# Stored data for newform 648.4.i.q, downloaded from the LMFDB on 25 April 2024.
{"label": "648.4.i.q", "space_label": "648.4.i", "level": 648, "weight": 4, "hecke_orbit": 17, "hecke_orbit_code": 72058143860851336, "dim": 4, "is_polredabs": true, "nf_label": "4.0.16641.1", "trace_hash": 1296530104219962014, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [15625, 500, 141, -4, 1]]], "qexp_display": "q+(2+2\\beta _{1}+\\beta _{3})q^{5}+(-3\\beta _{1}+\\beta _{2}+\\cdots)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": 12, "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": 16641, "field_disc_factorization": [[3, 2], [43, 2]], "field_poly": [121, -11, -10, -1, 1], "hecke_ring_index_factorization": [[2, 2], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "3.929", "prec": 17}, {"__RealLiteral__": 0, "data": "1.487", "prec": 17}, {"__RealLiteral__": 0, "data": "58.725", "prec": 20}, {"__RealLiteral__": 0, "data": "62.494", "prec": 20}, {"__RealLiteral__": 0, "data": "1528.267", "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, 4, 6], "traces": [0, 4, 0, 0, 0, 4, 0, 6, 0, 0, 0, 10, 0, 40, 0, 0, 0, 68, 0, 68, 0, 0, 0, -98, 0, -16, 0, 0, 0, -120, 0, 200, 0, 0, 0, 540, 0, 960, 0, 0, 0, -192, 0, 334, 0, 0, 0, -300, 0, 410, 0, 0, 0, 136, 0, 1588, 0, 0, 0, -620, 0, -200, 0, 0, 0, -1370, 0, 1406, 0, 0, 0, 2780, 0, 3604, 0, 0, 0, -804, 0, 334, 0, 0, 0, 500, 0, 1100, 0, 0, 0, 180, 0, 2820, 0, 0, 0, -1222, 0, 200, 0, 0, 0, -2688, 0, 2572, 0, 0, 0, 4752, 0, 6400, 0, 0, 0, -618, 0, 2002, 0, 0, 0, 1134, 0, 290, 0, 0, 0, -1128, 0, 172, 0, 0, 0, -1618, 0, -1188, 0, 0, 0, -3330, 0, 3420, 0, 0, 0, 8140, 0, 5196, 0, 0, 0, -1036, 0, 1172, 0, 0, 0, 1664, 0, -2372, 0, 0, 0, -4200, 0, -2376, 0, 0, 0, 486, 0, -2856, 0, 0, 0, -3528, 0, 1080, 0, 0, 0, -1968, 0, 3240, 0, 0, 0, 2766, 0, 3266, 0, 0, 0, 6810, 0, -2434, 0, 0, 0, -12240, 0, -7040, 0, 0, 0, -2478, 0, -2196, 0, 0, 0, -3700, 0, -650, 0, 0, 0, 14236, 0, -2928, 0, 0, 0, 5840, 0, -890, 0, 0, 0, 5286, 0, -5000, 0, 0, 0, -13940, 0, -20808, 0, 0, 0, 4556, 0, -3990, 0, 0, 0, 728, 0, -5770, 0, 0, 0, -9004, 0, -11816, 0, 0, 0, -886, 0, 3246, 0, 0, 0, 6052, 0, -8120, 0, 0, 0, -4648, 0, -13084, 0, 0, 0, 3176, 0, -1820, 0, 0, 0, 2810, 0, -712, 0, 0, 0, 4008, 0, -10240, 0, 0, 0, 2436, 0, -308, 0, 0, 0, 10990, 0, -7452, 0, 0, 0, -18860, 0, -21840, 0, 0, 0, 7392, 0, -870, 0, 0, 0, -1368, 0, -7914, 0, 0, 0, -9164, 0, -10960, 0, 0, 0, 10704, 0, 1790, 0, 0, 0, 26, 0, -6840, 0, 0, 0, -10384, 0, 3480, 0, 0, 0, -7734, 0, -5136, 0, 0, 0, 8564, 0, 2006, 0, 0, 0, -1932, 0, -13380, 0, 0, 0, -1040, 0, -13496, 0, 0, 0, -8052, 0, 1772, 0, 0, 0, 23580, 0, -21760, 0, 0, 0, 17370, 0, 5220, 0, 0, 0, -1100, 0, -8890, 0, 0, 0, -39428, 0, -4888, 0, 0, 0, -6198, 0, 6320, 0, 0, 0, 7818, 0, 3630, 0, 0, 0, -624, 0, 40184, 0, 0, 0, -21816, 0, 10700, 0, 0, 0, -4400, 0, 9630, 0, 0, 0, 35624, 0, 16444, 0, 0, 0, 7364, 0, -9300, 0, 0, 0, -19564, 0, 6372, 0, 0, 0, 19840, 0, 13560, 0, 0, 0, 11850, 0, -298, 0, 0, 0, 24100, 0, -12748, 0, 0, 0, -45672, 0, 2760, 0, 0, 0, -21020, 0, 4888, 0, 0, 0, -25090, 0, 18630, 0, 0, 0, 63752, 0, 33280, 0, 0, 0, -3978, 0, 9312, 0, 0, 0, 3396, 0, 18690, 0, 0, 0, 31680, 0, 4728, 0, 0, 0, -19500, 0, 762, 0, 0, 0, -14948, 0, 30912, 0, 0, 0, 9680, 0, 33940, 0, 0, 0, -4856, 0, 6890, 0, 0, 0, -9060, 0, 624, 0, 0, 0, -5188, 0, 36600, 0, 0, 0, 9238, 0, -8860, 0, 0, 0, -16230, 0, 19380, 0, 0, 0, 15040, 0, 77860, 0, 0, 0, -26420, 0, 8460, 0, 0, 0, 20650, 0, 3612, 0, 0, 0, 16016, 0, 2468, 0, 0, 0, -20592, 0, -24428, 0, 0, 0, -44870, 0, 13720, 0, 0, 0, 79444, 0, 19500, 0, 0, 0, 28320, 0, 30910, 0, 0, 0, 7160, 0, -622, 0, 0, 0, -110040, 0, 18200, 0, 0, 0, -510, 0, 16480, 0, 0, 0, 6462, 0, 28994, 0, 0, 0, 30768, 0, 103000, 0, 0, 0, -46010, 0, -460, 0, 0, 0, -4538, 0, 11316, 0, 0, 0, 107588, 0, 3088, 0, 0, 0, 2460, 0, -18694, 0, 0, 0, -33390, 0, -2320, 0, 0, 0, -3720, 0, -27972, 0, 0, 0, 28090, 0, -12962, 0, 0, 0, 17164, 0, -32076, 0, 0, 0, -103880, 0, -33960, 0, 0, 0, -39920, 0, 16250, 0, 0, 0, -29028, 0, 7056, 0, 0, 0, 54384, 0, -1740, 0, 0, 0, 324, 0, 5000, 0, 0, 0, -4648, 0, 30070, 0, 0, 0, 18988, 0, 35040, 0, 0, 0, 10392, 0, -23310, 0, 0, 0, 31478, 0, 6548, 0, 0, 0, -2968, 0, -42880, 0, 0, 0, 11512, 0, 25550, 0, 0, 0, 3000, 0, -21198, 0, 0, 0, -21112, 0, -20200, 0, 0, 0, 49598, 0, 12438, 0, 0, 0, 4660, 0, -38986, 0, 0, 0, -27000, 0, 13312, 0, 0, 0, -16164, 0, 4628, 0, 0, 0, 62794, 0, -11066, 0, 0, 0, -18156, 0, -98300, 0, 0, 0, -32180, 0, -44316, 0, 0, 0, -4922, 0, -22260, 0, 0, 0, 29180, 0, -64256, 0, 0, 0, 70380, 0, -26572, 0, 0, 0, 2640, 0, -16648, 0, 0, 0, -88900, 0, -46520, 0, 0, 0, 778, 0, 40050, 0, 0, 0, 46494, 0, 10360, 0, 0, 0, -114624, 0, -13740, 0, 0, 0, -36162, 0, 7148, 0, 0, 0, -57630, 0, 10836, 0, 0, 0, 110836, 0, -2244, 0, 0, 0, 59476, 0, -13930, 0, 0, 0, 26430, 0, -40260, 0, 0, 0, -97360, 0, -136024, 0, 0, 0, 7022, 0, -45924, 0, 0, 0, 43920, 0, -84528, 0, 0, 0, -69408, 0, -63736, 0, 0, 0, 20784, 0, -3464, 0, 0, 0, 17050, 0, -59776, 0, 0, 0, 34152, 0, -111260, 0, 0, 0, 23930, 0, -11064, 0, 0, 0, -10234, 0, 14710, 0, 0, 0, 49700, 0, -114588, 0, 0, 0, 13800, 0, 8652, 0, 0, 0, 60006, 0, 12820, 0, 0, 0, -112740, 0, -10428, 0, 0, 0, 20310, 0, 23070, 0, 0, 0, -54472, 0, -23974, 0, 0, 0, -47340, 0, 64896, 0, 0, 0, 2160, 0, 19026, 0, 0, 0, 26568, 0, -57390, 0, 0, 0, -123032, 0, -956, 0, 0, 0, -22520, 0, -62276, 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": "648.4.a.d", "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], [2, 2, 0, 1], [0, 0, 0, 0], [0, -3, 1, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -5, 3, -3], [0, 0, 0, 0], [20, 20, 0, 5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [17, 0, 4, 0], [0, 0, 0, 0], [17, 0, -5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-49, -49, 0, -7], [0, 0, 0, 0], [0, 8, -4, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 60, 11, -11], [0, 0, 0, 0], [100, 100, 0, -8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [135, 0, 5, 0], [0, 0, 0, 0], [240, 0, 7, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-96, -96, 0, 10], [0, 0, 0, 0], [0, -167, 25, -25], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 150, -38, 38], [0, 0, 0, 0], [205, 205, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [34, 0, -32, 0], [0, 0, 0, 0], [397, 0, 11, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-310, -310, 0, 6], [0, 0, 0, 0], [0, 100, -35, 35], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 685, -30, 30], [0, 0, 0, 0], [703, 703, 0, -11], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [695, 0, -3, 0], [0, 0, 0, 0], [901, 0, -18, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-402, -402, 0, -14], [0, 0, 0, 0], [0, -167, -79, 79], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -250, 74, -74], [0, 0, 0, 0], [550, 550, 0, 25], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [45, 0, 24, 0], [0, 0, 0, 0], [705, 0, 35, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-611, -611, 0, 7], [0, 0, 0, 0], [0, -100, 122, -122], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}