# Stored data for newform 882.4.g.bb, downloaded from the LMFDB on 19 April 2024. {"label": "882.4.g.bb", "space_label": "882.4.g", "level": 882, "weight": 4, "hecke_orbit": 28, "hecke_orbit_code": 121597602322973554, "dim": 4, "is_polredabs": true, "nf_label": "4.0.484416.7", "trace_hash": 716228948229278909, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [53824, 0, 232, 0, 1]], [11, [4, 2, 1]], [13, [-928, 0, 1]]], "qexp_display": "q+(-2-2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+\\beta _{1}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "g", "char_is_real": false, "Nk2": 14112, "analytic_conductor": 52.039684625063224, "hecke_ring_index": 4, "level_radical": 42, "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": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [882, 3, [785, 199], [3, 2]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [361, 667], "field_disc": 484416, "field_disc_factorization": [[2, 6], [3, 2], [29, 2]], "field_poly": [3364, 0, 58, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.616", "prec": 17}, {"__RealLiteral__": 0, "data": "0.081", "prec": 17}, {"__RealLiteral__": 0, "data": "77.361", "prec": 20}, {"__RealLiteral__": 0, "data": "15.953", "prec": 20}, {"__RealLiteral__": 0, "data": "2513.258", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [-4, 0, 0, 0], "traces": [0, 4, -4, 0, -8, 0, 0, 0, 32, 0, 0, -4, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 16, -60, 0, -214, 0, 0, 0, 848, 0, 0, -64, 0, 0, 0, 0, -492, 0, 0, 0, 0, 0, -1136, -16, 0, -120, 0, 0, 0, 856, 0, 0, -1096, 0, 0, 0, 0, -848, 0, 0, 0, 0, 0, 256, 928, 0, -1304, 0, 0, 0, 3080, 0, 0, -984, 0, 0, 0, 0, -944, 0, 0, 0, 0, 0, -2784, 1136, 0, -32, 0, 0, 0, 480, 0, 0, -4640, 0, 0, 0, 0, -856, 0, 0, 0, 0, 0, 4384, 3292, 0, -1964, 0, 0, 0, 5152, 0, 0, -1696, 0, 0, 0, 0, 2654, 0, 0, 0, 0, 0, -4288, -256, 0, 1856, 0, 0, 0, 5216, 0, 0, -5872, 0, 0, 0, 0, -3080, 0, 0, 0, 0, 0, 3936, 1928, 0, 3376, 0, 0, 0, 12992, 0, 0, -1888, 0, 0, 0, 0, 6648, 0, 0, 0, 0, 0, -5076, 2784, 0, 2272, 0, 0, 0, 128, 0, 0, -2508, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, 18560, -1812, 0, -364, 0, 0, 0, 13872, 0, 0, -1712, 0, 0, 0, 0, 9744, 0, 0, 0, 0, 0, -10480, -4384, 0, 6584, 0, 0, 0, 7856, 0, 0, -2784, 0, 0, 0, 0, -5152, 0, 0, 0, 0, 0, 6784, 1424, 0, -1856, 0, 0, 0, -10344, 0, 0, 5308, 0, 0, 0, 0, 9280, 0, 0, 0, 0, 0, 240, 4288, 0, -512, 0, 0, 0, -7424, 0, 0, 5156, 0, 0, 0, 0, -5216, 0, 0, 0, 0, 0, 23488, -428, 0, -3020, 0, 0, 0, -16032, 0, 0, -6160, 0, 0, 0, 0, 5650, 0, 0, 0, 0, 0, -40832, -3936, 0, 3856, 0, 0, 0, -13504, 0, 0, 15776, 0, 0, 0, 0, -12992, 0, 0, 0, 0, 0, 7552, -7560, 0, -848, 0, 0, 0, -27840, 0, 0, 13296, 0, 0, 0, 0, -12520, 0, 0, 0, 0, 0, -12664, 5076, 0, 5568, 0, 0, 0, -9088, 0, 0, 7236, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 10032, -260, 0, -32682, 0, 0, 0, -59392, 0, 0, -960, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, -19824, -18560, 0, -3624, 0, 0, 0, 1456, 0, 0, 26280, 0, 0, 0, 0, -13872, 0, 0, 0, 0, 0, 6848, -9648, 0, 12992, 0, 0, 0, 1968, 0, 0, 19488, 0, 0, 0, 0, -5568, 0, 0, 0, 0, 0, -17832, 10480, 0, -8768, 0, 0, 0, -26336, 0, 0, 32428, 0, 0, 0, 0, -7856, 0, 0, 0, 0, 0, 11136, -30012, 0, -21808, 0, 0, 0, 7296, 0, 0, -10304, 0, 0, 0, 0, 1172, 0, 0, 0, 0, 0, -352, -6784, 0, 2848, 0, 0, 0, 7424, 0, 0, 1136, 0, 0, 0, 0, 10344, 0, 0, 0, 0, 0, -21232, -9280, 0, 1648, 0, 0, 0, -61704, 0, 0, 18560, 0, 0, 0, 0, -11688, 0, 0, 0, 0, 0, 62176, -240, 0, 8576, 0, 0, 0, 2048, 0, 0, 17632, 0, 0, 0, 0, 7424, 0, 0, 0, 0, 0, -20624, 19488, 0, 22534, 0, 0, 0, 38976, 0, 0, -10432, 0, 0, 0, 0, 13252, 0, 0, 0, 0, 0, -79856, -23488, 0, -856, 0, 0, 0, 12080, 0, 0, -13560, 0, 0, 0, 0, 16032, 0, 0, 0, 0, 0, 24640, 384, 0, 46056, 0, 0, 0, 12840, 0, 0, 11300, 0, 0, 0, 0, -2192, 0, 0, 0, 0, 0, 129920, 40832, 0, -7872, 0, 0, 0, -15424, 0, 0, -36132, 0, 0, 0, 0, 13504, 0, 0, 0, 0, 0, -63104, 3712, 0, -31876, 0, 0, 0, -46784, 0, 0, -25984, 0, 0, 0, 0, 35102, 0, 0, 0, 0, 0, 47424, -7552, 0, -15120, 0, 0, 0, 3392, 0, 0, -11216, 0, 0, 0, 0, 27840, 0, 0, 0, 0, 0, -53184, 57272, 0, 83520, 0, 0, 0, 127144, 0, 0, -25040, 0, 0, 0, 0, -12720, 0, 0, 0, 0, 0, 99944, 12664, 0, 10152, 0, 0, 0, -22272, 0, 0, -60188, 0, 0, 0, 0, 9088, 0, 0, 0, 0, 0, -28944, -5568, 0, -29232, 0, 0, 0, 30640, 0, 0, -256, 0, 0, 0, 0, -21308, 0, 0, 0, 0, 0, -3712, -10032, 0, -520, 0, 0, 0, 130728, 0, 0, -45368, 0, 0, 0, 0, 59392, 0, 0, 0, 0, 0, 3840, -2608, 0, 16312, 0, 0, 0, -11640, 0, 0, 200, 0, 0, 0, 0, -27168, 0, 0, 0, 0, 0, 76216, 19824, 0, -37120, 0, 0, 0, 14496, 0, 0, -40832, 0, 0, 0, 0, -1456, 0, 0, 0, 0, 0, -105120, 97440, 0, -3080, 0, 0, 0, 209728, 0, 0, -27744, 0, 0, 0, 0, -31552, 0, 0, 0, 0, 0, -11136, -6848, 0, -19296, 0, 0, 0, -51968, 0, 0, -39552, 0, 0, 0, 0, -1968, 0, 0, 0, 0, 0, -77952, -59944, 0, 77632, 0, 0, 0, 137544, 0, 0, -11136, 0, 0, 0, 0, -92800, 0, 0, 0, 0, 0, 82220, 17832, 0, 20960, 0, 0, 0, 35072, 0, 0, -14760, 0, 0, 0, 0, 26336, 0, 0, 0, 0, 0, -129712, -61548, 0, -99760, 0, 0, 0, 3776, 0, 0, -15712, 0, 0, 0, 0, 33516, 0, 0, 0, 0, 0, -21872, -11136, 0, -60024, 0, 0, 0, 87232, 0, 0, -18560, 0, 0, 0, 0, -7296, 0, 0, 0, 0, 0, 41216, 93728, 0, 11752, 0, 0, 0, 71848, 0, 0, 2344, 0, 0, 0, 0, -106848, 0, 0, 0, 0, 0, 105288, 352, 0, -13568, 0, 0, 0, -11392, 0, 0, 2784, 0, 0, 0, 0, -7424, 0, 0, 0, 0, 0, -4544, -20404, 0, -59392, 0, 0, 0, -35424, 0, 0, 20688, 0, 0, 0, 0, -31362, 0, 0, 0, 0, 0, -163040, 21232, 0, -18560, 0, 0, 0, -6592, 0, 0, -46720, 0, 0, 0, 0, 61704, 0, 0, 0, 0, 0, -74240, 17040, 0, 38960, 0, 0, 0, -237568, 0, 0, -23376, 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, 7, 3, 1, 3, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 7, 2, -1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "882.4.a.x", "char_is_minimal": false, "conrey_index": 361, "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], [-2, 0, -2, 0], [0, 0, 0, 0], [0, 0, 4, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, -2], [0, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [-16, 0, -16, 0], [0, 3, 0, 3], [0, 0, 0, 0], [0, 10, 0, 0], [0, 0, 0, 4], [0, 0, 0, 0], [4, 0, 0, 0], [-30, 0, -30, 0], [0, 0, 0, 0], [0, 0, 107, 0], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [212, 0, 0, 0], [0, 0, 0, 0], [0, -14, 0, -14], [0, 0, 32, 0], [0, 0, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [-246, 0, -246, 0], [0, -20, 0, -20], [0, 0, 0, 0], [0, 8, 0, 0], [0, 0, 0, -21], [0, 0, 0, 0], [-284, 0, 0, 0], [-8, 0, -8, 0], [0, 0, 0, 0], [0, 0, 60, 0], [0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [214, 0, 0, 0], [0, 0, 0, 0], [0, 8, 0, 8], [0, 0, 548, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [-424, 0, -424, 0], [0, 44, 0, 44], [0, 0, 0, 0], [0, -34, 0, 0], [0, 0, 0, 28], [0, 0, 0, 0], [64, 0, 0, 0], [464, 0, 464, 0], [0, 0, 0, 0], [0, 0, 652, 0], [0, -12, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [770, 0, 0, 0], [0, 0, 0, 0], [0, 64, 0, 64], [0, 0, 492, 0], [0, 0, 0, 0], [0, 0, 0, 40], [0, 0, 0, 0], [0, 0, 0, 0], [-472, 0, -472, 0], [0, -16, 0, -16], [0, 0, 0, 0], [0, -42, 0, 0], [0, 0, 0, 12], [0, 0, 0, 0], [-696, 0, 0, 0], [568, 0, 568, 0], [0, 0, 0, 0], [0, 0, 16, 0], [0, 47, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [120, 0, 0, 0], [0, 0, 0, 0], [0, -8, 0, -8], [0, 0, 2320, 0], [0, 0, 0, 0], [0, 0, 0, 20], [0, 0, 0, 0], [0, 0, 0, 0], [-428, 0, -428, 0]]}