# Stored data for newform 55.3.d.c, downloaded from the LMFDB on 03 September 2025. {"Nk2": 495, "analytic_conductor": 1.498641453981633, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 55, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": -1, "char_values": [55, 2, [12, 46], [1, 1]], "cm_discs": [-55], "conrey_index": 54, "dim": 2, "field_disc": 44, "field_disc_factorization": [[2, 2], [11, 1]], "field_poly": [-11, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [-11, 0, 1]], [3, [0, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007405463502903, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 55, 4, -1, 2, -55], [1, 1, 5, 2, 1, 2, 0], [1, 1, 11, 2, -1, 2, 0]], "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": true, "label": "55.3.d.c", "level": 55, "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": true, "level_primes": [5, 11], "level_radical": 55, "minimal_twist": "55.3.d.c", "nf_label": "2.2.44.1", "prim_orbit_index": 4, "qexp_display": "q+\\beta q^{2}+7q^{4}-5q^{5}-4\\beta q^{7}+3\\beta q^{8}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "2.2.1.d2", "self_twist_discs": [-55], "self_twist_type": 1, "space_label": "55.3.d", "trace_display": [0, 0, -10, 0], "trace_hash": 1027769500859356827, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.909", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.570", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "296.830", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.757", "prec": 17}, "traces": [0, 2, 0, 0, 14, -10, 0, 0, 0, 18, 0, 22, 0, 0, -88, 0, 10, 0, 0, 0, -70, 0, 0, 0, 0, 50, 88, 0, 0, 0, 0, -36, 0, 0, -88, 0, 126, 0, 0, 0, 0, 0, 0, 0, 154, -90, 0, 0, 0, 254, 0, 0, 0, 0, 0, -110, -264, 0, 0, -204, 0, 0, 0, 0, -194, 0, 0, 0, 0, 0, 440, -156, 0, 0, 0, 0, 0, 0, 0, 0, -50, 162, 0, 0, 0, 0, 88, 0, 0, -4, 0, -352, 0, 0, 0, 0, 0, 0, 0, 198, 350, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352, 0, 242, 0, 0, -252, -250, -792, 0, 0, 0, -440, 0, 0, 0, 0, 0, -264, 0, 0, 0, 0, 0, 0, 0, 90, 0, 968, 0, 0, 0, 0, 0, 0, 0, -968, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 14, 440, 0, 0, 0, 0, 0, 110, 0, 0, 76, -630, 684, 0, 0, 0, 0, 0, 0, 0, 0, 0, -676, 0, 0, 0, 0, 1778, 0, 0, 356, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -968, 0, 0, 0, 0, 0, -770, -352, 0, 0, 616, 450, 0, 0, 0, -844, 0, 0, 0, 0, 792, 0, -1428, 0, 0, 0, 0, 0, 0, 0, 0, -1270, 0, 0, 0, 0, 0, 564, 0, 0, 1672, 0, -742, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -684, 0, 0, 0, 0, 0, 550, 0, 0, 0, -324, 1320, 0, 0, 0, -1092, 0, 968, 0, 0, -226, 0, 0, 0, 0, 0, 1020, 0, 0, 0, 0, 0, -352, 0, 0, 0, 0, -792, 0, 0, 0, 0, 804, 0, 0, 0, 0, 0, 0, 0, 0, 970, 0, 0, 0, 1134, 0, 0, 0, 0, 0, 0, -1236, 0, 0, 1672, 0, 0, 0, 0, 0, 0, -396, 0, 0, 264, 0, -1672, 0, 0, 0, -2200, 0, 0, 0, 0, 780, -28, 0, 0, 0, 0, 722, 0, 0, -2464, 0, 0, 0, 0, 0, 0, 0, 0, 0, -968, 0, 0, 0, 0, 1076, 0, 0, 0, 0, 0, 0, -2552, 0, 0, -204, 0, 0, 0, 0, 2552, 0, 1386, 0, 0, 0, 250, 1564, 0, 0, 0, -810, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -616, 0, 0, -884, 0, -276, 0, 0, 0, 0, 0, 0, 0, 0, -440, 0, 0, 0, 1584, 0, 0, 0, 0, 0, 0, 2286, 0, 0, 0, 20, 0, 0, 0, -1444, 0, 0, 0, 0, -2728, 1760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2464, 0, 0, 0, 0, 0, 0, 0, 1694, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -990, -180, 0, 0, -1964, -1750, 0, 0, 0, -2376, 0, 0, 0, 0, 276, 0, -3872, 0, 0, 0, 0, 0, 0, 0, 0, -1320, 1084, 0, 0, 0, 0, 968, 0, 0, 1058, 0, -1836, 0, 0, 0, 0, 0, 0, 0, 2794, 0, 0, 0, 0, 616, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2728, 0, 0, 0, 0, 352, 0, 0, 0, 0, 0, 0, 3608, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1746, 0, 0, 0, 0, -352, 0, 0, 2904, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, -1760, 0, 0, 0, -1604, 0, 0, 0, 0, 0, -1210, 0, 0, 0, 0, 0, 0, 0, 0, 2552, 0, -2904, 0, 0, 1836, 1260, 0, 0, 0, 0, 1250, 0, 0, 0, 0, 3960, 2084, 0, 0, 0, 0, 0, 0, 0, -1404, 0, 604, 0, 0, 0, 0, 0, 0, 0, -2244, 2200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 884, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3608, 0, 98, 0, 0, 0, 1320, 0, 0, 0, 0, 0, -6864, 0, 0, 0, 0, -1196, 0, 0, -2728, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2134, 0, 0, 0, 0, 2796, 0, 0, 0, 0, 0, 0, 532, 0, 0, 1436, -450, 0, 0, 0, 4788, 0, 0, 0, 0, 1458, -4840, -352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1672, 0, 0, 3872, 0, -956, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4732, 0, 0, 0, 0, 0, 4840, 0, 0, 0, 792, -900, 0, 0, 0, 0, 0, -1716, 0, 0, 1270, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2492, 0, 0, 0, 0, -36, 0, 0, 0, 0, -1584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3168, 0, 0, 0, 0, 0, 0, 8976, 0, 0, 2316, -440, 0, 0, 0, 0, 0, 0, 0, 0, 2916, 0, 1682, 0, 0, 0, -70, 0, 0, 0, 0, -2200, 0, 0, 0, 0, 0, -2904, 0, 0, 876, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -550, -3516, 0, 0, -2464, 0, 0, 0, 0, -6688, 0, 1782, 0, 0, 0, -380, 6072, 0, 0, 0, 3150, 0, 0, 0, 0, -3420, 0, 0, 0, 0, 0, 3484, 0, 0, -5368, 0, -5908, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3324, 0, 0, 0, 0, 0, 0, 2376, 0, 0, 0, 0, 0, 0, 0, -1020, 0, 968, 0, 0, 3872, 0, 0, 0, 0, 0, 3380, 0, 0, 0, 0, 0, -1274, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3244, 0, 0, 0, 0, 0, 0, 0, -44, -8890, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3876, 0, 0, 6864, -1780, 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, 1], [0, 0], [7, 0], [-5, 0], [0, 0], [0, -4], [0, 3], [9, 0], [0, -5], [11, 0], [0, 0], [0, 4], [-44, 0], [0, 0], [5, 0], [0, -4], [0, 9], [0, 0], [-35, 0], [0, 0], [0, 11], [0, 0], [0, 0], [25, 0], [44, 0], [0, 0], [0, -28], [0, 0], [0, 0], [-18, 0], [0, -7], [0, 0], [-44, 0], [0, 20], [63, 0], [0, 0], [0, 0], [0, 0], [0, -15], [0, 0], [0, 0], [0, 4], [77, 0], [-45, 0], [0, 0], [0, 0], [0, 0], [127, 0], [0, 25], [0, 0], [0, 28], [0, 0], [0, 0], [-55, 0], [-132, 0], [0, 0], [0, 0], [-102, 0], [0, 0], [0, 0], [0, -18], [0, -36], [-97, 0], [0, -20], [0, 0], [0, 0], [0, -28], [0, 0], [220, 0], [-78, 0], [0, 27], [0, 44], [0, 0], [0, 0], [0, 0], [0, -44], [0, 0], [0, 0], [-25, 0], [81, 0], [0, 0], [0, 4], [0, 0], [0, 20], [44, 0], [0, 0], [0, 33], [-2, 0], [0, -45], [-176, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 127], [99, 0], [175, 0]]}