# Stored data for newform 784.3.s.b, downloaded from the LMFDB on 17 September 2025. {"Nk2": 7056, "analytic_conductor": 21.362452725847277, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 19, "char_orbit_label": "s", "char_order": 6, "char_parity": -1, "char_values": [784, 6, [687, 197, 689], [6, 6, 1]], "cm_discs": [], "conrey_index": 129, "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, -3, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504836628284176, "hecke_ring_generator_nbound": 3, "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, 7, 4, -1, 6, 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.s.b", "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": 4, "qexp_display": "q+(1+\\zeta_{6})q^{3}+(-2+\\zeta_{6})q^{5}-6\\zeta_{6}q^{9}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "2.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "784.3.s", "trace_display": [0, 3, -3, 0], "trace_hash": 1676115574368450309, "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "2.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.097", "prec": 17}, {"__RealLiteral__": 0, "data": "11.742", "prec": 20}, {"__RealLiteral__": 0, "data": "0.603", "prec": 17}, {"__RealLiteral__": 0, "data": "94.367", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.168", "prec": 17}, "traces": [0, 2, 0, 3, 0, -3, 0, 0, 0, -6, 0, 15, 0, 0, 0, -6, 0, -51, 0, 27, 0, 0, 0, -9, 0, -22, 0, 0, 0, -12, 0, -21, 0, 45, 0, 0, 0, -31, 0, -24, 0, 0, 0, -20, 0, 18, 0, 75, 0, 0, 0, -51, 0, 57, 0, 0, 0, 54, 0, -141, 0, 141, 0, 0, 0, -24, 0, -49, 0, 0, 0, 252, 0, 45, 0, -66, 0, 0, 0, -73, 0, -9, 0, 0, 0, 102, 0, -18, 0, -99, 0, 0, 0, -21, 0, -27, 0, 0, 0, -180, 0, -171, 0, 123, 0, 0, 0, 39, 0, -103, 0, 0, 0, -156, 0, 27, 0, 144, 0, 0, 0, -104, 0, 96, 0, 0, 0, -100, 0, -30, 0, 171, 0, 0, 0, 45, 0, -63, 0, 0, 0, 150, 0, 360, 0, 18, 0, 0, 0, 177, 0, 55, 0, 0, 0, 42, 0, -171, 0, 171, 0, 0, 0, 23, 0, -45, 0, 0, 0, -46, 0, -162, 0, -243, 0, 0, 0, -141, 0, 63, 0, 0, 0, 282, 0, 93, 0, -765, 0, 0, 0, -57, 0, 209, 0, 0, 0, -300, 0, -357, 0, -147, 0, 0, 0, 96, 0, -54, 0, 0, 0, -692, 0, 378, 0, 30, 0, 0, 0, 45, 0, 408, 0, 0, 0, 264, 0, 243, 0, -291, 0, 0, 0, 273, 0, -75, 0, 0, 0, 444, 0, 381, 0, -432, 0, 0, 0, 216, 0, -24, 0, 0, 0, -270, 0, 153, 0, 333, 0, 0, 0, 36, 0, -153, 0, 0, 0, -198, 0, 789, 0, 123, 0, 0, 0, 330, 0, -359, 0, 0, 0, -444, 0, 3, 0, -81, 0, 0, 0, 578, 0, -48, 0, 0, 0, 282, 0, -675, 0, 216, 0, 0, 0, -171, 0, -141, 0, 0, 0, 246, 0, 843, 0, -387, 0, 0, 0, -447, 0, -90, 0, 0, 0, -918, 0, -528, 0, -309, 0, 0, 0, 151, 0, -186, 0, 0, 0, 548, 0, -234, 0, -315, 0, 0, 0, 27, 0, 543, 0, 0, 0, 720, 0, 525, 0, -378, 0, 0, 0, 39, 0, -118, 0, 0, 0, -90, 0, 603, 0, -576, 0, 0, 0, -383, 0, 141, 0, 0, 0, 460, 0, -150, 0, 555, 0, 0, 0, 60, 0, 201, 0, 0, 0, 342, 0, 219, 0, 93, 0, 0, 0, 177, 0, 168, 0, 0, 0, -930, 0, -579, 0, -189, 0, 0, 0, -24, 0, 408, 0, 0, 0, -44, 0, -450, 0, 1122, 0, 0, 0, 360, 0, 327, 0, 0, 0, 36, 0, -243, 0, 1035, 0, 0, 0, -729, 0, 99, 0, 0, 0, -540, 0, -1440, 0, 165, 0, 0, 0, -799, 0, -765, 0, 0, 0, 1628, 0, 63, 0, -693, 0, 0, 0, -171, 0, -150, 0, 0, 0, -684, 0, -933, 0, 744, 0, 0, 0, -48, 0, -857, 0, 0, 0, -1140, 0, 306, 0, 270, 0, 0, 0, -425, 0, -480, 0, 0, 0, 342, 0, -69, 0, 669, 0, 0, 0, -405, 0, -123, 0, 0, 0, -486, 0, 429, 0, 1371, 0, 0, 0, 357, 0, 448, 0, 0, 0, 1536, 0, -117, 0, 189, 0, 0, 0, 721, 0, -216, 0, 0, 0, 236, 0, -846, 0, -162, 0, 0, 0, 93, 0, 633, 0, 0, 0, -1530, 0, -477, 0, 234, 0, 0, 0, -447, 0, 527, 0, 0, 0, 396, 0, -291, 0, 627, 0, 0, 0, -855, 0, -144, 0, 0, 0, -378, 0, -450, 0, 525, 0, 0, 0, -357, 0, 807, 0, 0, 0, 588, 0, 312, 0, -1269, 0, 0, 0, 600, 0, -503, 0, 0, 0, 1860, 0, 915, 0, -405, 0, 0, 0, -409, 0, 405, 0, 0, 0, -388, 0, -1038, 0, 150, 0, 0, 0, -756, 0, 33, 0, 0, 0, 60, 0, 1323, 0, -2115, 0, 0, 0, 33, 0, -171, 0, 0, 0, 1740, 0, -1755, 0, 1224, 0, 0, 0, 54, 0, -576, 0, 0, 0, -28, 0, 990, 0, 477, 0, 0, 0, 243, 0, -273, 0, 0, 0, -582, 0, 1368, 0, 267, 0, 0, 0, 408, 0, -1632, 0, 0, 0, 1812, 0, -837, 0, -225, 0, 0, 0, -703, 0, -438, 0, 0, 0, -720, 0, 666, 0, -1029, 0, 0, 0, 381, 0, 132, 0, 0, 0, -702, 0, 510, 0, 1677, 0, 0, 0, 735, 0, -577, 0, 0, 0, -324, 0, -531, 0, 144, 0, 0, 0, 775, 0, 168, 0, 0, 0, -1900, 0, -405, 0, -339, 0, 0, 0, -306, 0, 1128, 0, 0, 0, 666, 0, 309, 0, 462, 0, 0, 0, -864, 0, 1890, 0, 0, 0, 342, 0, 579, 0, -459, 0, 0, 0, 1128, 0, -171, 0, 0, 0, -2550, 0, 594, 0, 675, 0, 0, 0, 789, 0, 465, 0, 0, 0, 246, 0, -69, 0, -270, 0, 0, 0, 753, 0, -25, 0, 0, 0, 492, 0, 2565, 0, -1077, 0, 0, 0, -480, 0, -315, 0, 0, 0, -1610, 0, -666, 0, 69, 0, 0, 0, 3, 0, -279, 0, 0, 0, 324, 0, -339, 0, -2469, 0, 0, 0, 855, 0, 243, 0, 0, 0, -2190, 0, -1176, 0, 288, 0, 0, 0, 241, 0, -408, 0, 0, 0, 2572, 0, 423, 0, -2229, 0, 0, 0, 135, 0, 675, 0, 0, 0, 432, 0, 126, 0, -2907, 0, 0, 0, -216, 0, -737, 0, 0, 0, -2532, 0, 360, 0, -423, 0, 0, 0, -473, 0, 168, 0, 0, 0, 1364, 0, -738, 0, -579, 0, 0, 0, 843, 0, 765, 0, 0, 0, -774, 0, 213, 0, -864, 0, 0, 0, -201, 0, -360, 0, 0, 0, 132, 0, 171, 0, -270, 0, 0, 0, -814, 0, 234, 0, 0, 0, -388, 0, -1377, 0, 2571, 0, 0, 0, -528, 0, 1521, 0, 0, 0, 1236, 0, 1947, 0, 450, 0, 0, 0, 90, 0, 823, 0, 0, 0, 714, 0, -219, 0, -1395, 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], [1, 1], [0, 0], [-2, 1], [0, 0], [0, 0], [0, 0], [0, -6], [0, 0], [15, -15], [0, 0], [-8, 16], [0, 0], [-3, 0], [0, 0], [-17, -17], [0, 0], [18, -9], [0, 0], [0, 0], [0, 0], [0, -9], [0, 0], [-22, 22], [0, 0], [15, -30], [0, 0], [-6, 0], [0, 0], [-7, -7], [0, 0], [30, -15], [0, 0], [0, 0], [0, 0], [0, -31], [0, 0], [-24, 24], [0, 0], [32, -64], [0, 0], [-10, 0], [0, 0], [6, 6], [0, 0], [50, -25], [0, 0], [0, 0], [0, 0], [0, -51], [0, 0], [57, -57], [0, 0], [-15, 30], [0, 0], [27, 0], [0, 0], [-47, -47], [0, 0], [94, -47], [0, 0], [0, 0], [0, 0], [0, -24], [0, 0], [-49, 49], [0, 0], [9, -18], [0, 0], [126, 0], [0, 0], [15, 15], [0, 0], [-44, 22], [0, 0], [0, 0], [0, 0], [0, -73], [0, 0], [-9, 9], [0, 0], [-8, 16], [0, 0], [51, 0], [0, 0], [-6, -6], [0, 0], [-66, 33], [0, 0], [0, 0], [0, 0], [0, -21], [0, 0], [-27, 27], [0, 0], [-16, 32], [0, 0], [-90, 0], [0, 0]]}