# Stored data for newform 95.5.d.c, downloaded from the LMFDB on 04 December 2023. {"label": "95.5.d.c", "space_label": "95.5.d", "level": 95, "weight": 5, "hecke_orbit": 3, "hecke_orbit_code": 9007405497057375, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 1183301789607447072, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-45, 0, 1]]], "qexp_display": "q-3\\beta q^{2}-2\\beta q^{3}+29q^{4}+5^{2}q^{5}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 95, "char_orbit_label": "d", "char_is_real": true, "Nk2": 2375, "analytic_conductor": 9.820146492965211, "hecke_ring_index": 2, "level_radical": 95, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.760", "prec": 17}, "analytic_rank_proved": true, "char_values": [95, 2, [77, 21], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [5, 19], "conrey_indexes": [94], "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.932", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.791", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "299.336", "prec": 24}], "related_objects": [], "self_twist_discs": [-95], "cm_discs": [-95], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "4.2.1.d2", "trace_display": [0, 0, 50, 0], "traces": [0, 2, 0, 0, 58, 50, 60, 0, 0, -122, 0, -124, 0, 0, 0, 0, 242, 0, 0, 722, 1450, 0, 0, 0, 780, 1250, -900, 0, 0, 0, 1500, 0, 0, 0, 0, 0, -3538, 0, 0, -600, 0, 0, 0, 0, -3596, -3050, 0, 0, 0, 4802, 0, 0, 0, 0, -8520, -3100, 0, 0, 0, 0, 0, 14276, 0, 0, -11702, 0, -3720, 0, 0, 0, 0, 0, 0, 0, -35460, 0, 20938, 0, 0, 0, 6050, 4202, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18050, -5220, 0, 0, 7564, 36250, 40196, 0, 0, -11700, 0, 10620, 0, 0, 0, 0, -23640, 0, 0, 21660, 0, 0, 0, 0, 0, 19500, -21594, 0, 0, 0, 31250, 0, 0, 0, 0, -22500, -40796, 0, 0, -81540, 0, 0, 0, 0, 3716, 0, 0, 0, 0, -14762, 0, 0, 0, 0, 15236, 37500, 0, 0, 0, 0, 0, -17400, 0, 0, 7080, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48122, 0, -44042, 0, 0, 0, 0, -15004, 0, 0, 0, -88450, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36484, 0, 0, -206820, -15000, 139258, 0, 0, 48964, 0, -54360, 0, 0, 0, 0, 196380, 0, 0, -44764, 0, 0, 0, 0, 232380, 0, -110760, 0, 0, 0, -89900, 0, 0, 0, 0, -76250, 320220, 0, 0, 136196, 0, 0, 0, 0, 54900, 0, 0, 0, 0, -209276, 0, 0, 0, 0, 414004, 120050, 0, 0, 0, 0, 0, -185756, 0, 0, 190620, 0, -214078, 0, 0, 0, 0, 0, 0, 0, -48360, 0, 0, 0, 0, 0, -213000, -290524, 0, 0, 0, -77500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55800, 0, 0, 167042, 0, -137880, 0, 0, 144060, 0, -460980, 0, 0, 0, 0, 0, 0, 0, 87362, 356900, 0, 0, 0, 130920, 0, -124444, 0, 0, 0, 0, 0, 0, 0, 0, -292550, 154920, 0, 0, 121858, 0, 0, 0, 0, 0, -93000, 0, 0, 0, -728100, 0, 0, 0, 0, 213480, 0, 0, 0, 0, 0, 0, -398340, 0, 0, 49444, 0, 85200, 0, 0, 0, 0, 0, 0, 0, -506524, 0, 260642, 0, 0, 0, 0, 428280, 0, 0, 0, -886500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 523450, 127080, 0, 0, -267540, 0, 939420, 0, 0, 495844, 0, 0, 0, 0, 0, 0, 219356, 0, 0, 0, 151250, 0, 0, 0, 1165684, 105050, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78300, 0, 0, -282716, 0, 0, 0, 0, 138060, 0, 0, 0, 0, 37200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -292922, 0, 0, -685560, 0, -667620, 0, 0, 0, 0, 0, 0, 0, -1239300, 0, 281580, 0, 0, 0, 0, -134876, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 451250, 0, 0, 0, 698276, -130500, 354600, 0, 0, -626226, 0, 816180, 0, 0, 0, 0, -786716, 0, 0, -324900, 189100, 0, 0, 0, 922436, 906250, -485400, 0, 0, 0, 1004900, 0, 0, 0, 0, 0, 0, 0, 0, -1641060, 0, 0, 0, 0, -265560, -292500, 0, 0, 0, -1183084, 0, 0, 0, 0, 559682, 265500, 0, 0, 0, 0, 0, -1060020, 0, 0, -297724, 0, -945724, 0, 0, 0, 0, 0, 0, 0, -870836, 0, 0, 0, 0, 0, -591000, 107764, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 541500, -958204, 0, 0, 0, 0, 713822, 0, 0, 626280, 0, 0, 0, 0, 0, 0, 2303100, 0, 0, 0, 0, 0, 0, 0, 528240, 0, 441844, 0, 0, 0, 487500, 0, 0, 0, 0, -539850, 1205880, 0, 0, 0, 0, 0, 0, 0, 2498940, 0, 0, 0, 0, -1532284, 0, 0, 0, 0, -72600, 781250, 0, 0, 0, 0, 0, 1008356, 0, 0, -876420, 0, 205320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -562500, 0, 0, 0, 0, -1019900, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2163060, 0, 0, -445080, -2038500, -885112, 0, 0, 2998620, 0, -1395538, 0, 0, 0, 0, -826200, 0, 0, -1277218, 0, 0, 0, 0, -106200, 0, 1909316, 0, 0, 0, 92900, 0, 0, 0, 0, 0, -150844, 0, 0, 725524, 0, 0, 0, 0, -1929116, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1045796, -369050, 0, 0, 0, 0, 0, -647820, 0, 0, 203758, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1746724, 0, -216600, 0, 0, 0, 380900, -2996100, 0, 0, 0, 937500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1805156, 0, 0, 1058036, 0, -3711780, 0, 0, -1429084, 0, -1094040, 0, 0, 0, 0, -2688660, 0, 0, 0, -435000, 0, 0, 0, 581042, 0, -1223880, 0, 0, 0, 0, 0, 0, 0, 0, 177000, 1419956, 0, 0, 0, 0, 0, 0, 0, -1576440, 0, 0, 0, 0, -118076, 0, 0, 0, 0, 2198520, 0, 0, 0, 0, 0, 0, -2666396, 0, 0, 2552940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 111480, 0, -1298156, 0, 0, 0, 0, 1414562, 0, 0, 0, -1203050, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1101050, 3020940, 0, 0, 2842084, 0, 0, 0, 0, 741240, 0, -1165860, 0, 0, 0, 0, 815400, 0, 0, 0, 0, 0, 0, 0, 1535400, -375100, 2520356, 0, 0, 0, 0, 0, 0, 0, 0, 0, -260524, 0, 0, 457080, 0, 0, 0, 0, 0, -2211250, 0, 0, 0, 4162860, 0, 0, 0, 0, -2451956, 0, 0, 0, 0, 0, 0, 3949684, 0, 0, 1627204, 0, 1665960, 0, 0, 0, 0, 0, 0, 0, -1910396, 0, 1733522, 0, 0, 0, 0, 713700, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -584280, 0, 0, -647820, 912100, -6069004, 0, 0, 0, 0, 1847042, 0, 0, 0, 0, 0, 0, 0, 0, -5170500, 0, 0, 0, -6306660, -375000, 1727396, 0, 0, 0, 3481450, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1224100, 0, 0, 0, 3356880, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 95, 4, -1, 2, -95], [1, 1, 5, 2, 1, 2, 0], [1, 1, 19, 2, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "95.5.d.c", "char_is_minimal": true, "conrey_index": 94, "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], [1, 0], [0, -3], [0, -2], [29, 0], [25, 0], [30, 0], [0, 0], [0, -39], [-61, 0], [0, -75], [-62, 0], [0, -58], [0, 30], [0, 0], [0, -50], [121, 0], [0, 0], [0, 183], [361, 0], [725, 0], [0, 0], [0, 186], [0, 0], [390, 0], [625, 0], [-450, 0], [0, 284], [0, 0], [0, 0], [750, 0], [0, 0], [0, 261], [0, 124], [0, 0], [0, 0], [-1769, 0], [0, 1182], [0, -1083], [-300, 0], [0, -975], [0, 0], [0, 0], [0, 0], [-1798, 0], [-1525, 0], [0, 0], [0, 0], [0, -242], [2401, 0], [0, -1875], [0, 0], [0, 870], [0, -354], [-4260, 0], [-1550, 0], [0, 0], [0, -722], [0, 0], [0, 0], [0, -1450], [7138, 0], [0, 0], [0, 0], [-5851, 0], [0, 750], [-1860, 0], [0, 2718], [0, 0], [0, 0], [0, 0], [0, 0], [0, 2379], [0, 0], [-17730, 0], [0, -1250], [10469, 0], [0, 0], [0, 900], [0, 0], [3025, 0], [2101, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 2418], [0, 0], [0, 4575], [0, 0], [0, 0], [0, 0], [0, 0], [9025, 0], [-2610, 0], [0, 6894], [0, -7203], [3782, 0], [18125, 0]]}