# Stored data for newform 96.4.a.f, downloaded from the LMFDB on 22 May 2025. {"Nk2": 1536, "analytic_conductor": 5.664183360551099, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [96, 1, [31, 37, 65], [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": [[5, [-10, 1]], [7, [-4, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998203961440, "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": true, "label": "96.4.a.f", "level": 96, "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, 3], "level_radical": 6, "minimal_twist": "96.4.a.c", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+3q^{3}+10q^{5}+4q^{7}+9q^{9}-20q^{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": "96.4.a", "trace_display": [0, 3, 10, 4], "trace_hash": 460648734937496183, "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "0.968", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.894", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.655", "prec": 17}], "trace_zratio": 0, "traces": [0, 1, 0, 3, 0, 10, 0, 4, 0, 9, 0, -20, 0, 70, 0, 30, 0, 90, 0, -140, 0, 12, 0, 192, 0, -25, 0, 27, 0, -134, 0, -100, 0, -60, 0, 40, 0, -170, 0, 210, 0, -110, 0, -532, 0, 90, 0, 56, 0, -327, 0, 270, 0, -430, 0, -200, 0, -420, 0, 20, 0, 270, 0, 36, 0, 700, 0, 524, 0, 576, 0, 80, 0, 330, 0, -75, 0, -80, 0, -1060, 0, 81, 0, 1188, 0, 900, 0, -402, 0, 1274, 0, 280, 0, -300, 0, -1400, 0, -590, 0, -180, 0, -798, 0, 1548, 0, 120, 0, -1324, 0, 470, 0, -510, 0, 610, 0, 1920, 0, 630, 0, 360, 0, -931, 0, -330, 0, -1500, 0, 884, 0, -1596, 0, -500, 0, -560, 0, 270, 0, -1950, 0, -220, 0, 168, 0, -1400, 0, -1340, 0, -981, 0, -390, 0, 2100, 0, 810, 0, -1000, 0, -2050, 0, -1290, 0, 768, 0, -332, 0, -600, 0, 2744, 0, 2703, 0, -1260, 0, 3570, 0, -100, 0, 60, 0, -1380, 0, 1358, 0, 810, 0, -1700, 0, -1800, 0, 108, 0, 3840, 0, 3090, 0, 2100, 0, -1070, 0, 380, 0, 1572, 0, -536, 0, -1100, 0, 1728, 0, 2800, 0, -2180, 0, 240, 0, -5320, 0, -400, 0, 990, 0, 6300, 0, -668, 0, -225, 0, 4836, 0, 4334, 0, -240, 0, -2550, 0, 560, 0, -3180, 0, -1920, 0, -1070, 0, 243, 0, -3270, 0, -9800, 0, 3564, 0, 1020, 0, -3840, 0, 2700, 0, -5630, 0, -680, 0, -1206, 0, 7128, 0, -4300, 0, 3822, 0, 4650, 0, -3180, 0, 840, 0, 500, 0, -5330, 0, -900, 0, -7830, 0, -268, 0, -4200, 0, -440, 0, 3187, 0, -1770, 0, -1950, 0, 200, 0, -540, 0, 13440, 0, -2128, 0, -2394, 0, 2700, 0, -2916, 0, 4644, 0, -9000, 0, 8890, 0, 360, 0, 1290, 0, 2680, 0, -3972, 0, -12600, 0, -1750, 0, 1410, 0, 224, 0, 5300, 0, -1530, 0, 5240, 0, -9310, 0, 1830, 0, 2000, 0, -2680, 0, 5760, 0, -2596, 0, 814, 0, 1890, 0, 7730, 0, 800, 0, 1080, 0, -5840, 0, 12741, 0, -2793, 0, 3300, 0, 6636, 0, -990, 0, -1720, 0, 12950, 0, -4500, 0, -9380, 0, 6220, 0, 2652, 0, 8672, 0, -800, 0, -4788, 0, 7530, 0, 17280, 0, -1500, 0, -10600, 0, -3650, 0, -1680, 0, 11498, 0, -7000, 0, 810, 0, 3400, 0, -3590, 0, -5850, 0, 80, 0, 11880, 0, -660, 0, -380, 0, -5410, 0, 504, 0, -2250, 0, 1080, 0, -4200, 0, -8280, 0, -12590, 0, -4020, 0, -26880, 0, -15140, 0, -2943, 0, 5628, 0, 12740, 0, -1170, 0, 5450, 0, 2200, 0, 6300, 0, 2800, 0, -2710, 0, 2430, 0, -11982, 0, 6068, 0, -3000, 0, -5036, 0, 2096, 0, -6150, 0, 10640, 0, 3500, 0, -3870, 0, 4440, 0, -11900, 0, 2304, 0, -5900, 0, 4996, 0, -996, 0, -10700, 0, -12060, 0, -1800, 0, 320, 0, 13980, 0, 8232, 0, -13632, 0, -7980, 0, 8109, 0, 4746, 0, 1320, 0, -3780, 0, 15480, 0, -1120, 0, 10710, 0, -5838, 0, -8388, 0, -300, 0, -9000, 0, 24697, 0, 180, 0, -7700, 0, -13240, 0, -4140, 0, 6540, 0, 7078, 0, 4074, 0, 4700, 0, -8604, 0, 2430, 0, 18760, 0, -4240, 0, -5100, 0, 18850, 0, -37240, 0, -5400, 0, 5412, 0, 6100, 0, 324, 0, 13570, 0, -860, 0, 11520, 0, -4800, 0, 5010, 0, 9270, 0, 4752, 0, 8600, 0, 6300, 0, 16116, 0, 14000, 0, -3210, 0, 7170, 0, 3600, 0, 1140, 0, -9520, 0, 6010, 0, 4716, 0, -9310, 0, -24844, 0, -1608, 0, 3920, 0, 9990, 0, -3300, 0, 570, 0, -8700, 0, 5184, 0, 5096, 0, -11875, 0, 8400, 0, -15300, 0, 16340, 0, -6540, 0, 8840, 0, -22890, 0, 720, 0, 11210, 0, -12828, 0, -15960, 0, 24336, 0, -400, 0, -1200, 0, 770, 0, -5000, 0, 2970, 0, 4140, 0, 8390, 0, 18900, 0, -5600, 0, -25728, 0, -2004, 0, -5400, 0, 1730, 0, -675, 0, 23930, 0, -2360, 0, 14508, 0, -29892, 0, -19500, 0, 13002, 0, -30100, 0, 21220, 0, -720, 0, -2200, 0, -9900, 0, -7650, 0, -21750, 0, 23800, 0, 1680, 0, -3192, 0, -21554, 0, -9540, 0, -19200, 0, -14000, 0, -5760, 0, -13000, 0, 6192, 0, -3210, 0, 3350, 0, -3276, 0, 729, 0, -47880, 0, 21110, 0, -9810, 0, -10480, 0, 17980, 0, -29400, 0, 33192, 0, -3900, 0, 10692, 0, -5296, 0, 23900, 0, 3060, 0, 21000, 0, 1950, 0, -11520, 0, 8082, 0, 1880, 0, 8100, 0, 1400, 0, -36494, 0, -16890, 0, 28050, 0, 2500, 0, -2040, 0, 15400, 0, -1600, 0, -3618, 0, -20500, 0, -23004, 0, 21384, 0, 2440, 0, 18900, 0, -12900, 0, 19410, 0, 5040, 0, 11466, 0, -6600, 0, 7680, 0, 13950, 0, 34946, 0, 28300, 0, -9540, 0, -3320, 0, 74480, 0, 2520, 0, 16930, 0, 24772, 0, 1500, 0, 12004, 0, -22330, 0, -15990, 0, -29430, 0, 27440, 0, -2700, 0, -45280, 0, -6433, 0, -23490, 0, 27030, 0, -3724, 0, -804, 0, -32640, 0, -26970, 0, -12600, 0, -12190, 0, 9260, 0, -1320, 0, 4832, 0, 35700, 0, 9561, 0, 21200, 0, 36680, 0, -5310, 0, -6000, 0, 37630, 0, -5850, 0, -15630, 0, -12988, 0, 600, 0, -5976, 0, 3536, 0, -1620, 0, -7840, 0, -13800, 0, 40320, 0, 13400, 0, -38700, 0, -6384, 0, 13580, 0, 15004, 0, -7182, 0, -21120, 0, -23760, 0, 8100, 0, -2000, 0, -25500, 0, -8748, 0, 5600, 0, 4250, 0, 13932, 0, -390, 0, 45780, 0, -27000, 0, -18000, 0, 890, 0, 26670, 0, -3022, 0, -21120, 0, 1080, 0, -2916, 0, 23100, 0, 3870, 0, -12990, 0, 38400, 0, 8040, 0, -7800, 0, -19791, 0, -11916, 0, 30900, 0, -41844, 0, -37800, 0, 43900, 0, -880, 0, -5250, 0, -8630, 0, -25480, 0, 4230, 0, 168, 0, -10700, 0, 672, 0, -102144, 0, 25580, 0, 15900, 0, 3800, 0, -47610, 0, -4590, 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, 3, 0, 10, 0, 4, 0, 9, 0, -20, 0, 70, 0, 30, 0, 90, 0, -140, 0, 12, 0, 192, 0, -25, 0, 27, 0, -134, 0, -100, 0, -60, 0, 40, 0, -170, 0, 210, 0, -110, 0, -532, 0, 90, 0, 56, 0, -327, 0, 270, 0, -430, 0, -200, 0, -420, 0, 20, 0, 270, 0, 36, 0, 700, 0, 524, 0, 576, 0, 80, 0, 330, 0, -75, 0, -80, 0, -1060, 0, 81, 0, 1188, 0, 900, 0, -402, 0, 1274, 0, 280, 0, -300, 0, -1400, 0, -590, 0, -180, 0, -798, 0, 1548, 0, 120, 0, -1324, 0, 470, 0, -510, 0, 610, 0, 1920, 0, 630, 0, 360, 0, -931, 0, -330, 0, -1500, 0, 884, 0, -1596, 0, -500, 0, -560, 0, 270, 0, -1950, 0, -220, 0, 168, 0, -1400, 0, -1340, 0, -981, 0, -390, 0, 2100, 0, 810, 0, -1000, 0, -2050, 0, -1290, 0, 768, 0, -332, 0, -600, 0, 2744, 0, 2703, 0, -1260, 0, 3570, 0, -100, 0, 60, 0, -1380, 0, 1358, 0, 810, 0, -1700, 0, -1800, 0, 108, 0, 3840, 0, 3090, 0, 2100, 0, -1070, 0, 380, 0, 1572, 0, -536, 0, -1100, 0, 1728, 0, 2800, 0, -2180, 0, 240, 0, -5320, 0, -400, 0, 990, 0, 6300, 0, -668, 0, -225, 0, 4836, 0, 4334, 0, -240, 0, -2550, 0, 560, 0, -3180, 0, -1920, 0, -1070, 0, 243, 0, -3270, 0, -9800, 0, 3564, 0, 1020, 0, -3840, 0, 2700, 0, -5630, 0, -680, 0, -1206, 0, 7128, 0, -4300, 0, 3822, 0, 4650, 0, -3180, 0, 840, 0, 500, 0, -5330, 0, -900, 0, -7830, 0, -268, 0, -4200, 0, -440, 0, 3187, 0, -1770, 0, -1950, 0, 200, 0, -540, 0, 13440, 0, -2128, 0, -2394, 0, 2700, 0, -2916, 0, 4644, 0, -9000, 0, 8890, 0, 360, 0, 1290, 0, 2680, 0, -3972, 0, -12600, 0, -1750, 0, 1410, 0, 224, 0, 5300, 0, -1530, 0, 5240, 0, -9310, 0, 1830, 0, 2000, 0, -2680, 0, 5760, 0, -2596, 0, 814, 0, 1890, 0, 7730, 0, 800, 0, 1080, 0, -5840, 0, 12741, 0, -2793, 0, 3300, 0, 6636, 0, -990, 0, -1720, 0, 12950, 0, -4500, 0, -9380, 0, 6220, 0, 2652, 0, 8672, 0, -800, 0, -4788, 0, 7530, 0, 17280, 0, -1500, 0, -10600, 0, -3650, 0, -1680, 0, 11498, 0, -7000, 0, 810, 0, 3400, 0, -3590, 0, -5850, 0, 80, 0, 11880, 0, -660, 0, -380, 0, -5410, 0, 504, 0, -2250, 0, 1080, 0, -4200, 0, -8280, 0, -12590, 0, -4020, 0, -26880, 0, -15140, 0, -2943, 0, 5628, 0, 12740, 0, -1170, 0, 5450, 0, 2200, 0, 6300, 0, 2800, 0, -2710, 0, 2430, 0, -11982, 0, 6068, 0, -3000, 0, -5036, 0, 2096, 0, -6150, 0, 10640, 0, 3500, 0, -3870, 0, 4440, 0, -11900, 0, 2304, 0, -5900, 0, 4996, 0, -996, 0, -10700, 0, -12060, 0, -1800, 0, 320, 0, 13980, 0, 8232, 0, -13632, 0, -7980, 0, 8109, 0, 4746, 0, 1320, 0, -3780, 0, 15480, 0, -1120, 0, 10710, 0, -5838, 0, -8388, 0, -300, 0, -9000, 0, 24697, 0, 180, 0, -7700, 0, -13240, 0, -4140, 0, 6540, 0, 7078, 0, 4074, 0, 4700, 0, -8604, 0, 2430, 0, 18760, 0, -4240, 0, -5100, 0, 18850, 0, -37240, 0, -5400, 0, 5412, 0, 6100, 0, 324, 0, 13570, 0, -860, 0, 11520, 0, -4800, 0, 5010, 0, 9270, 0, 4752, 0, 8600, 0, 6300, 0, 16116, 0, 14000, 0, -3210, 0, 7170, 0, 3600, 0, 1140, 0, -9520, 0, 6010, 0, 4716, 0, -9310, 0, -24844, 0, -1608, 0, 3920, 0, 9990, 0, -3300, 0, 570, 0, -8700, 0, 5184, 0, 5096, 0, -11875, 0, 8400, 0, -15300, 0, 16340, 0, -6540, 0, 8840, 0, -22890, 0, 720, 0, 11210, 0, -12828, 0, -15960, 0, 24336, 0, -400, 0, -1200, 0, 770, 0, -5000, 0, 2970, 0, 4140, 0, 8390, 0, 18900, 0, -5600, 0, -25728, 0, -2004, 0, -5400, 0, 1730, 0, -675, 0, 23930, 0, -2360, 0, 14508, 0, -29892, 0, -19500, 0, 13002, 0, -30100, 0, 21220, 0, -720, 0, -2200, 0, -9900, 0, -7650, 0, -21750, 0, 23800, 0, 1680, 0, -3192, 0, -21554, 0, -9540, 0, -19200, 0, -14000, 0, -5760, 0, -13000, 0, 6192, 0, -3210, 0, 3350, 0, -3276, 0, 729, 0, -47880, 0, 21110, 0, -9810, 0, -10480, 0, 17980, 0, -29400, 0, 33192, 0, -3900, 0, 10692, 0, -5296, 0, 23900, 0, 3060, 0, 21000, 0, 1950, 0, -11520, 0, 8082, 0, 1880, 0, 8100, 0, 1400, 0, -36494, 0, -16890, 0, 28050, 0, 2500, 0, -2040, 0, 15400, 0, -1600, 0, -3618, 0, -20500, 0, -23004, 0, 21384, 0, 2440, 0, 18900, 0, -12900, 0, 19410, 0, 5040, 0, 11466, 0, -6600, 0, 7680, 0, 13950, 0, 34946, 0, 28300, 0, -9540, 0, -3320, 0, 74480, 0, 2520, 0, 16930, 0, 24772, 0, 1500, 0, 12004, 0, -22330, 0, -15990, 0, -29430, 0, 27440, 0, -2700, 0, -45280, 0, -6433, 0, -23490, 0, 27030, 0, -3724, 0, -804, 0, -32640, 0, -26970, 0, -12600, 0, -12190, 0, 9260, 0, -1320, 0, 4832, 0, 35700, 0, 9561, 0, 21200, 0, 36680, 0, -5310, 0, -6000, 0, 37630, 0, -5850, 0, -15630, 0, -12988, 0, 600, 0, -5976, 0, 3536, 0, -1620, 0, -7840, 0, -13800, 0, 40320, 0, 13400, 0, -38700, 0, -6384, 0, 13580, 0, 15004, 0, -7182, 0, -21120, 0, -23760, 0, 8100, 0, -2000, 0, -25500, 0, -8748, 0, 5600, 0, 4250, 0, 13932, 0, -390, 0, 45780, 0, -27000, 0, -18000, 0, 890, 0, 26670, 0, -3022, 0, -21120, 0, 1080, 0, -2916, 0, 23100, 0, 3870, 0, -12990, 0, 38400, 0, 8040, 0, -7800, 0, -19791, 0, -11916, 0, 30900, 0, -41844, 0, -37800, 0, 43900, 0, -880, 0, -5250, 0, -8630, 0, -25480, 0, 4230, 0, 168, 0, -10700, 0, 672, 0, -102144, 0, 25580, 0, 15900, 0, 3800, 0, -47610, 0, -4590, 0]}