# Stored data for newform 784.3.c.a, downloaded from the LMFDB on 07 June 2024.
{"Nk2": 7056, "analytic_conductor": 21.362452725847277, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "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": [784, 2, [687, 197, 689], [2, 2, 1]], "cm_discs": [], "conrey_index": 97, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[3, [3, 0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 137489285904, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 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": false, "label": "784.3.c.a", "level": 784, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2, 7], "level_radical": 14, "minimal_twist": "28.3.h.a", "nf_label": "2.0.3.1", "prim_orbit_index": 2, "qexp_display": "q-\\zeta_{6}q^{3}-\\zeta_{6}q^{5}+6q^{9}-15q^{11}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "2.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "784.3.c", "trace_display": [0, 0, 0, 0], "trace_hash": 960060719961249903, "trace_moments": [{"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "1.931", "prec": 17}, {"__RealLiteral__": 0, "data": "0.164", "prec": 17}, {"__RealLiteral__": 0, "data": "15.257", "prec": 20}, {"__RealLiteral__": 0, "data": "1.514", "prec": 17}, {"__RealLiteral__": 0, "data": "150.625", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, 12, 0, -30, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 18, 0, 44, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 62, 0, 48, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 102, 0, -114, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 48, 0, 98, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0, 146, 0, 18, 0, 0, 0, 102, 0, 0, 0, 0, 0, 0, 0, 42, 0, 54, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, -78, 0, 206, 0, 0, 0, -156, 0, 0, 0, 0, 0, 0, 0, 208, 0, -192, 0, 0, 0, -100, 0, 0, 0, 0, 0, 0, 0, -90, 0, 126, 0, 0, 0, 150, 0, 0, 0, 0, 0, 0, 0, -354, 0, -110, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, -46, 0, 90, 0, 0, 0, -46, 0, 0, 0, 0, 0, 0, 0, 282, 0, -126, 0, 0, 0, 282, 0, 0, 0, 0, 0, 0, 0, 114, 0, -418, 0, 0, 0, -300, 0, 0, 0, 0, 0, 0, 0, -192, 0, 108, 0, 0, 0, -692, 0, 0, 0, 0, 0, 0, 0, -90, 0, -816, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, -546, 0, 150, 0, 0, 0, 444, 0, 0, 0, 0, 0, 0, 0, -432, 0, 48, 0, 0, 0, -270, 0, 0, 0, 0, 0, 0, 0, -72, 0, 306, 0, 0, 0, -198, 0, 0, 0, 0, 0, 0, 0, -660, 0, 718, 0, 0, 0, -444, 0, 0, 0, 0, 0, 0, 0, -1156, 0, 96, 0, 0, 0, 282, 0, 0, 0, 0, 0, 0, 0, 342, 0, 282, 0, 0, 0, 246, 0, 0, 0, 0, 0, 0, 0, 894, 0, 180, 0, 0, 0, -918, 0, 0, 0, 0, 0, 0, 0, -302, 0, 372, 0, 0, 0, 548, 0, 0, 0, 0, 0, 0, 0, -54, 0, -1086, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, -78, 0, 236, 0, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 766, 0, -282, 0, 0, 0, 460, 0, 0, 0, 0, 0, 0, 0, -120, 0, -402, 0, 0, 0, 342, 0, 0, 0, 0, 0, 0, 0, -354, 0, -336, 0, 0, 0, -930, 0, 0, 0, 0, 0, 0, 0, 48, 0, -816, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, -720, 0, -654, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 1458, 0, -198, 0, 0, 0, -540, 0, 0, 0, 0, 0, 0, 0, 1598, 0, 1530, 0, 0, 0, 1628, 0, 0, 0, 0, 0, 0, 0, 342, 0, 300, 0, 0, 0, -684, 0, 0, 0, 0, 0, 0, 0, 96, 0, 1714, 0, 0, 0, -1140, 0, 0, 0, 0, 0, 0, 0, 850, 0, 960, 0, 0, 0, 342, 0, 0, 0, 0, 0, 0, 0, 810, 0, 246, 0, 0, 0, -486, 0, 0, 0, 0, 0, 0, 0, -714, 0, -896, 0, 0, 0, 1536, 0, 0, 0, 0, 0, 0, 0, -1442, 0, 432, 0, 0, 0, 236, 0, 0, 0, 0, 0, 0, 0, -186, 0, -1266, 0, 0, 0, -1530, 0, 0, 0, 0, 0, 0, 0, 894, 0, -1054, 0, 0, 0, 396, 0, 0, 0, 0, 0, 0, 0, 1710, 0, 288, 0, 0, 0, -378, 0, 0, 0, 0, 0, 0, 0, 714, 0, -1614, 0, 0, 0, 588, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 1006, 0, 0, 0, 1860, 0, 0, 0, 0, 0, 0, 0, 818, 0, -810, 0, 0, 0, -388, 0, 0, 0, 0, 0, 0, 0, 1512, 0, -66, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, -66, 0, 342, 0, 0, 0, 1740, 0, 0, 0, 0, 0, 0, 0, -108, 0, 1152, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, -486, 0, 546, 0, 0, 0, -582, 0, 0, 0, 0, 0, 0, 0, -816, 0, 3264, 0, 0, 0, 1812, 0, 0, 0, 0, 0, 0, 0, 1406, 0, 876, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, -762, 0, -264, 0, 0, 0, -702, 0, 0, 0, 0, 0, 0, 0, -1470, 0, 1154, 0, 0, 0, -324, 0, 0, 0, 0, 0, 0, 0, -1550, 0, -336, 0, 0, 0, -1900, 0, 0, 0, 0, 0, 0, 0, 612, 0, -2256, 0, 0, 0, 666, 0, 0, 0, 0, 0, 0, 0, 1728, 0, -3780, 0, 0, 0, 342, 0, 0, 0, 0, 0, 0, 0, -2256, 0, 342, 0, 0, 0, -2550, 0, 0, 0, 0, 0, 0, 0, -1578, 0, -930, 0, 0, 0, 246, 0, 0, 0, 0, 0, 0, 0, -1506, 0, 50, 0, 0, 0, 492, 0, 0, 0, 0, 0, 0, 0, 960, 0, 630, 0, 0, 0, -1610, 0, 0, 0, 0, 0, 0, 0, -6, 0, 558, 0, 0, 0, 324, 0, 0, 0, 0, 0, 0, 0, -1710, 0, -486, 0, 0, 0, -2190, 0, 0, 0, 0, 0, 0, 0, -482, 0, 816, 0, 0, 0, 2572, 0, 0, 0, 0, 0, 0, 0, -270, 0, -1350, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, 432, 0, 1474, 0, 0, 0, -2532, 0, 0, 0, 0, 0, 0, 0, 946, 0, -336, 0, 0, 0, 1364, 0, 0, 0, 0, 0, 0, 0, -1686, 0, -1530, 0, 0, 0, -774, 0, 0, 0, 0, 0, 0, 0, 402, 0, 720, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 1628, 0, -468, 0, 0, 0, -388, 0, 0, 0, 0, 0, 0, 0, 1056, 0, -3042, 0, 0, 0, 1236, 0, 0, 0, 0, 0, 0, 0, -180, 0, -1646, 0, 0, 0, 714, 0, 0, 0, 0, 0], "weight": 3, "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, 0], [0, -1], [0, 0], [0, -1], [0, 0], [0, 0], [0, 0], [6, 0], [0, 0], [-15, 0], [0, 0], [0, 8], [0, 0], [-3, 0], [0, 0], [0, 17], [0, 0], [0, 9], [0, 0], [0, 0], [0, 0], [9, 0], [0, 0], [22, 0], [0, 0], [0, -15], [0, 0], [-6, 0], [0, 0], [0, 7], [0, 0], [0, 15], [0, 0], [0, 0], [0, 0], [31, 0], [0, 0], [24, 0], [0, 0], [0, -32], [0, 0], [-10, 0], [0, 0], [0, -6], [0, 0], [0, 25], [0, 0], [0, 0], [0, 0], [51, 0], [0, 0], [-57, 0], [0, 0], [0, 15], [0, 0], [27, 0], [0, 0], [0, 47], [0, 0], [0, 47], [0, 0], [0, 0], [0, 0], [24, 0], [0, 0], [49, 0], [0, 0], [0, -9], [0, 0], [126, 0], [0, 0], [0, -15], [0, 0], [0, -22], [0, 0], [0, 0], [0, 0], [73, 0], [0, 0], [9, 0], [0, 0], [0, 8], [0, 0], [51, 0], [0, 0], [0, 6], [0, 0], [0, -33], [0, 0], [0, 0], [0, 0], [21, 0], [0, 0], [27, 0], [0, 0], [0, 16], [0, 0], [-90, 0], [0, 0]]}