# Stored data for newform 112.5.c.a, downloaded from the LMFDB on 14 July 2026. {"Nk2": 2800, "analytic_conductor": 11.577435865390564, "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": [112, 2, [15, 85, 17], [2, 2, 1]], "cm_discs": [-7], "conrey_index": 97, "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, "has_non_self_twist": 0, "hecke_cutters": [[3, [0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 137522839664, "hecke_ring_generator_nbound": 1, "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, 2, -1, 2, -7]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": false, "label": "112.5.c.a", "level": 112, "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, 7], "level_radical": 14, "minimal_twist": "7.5.b.a", "nf_label": "1.1.1.1", "prim_orbit_index": 2, "qexp_display": "q-7^{2}q^{7}+3^{4}q^{9}+206q^{11}+734q^{23}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "4.2.1.d2", "self_twist_discs": [-7], "self_twist_type": 1, "space_label": "112.5.c", "trace_display": [0, 0, 0, -49], "trace_hash": 416619433149578963, "trace_moments": [{"__RealLiteral__": 0, "data": "0.010", "prec": 17}, {"__RealLiteral__": 0, "data": "0.971", "prec": 17}, {"__RealLiteral__": 0, "data": "0.024", "prec": 17}, {"__RealLiteral__": 0, "data": "2.884", "prec": 17}, {"__RealLiteral__": 0, "data": "0.084", "prec": 17}, {"__RealLiteral__": 0, "data": "9.518", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "traces": [0, 1, 0, 0, 0, 0, 0, -49, 0, 81, 0, 206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 734, 0, 625, 0, 0, 0, 1234, 0, 0, 0, 0, 0, 0, 0, -1294, 0, 0, 0, 0, 0, 334, 0, 0, 0, 0, 0, 2401, 0, 0, 0, -5582, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3969, 0, 0, 0, -4946, 0, 0, 0, -2914, 0, 0, 0, 0, 0, -10094, 0, 3646, 0, 6561, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16686, 0, 0, 0, 0, 0, 0, 0, -11698, 0, -12526, 0, 0, 0, 23746, 0, 0, 0, 0, 0, 0, 0, 27795, 0, 0, 0, 0, 0, 32254, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7262, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9806, 0, -29474, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35966, 0, 47662, 0, 0, 0, 0, 0, 28561, 0, 0, 0, 0, 0, -30625, 0, 0, 0, -52882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28162, 0, -70654, 0, 0, 0, 1906, 0, 0, 0, 0, 0, -60466, 0, 0, 0, 59454, 0, 0, 0, 11758, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50625, 0, 0, 0, 0, 0, 0, 0, -108254, 0, 0, 0, 0, 0, 64958, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151204, 0, 0, 0, 0, 0, 63406, 0, 99954, 0, -109666, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128750, 0, 52658, 0, 0, 0, -144926, 0, 0, 0, 0, 0, 0, 0, 83521, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71506, 0, 254204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -182834, 0, -104814, 0, 0, 0, -176062, 0, 0, 0, 0, 0, -117649, 0, 0, 0, -218866, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -169954, 0, 130321, 0, 0, 0, 0, 0, 0, 0, 0, 0, 273518, 0, -209614, 0, 0, 0, 0, 0, -89714, 0, 0, 0, 0, 0, 0, 0, 27054, 0, 140914, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -196286, 0, 0, 0, 0, 0, -266564, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -326926, 0, 0, 0, 0, 0, 0, 0, 0, 0, 345278, 0, 0, 0, 0, 0, 0, 0, 0, 0, 194481, 0, 156302, 0, 0, 0, 0, 0, 396034, 0, 0, 0, 0, 0, 0, 0, 353186, 0, 0, 0, 0, 0, -25538, 0, 0, 0, 0, 0, 242354, 0, 0, 0, 68804, 0, 0, 0, -452142, 0, 0, 0, 0, 0, 0, 0, 0, 0, 315934, 0, 0, 0, -427954, 0, 0, 0, 0, 0, 142786, 0, 409198, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 494606, 0, -579886, 0, 0, 0, 0, 0, -110546, 0, 0, 0, 0, 0, -178654, 0, 0, 0, 383506, 0, 0, 0, 0, 0, 0, 0, 0, 0, -321489, 0, -219806, 0, -615794, 0, 0, 0, 458750, 0, 0, 0, 0, 0, 0, 0, -1149892, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 687326, 0, 0, 0, -400626, 0, 0, 0, 0, 0, 0, 0, 0, 0, -704014, 0, 0, 0, -450014, 0, 0, 0, 0, 0, 0, 0, 390625, 0, 0, 0, 0, 0, -215714, 0, 0, 0, 0, 0, 0, 0, -236034, 0, -126206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572818, 0, 0, 0, 0, 0, 486638, 0, 0, 0, 0, 0, 0, 0, 905756, 0, 0, 0, 0, 0, -706942, 0, 0, 0, 0, 0, 0, 0, 0, 0, -857266, 0, 0, 0, 0, 0, 0, 0, 0, 0, -817614, 0, 0, 0, 0, 0, 0, 0, 971602, 0, 0, 0, 0, 0, 0, 0, 904562, 0, 295326, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 771250, 0, 0, 0, 531441, 0, 0, 0, 0, 0, 0, 0, -1018876, 0, -410834, 0, 0, 0, 1091102, 0, 0, 0, 0, 0, 573202, 0, 484798, 0, 0, 0, 0, 0, 819506, 0, 0, 0, 0, 0, 613774, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -600284, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1163554, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1278686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7118, 0, 967774, 0, 0, 0, 1288334, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 815475, 0, 0, 0, 0, 0, -1361955, 0, 0, 0, -949796, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1272706, 0, 0, 0, 0, 0, 751076, 0, 0, 0, 0, 0, 0, 0, -981742, 0, 0, 0, 0, 0, -1071506, 0, 0, 0, 0, 0, -1580446, 0, 1351566, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1544498, 0, 0, 0, -792514, 0, 0, 0, 0, 0, 0, 0, 1471966, 0, 0, 0, 0, 0, -808750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -438418, 0, 0, 0, 0, 0, 309346, 0, 0, 0, 0, 0, 355838, 0, 923521, 0, -947538, 0, 0, 0, 1758622, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1882814, 0, 0, 0, -1014606, 0, 0, 0, 0, 0, 0, 0, 245156, 0, -12674, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 5, "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], 1, 0, 0, 0, 0, 0, -49, 0, 81, 0, 206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 734, 0, 625, 0, 0, 0, 1234, 0, 0, 0, 0, 0, 0, 0, -1294, 0, 0, 0, 0, 0, 334, 0, 0, 0, 0, 0, 2401, 0, 0, 0, -5582, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3969, 0, 0, 0, -4946, 0, 0, 0, -2914, 0, 0, 0, 0, 0, -10094, 0, 3646, 0, 6561, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16686, 0, 0, 0, 0, 0, 0, 0, -11698, 0, -12526, 0, 0, 0, 23746, 0, 0, 0, 0, 0, 0, 0, 27795, 0, 0, 0, 0, 0, 32254, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7262, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9806, 0, -29474, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35966, 0, 47662, 0, 0, 0, 0, 0, 28561, 0, 0, 0, 0, 0, -30625, 0, 0, 0, -52882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28162, 0, -70654, 0, 0, 0, 1906, 0, 0, 0, 0, 0, -60466, 0, 0, 0, 59454, 0, 0, 0, 11758, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50625, 0, 0, 0, 0, 0, 0, 0, -108254, 0, 0, 0, 0, 0, 64958, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151204, 0, 0, 0, 0, 0, 63406, 0, 99954, 0, -109666, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128750, 0, 52658, 0, 0, 0, -144926, 0, 0, 0, 0, 0, 0, 0, 83521, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71506, 0, 254204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -182834, 0, -104814, 0, 0, 0, -176062, 0, 0, 0, 0, 0, -117649, 0, 0, 0, -218866, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -169954, 0, 130321, 0, 0, 0, 0, 0, 0, 0, 0, 0, 273518, 0, -209614, 0, 0, 0, 0, 0, -89714, 0, 0, 0, 0, 0, 0, 0, 27054, 0, 140914, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -196286, 0, 0, 0, 0, 0, -266564, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -326926, 0, 0, 0, 0, 0, 0, 0, 0, 0, 345278, 0, 0, 0, 0, 0, 0, 0, 0, 0, 194481, 0, 156302, 0, 0, 0, 0, 0, 396034, 0, 0, 0, 0, 0, 0, 0, 353186, 0, 0, 0, 0, 0, -25538, 0, 0, 0, 0, 0, 242354, 0, 0, 0, 68804, 0, 0, 0, -452142, 0, 0, 0, 0, 0, 0, 0, 0, 0, 315934, 0, 0, 0, -427954, 0, 0, 0, 0, 0, 142786, 0, 409198, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 258915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 494606, 0, -579886, 0, 0, 0, 0, 0, -110546, 0, 0, 0, 0, 0, -178654, 0, 0, 0, 383506, 0, 0, 0, 0, 0, 0, 0, 0, 0, -321489, 0, -219806, 0, -615794, 0, 0, 0, 458750, 0, 0, 0, 0, 0, 0, 0, -1149892, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 687326, 0, 0, 0, -400626, 0, 0, 0, 0, 0, 0, 0, 0, 0, -704014, 0, 0, 0, -450014, 0, 0, 0, 0, 0, 0, 0, 390625, 0, 0, 0, 0, 0, -215714, 0, 0, 0, 0, 0, 0, 0, -236034, 0, -126206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572818, 0, 0, 0, 0, 0, 486638, 0, 0, 0, 0, 0, 0, 0, 905756, 0, 0, 0, 0, 0, -706942, 0, 0, 0, 0, 0, 0, 0, 0, 0, -857266, 0, 0, 0, 0, 0, 0, 0, 0, 0, -817614, 0, 0, 0, 0, 0, 0, 0, 971602, 0, 0, 0, 0, 0, 0, 0, 904562, 0, 295326, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 771250, 0, 0, 0, 531441, 0, 0, 0, 0, 0, 0, 0, -1018876, 0, -410834, 0, 0, 0, 1091102, 0, 0, 0, 0, 0, 573202, 0, 484798, 0, 0, 0, 0, 0, 819506, 0, 0, 0, 0, 0, 613774, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -600284, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1163554, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1278686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7118, 0, 967774, 0, 0, 0, 1288334, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 815475, 0, 0, 0, 0, 0, -1361955, 0, 0, 0, -949796, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1272706, 0, 0, 0, 0, 0, 751076, 0, 0, 0, 0, 0, 0, 0, -981742, 0, 0, 0, 0, 0, -1071506, 0, 0, 0, 0, 0, -1580446, 0, 1351566, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1544498, 0, 0, 0, -792514, 0, 0, 0, 0, 0, 0, 0, 1471966, 0, 0, 0, 0, 0, -808750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -438418, 0, 0, 0, 0, 0, 309346, 0, 0, 0, 0, 0, 355838, 0, 923521, 0, -947538, 0, 0, 0, 1758622, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1882814, 0, 0, 0, -1014606, 0, 0, 0, 0, 0, 0, 0, 245156, 0, -12674, 0, 0, 0, 0, 0, 0, 0, 0, 0]}