0, 0, 0, 0, 0, 0, 0, -2812, 7820, 0, 0, -2662, 0, -2944, -10320, 0, 0, -5216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2116, -824, 0, 6164, -2116, 0, -1558, 0, 0, 1372, 0, 0, 5750, -7232, 0, 0, 0, 0, -4440, 0, 0, 0, 0, 0, 6992, -3272, 0, 0, 0, 0, 0, 6558, 0, 0, 0, 0, -2576, 0, 0, 7820, 0, 0, 0, 0, 0, 0, 7406, 0, -15824, 0, 0, 0, 0, 0, 2692, 8572, 0, 0, -10290, 0, 0, 0, 0, 0, 11960, 0, 0, 0, 0, -4232, 6068, 0, 0, 4936, 0, -2116, 0, 0, -3542, 0, 0, 4904, 0, 0, 0, -9680, 0, 4750, 0, 0, 0, 0, 0, 0, 9016, 0, -13616, 0, 0, 0, 0, 0, 0, 0, 0, 6964, 0, 0, -5888, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14670, 0, 0, 0, 0, -5152, -10396, 0, 0, 0, 0, 0, 0, 0, 0, 17824, 0, 0, 0, 0, 15870, 3676, 0, -13072, 0, 0, 12328, 0, 0, 0, 0, 0, 2760, -9826, 0, 0, -36780, 0, -15778, 0, 0, 0, 0, 0, 7500, 0, 0, 11960, 0, 0, 0, -20840, 0, 0, 0, 0, 23828, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 210, -18500, 0, 0, 20608, 0, 0, 24088, 0, 0, 37628, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27784, 0, 19320, 19444, 0, -19240, 0, 0, 15640, 0, 0, 0, 37628, 0, 0, 13718, 0, -5324, 0, 0, 0, 0, 0, -11776, 0, 0, -20640, 0, 0, 0, -43148, 0, 0, 0, 0, -10432, 0, 0, -25438, 0, 0, 0, 0, 0, 0, 0, 0, -10396, 5336, 0, 0, -30164, 0, 0, -10250, 0, 0, 50912, 0, 0, 0, 0, 0, -10004, 0, 0, 0, 0, 20102, 0, 0, -1648, 0, 0, 0, 0, 0, 24656, 0, 0, -4232, 0, 0, 0, 0, 0, -10660, 0, 0, 0, 0, 0, -56396, -14576, 0, -13034, 0, 0, 0, 0, 0, 0, 0, 0, 23000, 0, 0, -14464, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23360, 0, 0, 40112, 0, 42180, 0, 0, 0, -54740, 0, 0, 0, 0, 0, -5428, 0, 0, 0, 0, 0, 39930, 0, 14306, -39344, 0, -6544, 0, 0, 44160, 0, 0, 0, 28208, 0, 0, 31576, 0, 37628, 0, 0, 0, 0, 0, 13116, 78240, 0, 0, 0, 0, 0, -72496, 0, 0, 0, 0, -27784, 0, 0, 24472, 0, 0, 0, 0, 0, 0, -24334, 0, 31280, 0, 0, 0, 0, 0, 37628, -84088, 0, 0, -1868, 0, 0, 0, 0, 0, 42664, 0, 0, 0, 0, 14812, 0, 0, 0, 12360, 0, -63296, 0, 0, 0, 0, 0, -92460, 0, 0, 0, 14812, 0, 0, 0, 0, 0, 0, 0, -25574, -43556, 0, 17144, 0, 0, 0, 0, 0, 0, 0, 0, -20580, 0, 0, 5336, 0, 0, 0, 0, 0, 0, -78292, 0, -40250, 652, 0, 0, 108480, 0, 23920, 17680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11638, 88964, 0, 12136, 31250, 0, 0, 0, 0, 0, 0, 0, 9872, -107272, 0, 0, 50764, 0, -8464, 0, 0, 0, 0, 0, 0, 0, 0, -48944, 0, 0, 0, 49080, 0, 0, 0, 0, -46588, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29624, 0, -19360, 0, 0, 0, -67172, 0, 32500, -98370, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12056, 0, 0, 87308, 0, 18032, 0, 0, 40112, 0, 0, 37444, 0, 0, 0, 122912, 0, -117300, 0, 0, 0, 0, 0, 0, 0, 0, -5428, 0, 0, 0, 0, 0, 0, 0, 0, 61226, 0, 0, 28234, 0, 0, 0, 0, 0, 0, 15870, 0, 55936, 61096, 0, 0, 0, 0, 110768, 0, 0, 0, 0, 0, 0, 0, 0, 0, -95312, 0, 0, 0, 0, 0, 0, 0, 119968, 0, 0, 0, 0, 0, -29340, 0, 0, -72496, -128580, 0, 0, -86000, 0, 0, 0, 0, 0, 0, 0, 14168, 28126, 0, -20792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84088, -83720, 0, 0, -6728, 0, 35648, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35168, 0, 0, 0, 0, 63480, -9932, 0, 7352, 99604, 0, 18952, 0, 0, -89440, 0, 0, 0, 12714, 0, 0, -74040, 0, -117116, 0, 0, 0, 0, 0, 31740, 49180, 0, 0, 0, 0, 0, 100696, 0, 0, 0, 0, -7590, 0, 0, -19652, 0, 0, 0, 0, 0, 0, 0, 0, -73560, -68180, 0, 0, 0, 0, -63112, -5720, 0, 0, -53452, 0, 0, 0, 0, 0, 145200, 0, 0, 0, 0, -78292, -46000, 0, -71250, 0, 0, 0, 0, 0, 166336, 0, 0, 47840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -41680, 187496, 0, 0, 0, 0, 0, 19320, 0, 0, 0, 0, 88964, 0, 0, 95312, 0, 0, 0, 0, 0, 0, -67712, 0, 0, 0, 0, 0, 181448, 0, -107272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 177090, 0, 0, 0, 0, 0, -17024, 0, 0, 0, 0, -104460, 0, 0, -37000, 0, 0, 75256, 0, 0, 0, -65044, 0, 41216, 0, 0, 0, 0, 0, 0, 18256, 0, 48176, 0, 0, 0, -120380, 0, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 23, 2, -1, 2, -23], [1, 1, 3, 2, -1, 2, 0], [1, 1, 69, 3, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "69.4.c.a", "char_is_minimal": true, "conrey_index": 68, "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], [0, -1], [2, -1], [-15, 0], [0, 0], [-23, -2], [0, 0], [0, 7], [-19, -4], [0, 0], [0, 0], [-30, 15], [74, 0], [0, 0], [0, 0], [41, 0], [0, 0], [-92, 19], [0, 0], [0, 0], [0, 0], [0, 0], [0, -23], [161, 14], [-125, 0], [0, -74], [-130, 11], [0, 0], [0, -28], [0, 0], [344, 0], [0, 15], [0, 0], [0, 0], [0, 0], [285, 60], [0, 0], [0, 0], [148, -74], [0, 0], [0, -64], [0, 0], [0, 0], [0, 0], [0, 0], [-529, 0], [0, 134], [82, -41], [343, 0], [0, 125], [0, 0], [-1110, 0], [0, 0], [253, 130], [0, 0], [0, 0], [0, 0], [-644, 0], [0, 170], [0, 0], [0, 0], [0, -344], [0, 0], [673, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-529, -46], [0, 0], [0, -46], [644, -133], [1226, 0], [0, 0], [-250, 125], [0, 0], [0, 0], [-1702, -148], [0, 0], [0, 0], [-7, 152], [-1472, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-644, -56], [0, 0], [0, 0], [0, 0], [0, 0], [0, 345], [688, -344], [3082, 0], [0, 0], [345, 30], [0, 0], [0, -343], [0, 0], [1875, 0]]}