# Stored data for newform 200.5.l.c, downloaded from the LMFDB on 16 October 2026. {"Nk2": 5000, "analytic_conductor": 20.673992616768864, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 12, "char_orbit_label": "l", "char_order": 4, "char_parity": -1, "char_values": [200, 4, [151, 101, 177], [4, 4, 1]], "cm_discs": [], "conrey_index": 57, "dim": 4, "field_disc": 13456, "field_disc_factorization": [[2, 4], [29, 2]], "field_poly": [49, 0, 15, 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": [[3, [18, -6, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007955252871368, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 800, "hecke_ring_index_factorization": [[2, 5], [5, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 3, -1, 4, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "200.5.l.c", "level": 200, "level_is_powerful": true, "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, 5], "level_radical": 10, "minimal_twist": "40.5.l.b", "nf_label": "4.0.13456.1", "prim_orbit_index": 3, "qexp_display": "q+(3-3\\beta _{1})q^{3}+(-11-11\\beta _{1}+\\beta _{2}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "4.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "200.5.l", "trace_display": [0, 12, 0, -44], "trace_hash": 2225772930903126674, "trace_moments": [{"__RealLiteral__": 0, "data": "0.058", "prec": 7}, {"__RealLiteral__": 0, "data": "3.993", "prec": 14}, {"__RealLiteral__": 0, "data": "0.223", "prec": 10}, {"__RealLiteral__": 0, "data": "59.313", "prec": 17}, 0, {"__RealLiteral__": 0, "data": "1359.096", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.248", "prec": 10}, "traces": [0, 4, 0, 12, 0, 0, 0, -44, 0, 0, 0, -296, 0, -316, 0, 0, 0, 220, 0, 0, 0, -264, 0, -652, 0, 0, 0, 1728, 0, 0, 0, -2760, 0, -888, 0, 0, 0, 2052, 0, 0, 0, -4312, 0, 1724, 0, 0, 0, 5252, 0, 0, 0, 1320, 0, -6924, 0, 0, 0, 2256, 0, 0, 0, -12120, 0, 2772, 0, 0, 0, 6012, 0, 0, 0, 2232, 0, -17812, 0, 0, 0, -19944, 0, 0, 0, -10044, 0, 16332, 0, 0, 0, 10032, 0, 0, 0, 30152, 0, -8280, 0, 0, 0, -11812, 0, 0, 0, 20104, 0, 48724, 0, 0, 0, -8180, 0, 0, 0, 12312, 0, -1284, 0, 0, 0, -19908, 0, 0, 0, 9740, 0, -12936, 0, 0, 0, -32188, 0, 0, 0, 25432, 0, 31472, 0, 0, 0, -10196, 0, 0, 0, 31512, 0, 184, 0, 0, 0, 43692, 0, 0, 0, 24568, 0, -13860, 0, 0, 0, -1932, 0, 0, 0, -55256, 0, -18868, 0, 0, 0, -83916, 0, 0, 0, -47376, 0, -18812, 0, 0, 0, 6768, 0, 0, 0, 44808, 0, -36360, 0, 0, 0, 76520, 0, 0, 0, -235400, 0, 59964, 0, 0, 0, 108004, 0, 0, 0, 36072, 0, -79216, 0, 0, 0, -41076, 0, 0, 0, 147736, 0, 6696, 0, 0, 0, 146360, 0, 0, 0, -127560, 0, -7484, 0, 0, 0, 133724, 0, 0, 0, -119664, 0, -3764, 0, 0, 0, -40704, 0, 0, 0, 21672, 0, -170100, 0, 0, 0, -82608, 0, 0, 0, -6120, 0, 117848, 0, 0, 0, 33180, 0, 0, 0, -210672, 0, 24820, 0, 0, 0, 20256, 0, 0, 0, 4216, 0, 90456, 0, 0, 0, 100484, 0, 0, 0, 204712, 0, -172996, 0, 0, 0, -370168, 0, 0, 0, -70872, 0, 4948, 0, 0, 0, -127872, 0, 0, 0, 472472, 0, 60312, 0, 0, 0, 91164, 0, 0, 0, -243144, 0, 157068, 0, 0, 0, 54356, 0, 0, 0, -49080, 0, -134160, 0, 0, 0, -101616, 0, 0, 0, 627992, 0, -129276, 0, 0, 0, -210148, 0, 0, 0, -27760, 0, 564960, 0, 0, 0, 68876, 0, 0, 0, -273024, 0, -111300, 0, 0, 0, -292920, 0, 0, 0, 333508, 0, 29220, 0, 0, 0, 67620, 0, 0, 0, 500328, 0, 274260, 0, 0, 0, -148176, 0, 0, 0, -193128, 0, 203396, 0, 0, 0, 108612, 0, 0, 0, 206680, 0, 76296, 0, 0, 0, 219412, 0, 0, 0, -269496, 0, 334040, 0, 0, 0, -546248, 0, 0, 0, -61176, 0, -833584, 0, 0, 0, -64656, 0, 0, 0, -12568, 0, -330876, 0, 0, 0, 922120, 0, 0, 0, -672776, 0, -490500, 0, 0, 0, -52976, 0, 0, 0, -917532, 0, 64124, 0, 0, 0, 45168, 0, 0, 0, 1154288, 0, 73704, 0, 0, 0, -136372, 0, 0, 0, -479352, 0, 358724, 0, 0, 0, 491836, 0, 0, 0, -11592, 0, -637976, 0, 0, 0, -436212, 0, 0, 0, 70184, 0, -165768, 0, 0, 0, 381076, 0, 0, 0, -888936, 0, 280080, 0, 0, 0, 833848, 0, 0, 0, -503496, 0, 587956, 0, 0, 0, 123348, 0, 0, 0, -211336, 0, -324864, 0, 0, 0, 5752, 0, 0, 0, 158280, 0, -854180, 0, 0, 0, -615800, 0, 0, 0, -142128, 0, -76952, 0, 0, 0, 188496, 0, 0, 0, 131592, 0, 134424, 0, 0, 0, 777948, 0, 0, 0, -396672, 0, 1149952, 0, 0, 0, 299956, 0, 0, 0, 459120, 0, 242668, 0, 0, 0, 110484, 0, 0, 0, 138840, 0, -706200, 0, 0, 0, -400164, 0, 0, 0, 1496696, 0, 164376, 0, 0, 0, -1252436, 0, 0, 0, 648024, 0, 208284, 0, 0, 0, 622752, 0, 0, 0, -174808, 0, -378756, 0, 0, 0, -979740, 0, 0, 0, -1224216, 0, 662900, 0, 0, 0, 459116, 0, 0, 0, -563328, 0, -1364128, 0, 0, 0, -27744, 0, 0, 0, 548920, 0, 443208, 0, 0, 0, -1660956, 0, 0, 0, 57896, 0, -291412, 0, 0, 0, 131796, 0, 0, 0, 878160, 0, 1599716, 0, 0, 0, -1122156, 0, 0, 0, 1498216, 0, -382680, 0, 0, 0, -893072, 0, 0, 0, -680720, 0, -1956, 0, 0, 0, 930724, 0, 0, 0, 802344, 0, 466492, 0, 0, 0, 156624, 0, 0, 0, 1479704, 0, 1256472, 0, 0, 0, 1433240, 0, 0, 0, 821928, 0, 8624, 0, 0, 0, -2355544, 0, 0, 0, 854784, 0, 101880, 0, 0, 0, 10944, 0, 0, 0, -1234328, 0, 65016, 0, 0, 0, 741044, 0, 0, 0, -1851960, 0, -948444, 0, 0, 0, -955288, 0, 0, 0, -495648, 0, 525620, 0, 0, 0, 1028916, 0, 0, 0, -398984, 0, -18360, 0, 0, 0, 178436, 0, 0, 0, 2150728, 0, 114608, 0, 0, 0, 680176, 0, 0, 0, 199080, 0, -1104460, 0, 0, 0, 1047768, 0, 0, 0, -1881968, 0, -1444608, 0, 0, 0, -847396, 0, 0, 0, 956248, 0, 1746280, 0, 0, 0, 1256276, 0, 0, 0, -425376, 0, 1921288, 0, 0, 0, 45264, 0, 0, 0, -2966504, 0, 12648, 0, 0, 0, -186288, 0, 0, 0, 1150248, 0, -3194252, 0, 0, 0, 381004, 0, 0, 0, 602904, 0, -2842620, 0, 0, 0, -1192320, 0, 0, 0, -1126460, 0, 614136, 0, 0, 0, 3326460, 0, 0, 0, -1852152, 0, 1005908, 0, 0, 0, 536076, 0, 0, 0, -2221008, 0, -178012, 0, 0, 0, 183948, 0, 0, 0, -439496, 0, 744156, 0, 0, 0, -426028, 0, 0, 0, -1275480, 0, -1229460, 0, 0, 0, -235596, 0, 0, 0, 743256, 0, -1381776, 0, 0, 0, -100248, 0, 0, 0, -2153640, 0, 1417416, 0, 0, 0, -3115764, 0, 0, 0, 2320952, 0, -3064568, 0, 0, 0, 3409048, 0, 0, 0, 546984, 0, 682072, 0, 0, 0, 3069612, 0, 0, 0, -3758832, 0, -729432, 0, 0, 0, -2462420, 0, 0, 0, 1759496, 0, 1955656, 0, 0, 0, 167580, 0, 0, 0, 326136, 0, 2420556, 0, 0, 0, -1438368, 0, 0, 0, -629684, 0, 515340, 0, 0, 0, 3729140, 0, 0, 0, 3492696, 0, -4250672, 0, 0, 0, 162556, 0, 0, 0, 2133936, 0, 528276, 0, 0, 0, -1529832, 0, 0, 0, 3307192, 0, 1883976, 0, 0, 0, 746564, 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, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [3, -3, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-11, -11, 1, 0], [0, 0, 0, 0], [0, 63, 0, 0], [0, 0, 0, 0], [-74, 0, -1, 1], [0, 0, 0, 0], [-79, 79, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [55, 55, -4, 0], [0, 0, 0, 0], [0, 188, -1, -1], [0, 0, 0, 0], [-66, 0, 3, -3], [0, 0, 0, 0], [-163, 163, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [432, 432, 0, 0], [0, 0, 0, 0], [0, 836, 5, 5], [0, 0, 0, 0], [-690, 0, 5, -5], [0, 0, 0, 0], [-222, 222, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [513, 513, 17, 0], [0, 0, 0, 0], [0, 474, -3, -3], [0, 0, 0, 0], [-1078, 0, -18, 18], [0, 0, 0, 0], [431, -431, 0, -22], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1313, 1313, -17, 0], [0, 0, 0, 0], [0, 3641, -22, -22], [0, 0, 0, 0], [330, 0, -12, 12], [0, 0, 0, 0], [-1731, 1731, 0, -15], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [564, 564, -6, 0], [0, 0, 0, 0], [0, 564, 37, 37], [0, 0, 0, 0], [-3030, 0, 34, -34], [0, 0, 0, 0], [693, -693, 0, 63], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1503, 1503, 22, 0], [0, 0, 0, 0], [0, 978, 9, 9], [0, 0, 0, 0], [558, 0, 37, -37], [0, 0, 0, 0], [-4453, 4453, 0, 26], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-4986, -4986, -52, 0], [0, 0, 0, 0], [0, -3392, -56, -56], [0, 0, 0, 0], [-2511, 0, 0, 0], [0, 0, 0, 0], [4083, -4083, 0, -80], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2508, 2508, 30, 0], [0, 0, 0, 0], [0, 1688, 62, 62], [0, 0, 0, 0], [7538, 0, -90, 90], [0, 0, 0, 0], [-2070, 2070, 0, -30], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2953, -2953, 36, 0], [0, 0, 0, 0], [0, -4662, -63, -63], [0, 0, 0, 0]]}