# Stored data for newform 176.4.a.c, downloaded from the LMFDB on 16 October 2026.
{"Nk2": 2816, "analytic_conductor": 10.384336161010348, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [11, 1]], "atkin_lehner_string": "-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [176, 1, [111, 133, 145], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[3, [1, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007199321850032, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "176.4.a.c", "level": 176, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 11], "level_radical": 22, "minimal_twist": "22.4.a.c", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-q^{3}-3q^{5}+10q^{7}-26q^{9}-11q^{11}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "176.4.a", "trace_display": [0, -1, -3, 10], "trace_hash": 266361276562939321, "trace_moments": [0, {"__RealLiteral__": 0, "data": "0.952", "prec": 10}, 0, {"__RealLiteral__": 0, "data": "1.878", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "4.643", "prec": 14}], "trace_zratio": 0, "traces": [0, 1, 0, -1, 0, -3, 0, 10, 0, -26, 0, -11, 0, -16, 0, 3, 0, 42, 0, -116, 0, -10, 0, -189, 0, -116, 0, 53, 0, -120, 0, 163, 0, 11, 0, -30, 0, -409, 0, 16, 0, 468, 0, -110, 0, 78, 0, -144, 0, -243, 0, -42, 0, 90, 0, 33, 0, 116, 0, 453, 0, 20, 0, -260, 0, 48, 0, 97, 0, 189, 0, 465, 0, 848, 0, 116, 0, -110, 0, 742, 0, 649, 0, -438, 0, -126, 0, 120, 0, -273, 0, -160, 0, -163, 0, 348, 0, 761, 0, 286, 0, -1578, 0, -1208, 0, 30, 0, 1446, 0, -1342, 0, 409, 0, 1761, 0, 567, 0, 416, 0, 420, 0, 121, 0, -468, 0, 723, 0, -2132, 0, 110, 0, -1782, 0, -1160, 0, -159, 0, 921, 0, -1442, 0, 144, 0, 176, 0, 360, 0, 243, 0, -1806, 0, 1402, 0, -1092, 0, -489, 0, -2947, 0, -90, 0, -1890, 0, -332, 0, -33, 0, -1920, 0, -1941, 0, 3016, 0, 1986, 0, -1160, 0, -453, 0, -111, 0, 899, 0, -20, 0, 1227, 0, -462, 0, 530, 0, 1509, 0, 20, 0, -48, 0, 1254, 0, -4688, 0, -97, 0, -1200, 0, -1404, 0, 4914, 0, 1276, 0, -4868, 0, -465, 0, 330, 0, 1630, 0, -848, 0, -672, 0, 4663, 0, 3016, 0, 5862, 0, 5051, 0, 110, 0, -720, 0, 432, 0, -742, 0, 522, 0, -5632, 0, -2080, 0, 729, 0, 1856, 0, 438, 0, 6345, 0, 2079, 0, 126, 0, 1494, 0, -4090, 0, 3120, 0, -1254, 0, -270, 0, 273, 0, 5442, 0, -2432, 0, 160, 0, 1276, 0, -1666, 0, -4238, 0, -3258, 0, 7804, 0, -348, 0, 4680, 0, -3149, 0, -761, 0, 12, 0, -1359, 0, -583, 0, 3024, 0, -1100, 0, 1578, 0, -60, 0, -5852, 0, 1208, 0, -2652, 0, -7153, 0, 780, 0, 6129, 0, 1320, 0, -1446, 0, -4872, 0, 1856, 0, 1342, 0, -1440, 0, 823, 0, 10634, 0, -291, 0, 5270, 0, -1761, 0, -1793, 0, -5860, 0, -567, 0, -6576, 0, -6286, 0, -848, 0, -10701, 0, -1395, 0, -420, 0, -8328, 0, 6597, 0, -121, 0, -2544, 0, 3643, 0, -12168, 0, 900, 0, -7942, 0, -723, 0, 1920, 0, 9331, 0, 2132, 0, 7731, 0, 330, 0, 2860, 0, 1461, 0, -7938, 0, 1782, 0, -2226, 0, -6466, 0, 1160, 0, 2010, 0, -2608, 0, -1947, 0, 4499, 0, -12622, 0, -921, 0, 4530, 0, 1314, 0, 1442, 0, -10980, 0, -538, 0, 3744, 0, -4872, 0, 200, 0, -176, 0, -5022, 0, -2587, 0, -360, 0, 21924, 0, -704, 0, 6318, 0, -4203, 0, 819, 0, 1806, 0, -933, 0, -5148, 0, -1402, 0, 480, 0, 10316, 0, 2226, 0, 132, 0, -7823, 0, 489, 0, -723, 0, 970, 0, 2947, 0, 1210, 0, 13456, 0, -2340, 0, 7416, 0, 6544, 0, 1890, 0, -2283, 0, 7171, 0, 332, 0, 12264, 0, -5040, 0, -858, 0, 4650, 0, 11860, 0, 1920, 0, -15450, 0, 4734, 0, 1941, 0, -17181, 0, 8480, 0, -6148, 0, 3624, 0, 1584, 0, -1986, 0, -2763, 0, 772, 0, 1160, 0, 6846, 0, 23554, 0, -11778, 0, -7488, 0, -4338, 0, 111, 0, 2673, 0, 19388, 0, -899, 0, 4026, 0, -1568, 0, -520, 0, 13920, 0, 7420, 0, -1227, 0, -4806, 0, 1760, 0, 462, 0, -9972, 0, -5283, 0, 6490, 0, -456, 0, -11132, 0, -1509, 0, 21924, 0, 11657, 0, -20, 0, -4380, 0, -990, 0, -1248, 0, 15204, 0, -18908, 0, -1254, 0, -4884, 0, -1260, 0, 4688, 0, -22008, 0, 19526, 0, -2522, 0, -363, 0, -4934, 0, 1200, 0, 2304, 0, -20608, 0, 1404, 0, -7038, 0, -14609, 0, -10017, 0, -2730, 0, 12331, 0, -1276, 0, -17178, 0, -15365, 0, 4868, 0, 6396, 0, 3888, 0, -12090, 0, -6753, 0, -5123, 0, -330, 0, -18075, 0, -4983, 0, -1630, 0, 15387, 0, 5346, 0, -22048, 0, -24222, 0, -12967, 0, 672, 0, 3480, 0, 22680, 0, -4663, 0, -220, 0, 17870, 0, -6148, 0, 12978, 0, 7610, 0, -5862, 0, 28488, 0, -2763, 0, -5051, 0, -1440, 0, -17855, 0, 2860, 0, 4326, 0, 19656, 0, 720, 0, -31674, 0, 47444, 0, -432, 0, -15780, 0, 371, 0, -19292, 0, -30807, 0, -528, 0, -522, 0, -27069, 0, -12080, 0, 5632, 0, 13920, 0, 20095, 0, -15443, 0, -4620, 0, -12220, 0, -729, 0, -1067, 0, 32818, 0, -1856, 0, -24396, 0, 5418, 0, 11388, 0, 14460, 0, 2485, 0, -6345, 0, -4206, 0, -14254, 0, -2079, 0, 17232, 0, -13420, 0, 3276, 0, -7248, 0, 25520, 0, -1494, 0, 14994, 0, -18908, 0, 4090, 0, -54288, 0, -5115, 0, -6360, 0, 8841, 0, 35224, 0, 1254, 0, 17610, 0, -320, 0, 270, 0, 18609, 0, -6048, 0, 7098, 0, -9328, 0, 5670, 0, -5442, 0, 16476, 0, 2722, 0, 2432, 0, 996, 0, 12760, 0, 4160, 0, -18402, 0, 39763, 0, -1276, 0, 1248, 0, -8659, 0, 1666, 0, -10206, 0, 5760, 0, 8639, 0, 41271, 0, -9989, 0, 3258, 0, 5823, 0, 1210, 0, -7804, 0, 77301, 0, 2198, 0, -9048, 0, 27192, 0, -27095, 0, -4680, 0, 16008, 0, -5958, 0, 3149, 0, -8162, 0, -1552, 0, -19786, 0, 7230, 0, 22424, 0, -12, 0, -11427, 0, -30020, 0, 1359, 0, -11958, 0, -21320, 0, -7139, 0, 16704, 0, 333, 0, -3024, 0, -19560, 0, 3780, 0, 1100, 0, -2697, 0, 13060, 0, 41028, 0, -10188, 0, 4818, 0, 60, 0, -17820, 0, 43738, 0, 5852, 0, -7440, 0, 47444, 0, 31408, 0, -16470, 0, 28188, 0, 2652, 0, 1386, 0, 23876, 0, 7153, 0, 22218, 0, -88452, 0, -1590, 0, 9909, 0, -13568, 0, -6129, 0, -45858, 0, -4527, 0, -1320, 0, 9210, 0, -3222, 0, -37596, 0, -60, 0, 33352, 0, 4872, 0, -37665, 0, -14420, 0, -1856, 0, -35715, 0, 3003, 0, 34892, 0, -5949, 0, -3762, 0, 1440, 0, 20790, 0, 23560, 0, -823, 0, 14064, 0, 26786, 0, -21677, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, -1, 0, -3, 0, 10, 0, -26, 0, -11, 0, -16, 0, 3, 0, 42, 0, -116, 0, -10, 0, -189, 0, -116, 0, 53, 0, -120, 0, 163, 0, 11, 0, -30, 0, -409, 0, 16, 0, 468, 0, -110, 0, 78, 0, -144, 0, -243, 0, -42, 0, 90, 0, 33, 0, 116, 0, 453, 0, 20, 0, -260, 0, 48, 0, 97, 0, 189, 0, 465, 0, 848, 0, 116, 0, -110, 0, 742, 0, 649, 0, -438, 0, -126, 0, 120, 0, -273, 0, -160, 0, -163, 0, 348, 0, 761, 0, 286, 0, -1578, 0, -1208, 0, 30, 0, 1446, 0, -1342, 0, 409, 0, 1761, 0, 567, 0, 416, 0, 420, 0, 121, 0, -468, 0, 723, 0, -2132, 0, 110, 0, -1782, 0, -1160, 0, -159, 0, 921, 0, -1442, 0, 144, 0, 176, 0, 360, 0, 243, 0, -1806, 0, 1402, 0, -1092, 0, -489, 0, -2947, 0, -90, 0, -1890, 0, -332, 0, -33, 0, -1920, 0, -1941, 0, 3016, 0, 1986, 0, -1160, 0, -453, 0, -111, 0, 899, 0, -20, 0, 1227, 0, -462, 0, 530, 0, 1509, 0, 20, 0, -48, 0, 1254, 0, -4688, 0, -97, 0, -1200, 0, -1404, 0, 4914, 0, 1276, 0, -4868, 0, -465, 0, 330, 0, 1630, 0, -848, 0, -672, 0, 4663, 0, 3016, 0, 5862, 0, 5051, 0, 110, 0, -720, 0, 432, 0, -742, 0, 522, 0, -5632, 0, -2080, 0, 729, 0, 1856, 0, 438, 0, 6345, 0, 2079, 0, 126, 0, 1494, 0, -4090, 0, 3120, 0, -1254, 0, -270, 0, 273, 0, 5442, 0, -2432, 0, 160, 0, 1276, 0, -1666, 0, -4238, 0, -3258, 0, 7804, 0, -348, 0, 4680, 0, -3149, 0, -761, 0, 12, 0, -1359, 0, -583, 0, 3024, 0, -1100, 0, 1578, 0, -60, 0, -5852, 0, 1208, 0, -2652, 0, -7153, 0, 780, 0, 6129, 0, 1320, 0, -1446, 0, -4872, 0, 1856, 0, 1342, 0, -1440, 0, 823, 0, 10634, 0, -291, 0, 5270, 0, -1761, 0, -1793, 0, -5860, 0, -567, 0, -6576, 0, -6286, 0, -848, 0, -10701, 0, -1395, 0, -420, 0, -8328, 0, 6597, 0, -121, 0, -2544, 0, 3643, 0, -12168, 0, 900, 0, -7942, 0, -723, 0, 1920, 0, 9331, 0, 2132, 0, 7731, 0, 330, 0, 2860, 0, 1461, 0, -7938, 0, 1782, 0, -2226, 0, -6466, 0, 1160, 0, 2010, 0, -2608, 0, -1947, 0, 4499, 0, -12622, 0, -921, 0, 4530, 0, 1314, 0, 1442, 0, -10980, 0, -538, 0, 3744, 0, -4872, 0, 200, 0, -176, 0, -5022, 0, -2587, 0, -360, 0, 21924, 0, -704, 0, 6318, 0, -4203, 0, 819, 0, 1806, 0, -933, 0, -5148, 0, -1402, 0, 480, 0, 10316, 0, 2226, 0, 132, 0, -7823, 0, 489, 0, -723, 0, 970, 0, 2947, 0, 1210, 0, 13456, 0, -2340, 0, 7416, 0, 6544, 0, 1890, 0, -2283, 0, 7171, 0, 332, 0, 12264, 0, -5040, 0, -858, 0, 4650, 0, 11860, 0, 1920, 0, -15450, 0, 4734, 0, 1941, 0, -17181, 0, 8480, 0, -6148, 0, 3624, 0, 1584, 0, -1986, 0, -2763, 0, 772, 0, 1160, 0, 6846, 0, 23554, 0, -11778, 0, -7488, 0, -4338, 0, 111, 0, 2673, 0, 19388, 0, -899, 0, 4026, 0, -1568, 0, -520, 0, 13920, 0, 7420, 0, -1227, 0, -4806, 0, 1760, 0, 462, 0, -9972, 0, -5283, 0, 6490, 0, -456, 0, -11132, 0, -1509, 0, 21924, 0, 11657, 0, -20, 0, -4380, 0, -990, 0, -1248, 0, 15204, 0, -18908, 0, -1254, 0, -4884, 0, -1260, 0, 4688, 0, -22008, 0, 19526, 0, -2522, 0, -363, 0, -4934, 0, 1200, 0, 2304, 0, -20608, 0, 1404, 0, -7038, 0, -14609, 0, -10017, 0, -2730, 0, 12331, 0, -1276, 0, -17178, 0, -15365, 0, 4868, 0, 6396, 0, 3888, 0, -12090, 0, -6753, 0, -5123, 0, -330, 0, -18075, 0, -4983, 0, -1630, 0, 15387, 0, 5346, 0, -22048, 0, -24222, 0, -12967, 0, 672, 0, 3480, 0, 22680, 0, -4663, 0, -220, 0, 17870, 0, -6148, 0, 12978, 0, 7610, 0, -5862, 0, 28488, 0, -2763, 0, -5051, 0, -1440, 0, -17855, 0, 2860, 0, 4326, 0, 19656, 0, 720, 0, -31674, 0, 47444, 0, -432, 0, -15780, 0, 371, 0, -19292, 0, -30807, 0, -528, 0, -522, 0, -27069, 0, -12080, 0, 5632, 0, 13920, 0, 20095, 0, -15443, 0, -4620, 0, -12220, 0, -729, 0, -1067, 0, 32818, 0, -1856, 0, -24396, 0, 5418, 0, 11388, 0, 14460, 0, 2485, 0, -6345, 0, -4206, 0, -14254, 0, -2079, 0, 17232, 0, -13420, 0, 3276, 0, -7248, 0, 25520, 0, -1494, 0, 14994, 0, -18908, 0, 4090, 0, -54288, 0, -5115, 0, -6360, 0, 8841, 0, 35224, 0, 1254, 0, 17610, 0, -320, 0, 270, 0, 18609, 0, -6048, 0, 7098, 0, -9328, 0, 5670, 0, -5442, 0, 16476, 0, 2722, 0, 2432, 0, 996, 0, 12760, 0, 4160, 0, -18402, 0, 39763, 0, -1276, 0, 1248, 0, -8659, 0, 1666, 0, -10206, 0, 5760, 0, 8639, 0, 41271, 0, -9989, 0, 3258, 0, 5823, 0, 1210, 0, -7804, 0, 77301, 0, 2198, 0, -9048, 0, 27192, 0, -27095, 0, -4680, 0, 16008, 0, -5958, 0, 3149, 0, -8162, 0, -1552, 0, -19786, 0, 7230, 0, 22424, 0, -12, 0, -11427, 0, -30020, 0, 1359, 0, -11958, 0, -21320, 0, -7139, 0, 16704, 0, 333, 0, -3024, 0, -19560, 0, 3780, 0, 1100, 0, -2697, 0, 13060, 0, 41028, 0, -10188, 0, 4818, 0, 60, 0, -17820, 0, 43738, 0, 5852, 0, -7440, 0, 47444, 0, 31408, 0, -16470, 0, 28188, 0, 2652, 0, 1386, 0, 23876, 0, 7153, 0, 22218, 0, -88452, 0, -1590, 0, 9909, 0, -13568, 0, -6129, 0, -45858, 0, -4527, 0, -1320, 0, 9210, 0, -3222, 0, -37596, 0, -60, 0, 33352, 0, 4872, 0, -37665, 0, -14420, 0, -1856, 0, -35715, 0, 3003, 0, 34892, 0, -5949, 0, -3762, 0, 1440, 0, 20790, 0, 23560, 0, -823, 0, 14064, 0, 26786, 0, -21677, 0]}