# Stored data for newform 648.4.i.s, downloaded from the LMFDB on 25 April 2024.
{"label": "648.4.i.s", "space_label": "648.4.i", "level": 648, "weight": 4, "hecke_orbit": 19, "hecke_orbit_code": 81065343115592328, "dim": 4, "is_polredabs": true, "nf_label": "4.0.1089.1", "trace_hash": 1726856266368237494, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [78961, 2248, 345, -8, 1]]], "qexp_display": "q+(4+4\\beta _{1}+\\beta _{3})q^{5}+(12\\beta _{1}-\\beta _{2}+\\beta _{3})q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "i", "char_is_real": false, "Nk2": 10368, "analytic_conductor": 38.23323768371992, "hecke_ring_index": 108, "level_radical": 6, "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": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [648, 3, [487, 325, 569], [3, 3, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [217, 433], "field_disc": 1089, "field_disc_factorization": [[3, 2], [11, 2]], "field_poly": [9, -3, -2, -1, 1], "hecke_ring_index_factorization": [[2, 2], [3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.878", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "56.363", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1373.087", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [0, 0, 8, -24], "traces": [0, 4, 0, 0, 0, 8, 0, -24, 0, 0, 0, 2, 0, -32, 0, 0, 0, 112, 0, 368, 0, 0, 0, 92, 0, -376, 0, 0, 0, -336, 0, -376, 0, 0, 0, -1380, 0, 696, 0, 0, 0, -312, 0, -80, 0, 0, 0, -228, 0, -196, 0, 0, 0, -304, 0, 16, 0, 0, 0, 680, 0, 112, 0, 0, 0, -2248, 0, -352, 0, 0, 0, -3632, 0, -1148, 0, 0, 0, 24, 0, 1360, 0, 0, 0, -782, 0, 2600, 0, 0, 0, -480, 0, -3984, 0, 0, 0, 1924, 0, 338, 0, 0, 0, -1656, 0, 112, 0, 0, 0, -2772, 0, 184, 0, 0, 0, -1464, 0, 2008, 0, 0, 0, -3048, 0, 2660, 0, 0, 0, -10512, 0, -656, 0, 0, 0, -2006, 0, -3396, 0, 0, 0, -2592, 0, -2832, 0, 0, 0, -64, 0, -312, 0, 0, 0, 4264, 0, 2936, 0, 0, 0, -1466, 0, 1528, 0, 0, 0, 2544, 0, 4944, 0, 0, 0, -780, 0, -5622, 0, 0, 0, 6504, 0, -9264, 0, 0, 0, 4788, 0, 8064, 0, 0, 0, -984, 0, 56, 0, 0, 0, -1680, 0, 998, 0, 0, 0, -4368, 0, 6256, 0, 0, 0, -2844, 0, -4692, 0, 0, 0, 184, 0, -6056, 0, 0, 0, 15992, 0, 3084, 0, 0, 0, 8608, 0, 4384, 0, 0, 0, 3480, 0, 3364, 0, 0, 0, 12512, 0, -11328, 0, 0, 0, -5756, 0, -3900, 0, 0, 0, 15040, 0, 1808, 0, 0, 0, 4672, 0, 184, 0, 0, 0, -7880, 0, -1800, 0, 0, 0, 4316, 0, 7114, 0, 0, 0, -2240, 0, 272, 0, 0, 0, 376, 0, 6016, 0, 0, 0, 568, 0, 2840, 0, 0, 0, -4392, 0, 2492, 0, 0, 0, -1248, 0, 11536, 0, 0, 0, 10976, 0, 7356, 0, 0, 0, 38912, 0, -32592, 0, 0, 0, 2220, 0, 4854, 0, 0, 0, 72, 0, 336, 0, 0, 0, 19808, 0, -25984, 0, 0, 0, -7488, 0, -3904, 0, 0, 0, 21604, 0, 11388, 0, 0, 0, -752, 0, 16752, 0, 0, 0, 5310, 0, -2868, 0, 0, 0, -920, 0, -136, 0, 0, 0, 13848, 0, 11172, 0, 0, 0, -2296, 0, 17128, 0, 0, 0, -5898, 0, -15256, 0, 0, 0, 20256, 0, 7424, 0, 0, 0, 20088, 0, -690, 0, 0, 0, 11336, 0, -6928, 0, 0, 0, -27136, 0, -20608, 0, 0, 0, -14208, 0, -17896, 0, 0, 0, 348, 0, -18558, 0, 0, 0, 12192, 0, 31760, 0, 0, 0, -1224, 0, -7168, 0, 0, 0, -29536, 0, 20352, 0, 0, 0, -29384, 0, 21076, 0, 0, 0, 3712, 0, -7560, 0, 0, 0, 13768, 0, -11652, 0, 0, 0, -38608, 0, -624, 0, 0, 0, -26976, 0, 11138, 0, 0, 0, -15736, 0, -7048, 0, 0, 0, -4836, 0, 48840, 0, 0, 0, 80, 0, -44096, 0, 0, 0, -20228, 0, -15072, 0, 0, 0, -6800, 0, 13792, 0, 0, 0, 29142, 0, -4656, 0, 0, 0, 14664, 0, -4512, 0, 0, 0, -31944, 0, -23940, 0, 0, 0, -1896, 0, 6888, 0, 0, 0, -31336, 0, 228, 0, 0, 0, -25520, 0, -27536, 0, 0, 0, 1352, 0, 10598, 0, 0, 0, -28752, 0, 27720, 0, 0, 0, -392, 0, 10224, 0, 0, 0, 45512, 0, -9304, 0, 0, 0, -28536, 0, -2688, 0, 0, 0, -59152, 0, 69088, 0, 0, 0, -29842, 0, 47436, 0, 0, 0, 14288, 0, 30408, 0, 0, 0, 3424, 0, -68296, 0, 0, 0, 9624, 0, -152, 0, 0, 0, -31918, 0, -28652, 0, 0, 0, -11680, 0, -114672, 0, 0, 0, -13188, 0, 5290, 0, 0, 0, -10640, 0, 39056, 0, 0, 0, -30720, 0, -14056, 0, 0, 0, -1992, 0, -43448, 0, 0, 0, 13572, 0, -30454, 0, 0, 0, 480, 0, 30448, 0, 0, 0, 12350, 0, 53888, 0, 0, 0, -14344, 0, 16032, 0, 0, 0, 55072, 0, 1360, 0, 0, 0, -2616, 0, 69800, 0, 0, 0, -25986, 0, 25724, 0, 0, 0, -164976, 0, -40416, 0, 0, 0, -112, 0, 6406, 0, 0, 0, -1744, 0, -696, 0, 0, 0, -39856, 0, -18360, 0, 0, 0, 33320, 0, -19744, 0, 0, 0, -48072, 0, 15024, 0, 0, 0, 62160, 0, 54528, 0, 0, 0, -25218, 0, -55096, 0, 0, 0, 29176, 0, 2248, 0, 0, 0, -80848, 0, -64464, 0, 0, 0, -53664, 0, 15384, 0, 0, 0, 31024, 0, -10972, 0, 0, 0, -704, 0, 11216, 0, 0, 0, 8912, 0, 1358, 0, 0, 0, -16632, 0, -34344, 0, 0, 0, 157732, 0, 7880, 0, 0, 0, 45040, 0, -46248, 0, 0, 0, 67904, 0, -47698, 0, 0, 0, 57216, 0, 93856, 0, 0, 0, -16824, 0, -1816, 0, 0, 0, 36656, 0, 45184, 0, 0, 0, 118296, 0, 148480, 0, 0, 0, -29800, 0, -25392, 0, 0, 0, -574, 0, 6276, 0, 0, 0, 56800, 0, -10352, 0, 0, 0, 81168, 0, 9272, 0, 0, 0, -9216, 0, -39832, 0, 0, 0, -125696, 0, 136, 0, 0, 0, -62512, 0, -82416, 0, 0, 0, 6984, 0, -10046, 0, 0, 0, 107088, 0, -63840, 0, 0, 0, 25512, 0, -26572, 0, 0, 0, 22008, 0, -16080, 0, 0, 0, -67312, 0, 29460, 0, 0, 0, -1360, 0, 75152, 0, 0, 0, 119502, 0, -5700, 0, 0, 0, 35632, 0, 28688, 0, 0, 0, -69152, 0, -9726, 0, 0, 0, -30480, 0, -23688, 0, 0, 0, 138216, 0, 53264, 0, 0, 0, 25632, 0, 18232, 0, 0, 0, 16460, 0, 782, 0, 0, 0, 171696, 0, 147664, 0, 0, 0, 57568, 0, -46416, 0, 0, 0, 84688, 0, -46544, 0, 0, 0, 5200, 0, -59412, 0, 0, 0, -49320, 0, 38112, 0, 0, 0, 49998, 0, 9184, 0, 0, 0, 68256, 0, -246288, 0, 0, 0, -29916, 0, -25956, 0, 0, 0, -27752, 0, 23192, 0, 0, 0, -55716, 0, -50832, 0, 0, 0, -12816, 0, -240, 0, 0, 0, 11868, 0, 136794, 0, 0, 0, -73888, 0, 57712, 0, 0, 0, -64114, 0, 89104, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "216.4.a.e", "char_is_minimal": false, "conrey_index": 217, "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, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [4, 4, 0, 1], [0, 0, 0, 0], [0, 12, -1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [-16, -16, 0, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [28, 0, 4, 0], [0, 0, 0, 0], [92, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [46, 46, 0, -4], [0, 0, 0, 0], [0, 188, -8, 8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 168, 2, -2], [0, 0, 0, 0], [-188, -188, 0, 5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-345, 0, -16, 0], [0, 0, 0, 0], [174, 0, -4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-156, -156, 0, 10], [0, 0, 0, 0], [0, 40, 14, -14], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 114, -8, 8], [0, 0, 0, 0], [-98, -98, 0, -24], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-76, 0, 13, 0], [0, 0, 0, 0], [4, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [340, 340, 0, -24], [0, 0, 0, 0], [0, -56, 32, -32], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1124, 0, 0], [0, 0, 0, 0], [-176, -176, 0, -34], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-908, 0, 12, 0], [0, 0, 0, 0], [-287, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [12, 12, 0, 1], [0, 0, 0, 0], [0, -680, -32, 32], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 391, 32, -32], [0, 0, 0, 0], [1300, 1300, 0, 44], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-120, 0, -18, 0], [0, 0, 0, 0], [-996, 0, -32, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [962, 962, 0, 100], [0, 0, 0, 0], [0, -169, -8, 8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}