# Stored data for newform 80.6.n.c, downloaded from the LMFDB on 18 April 2024.
{"label": "80.6.n.c", "space_label": "80.6.n", "level": 80, "weight": 6, "hecke_orbit": 3, "hecke_orbit_code": 9008092708601936, "dim": 4, "is_polredabs": true, "nf_label": "4.0.384400.3", "trace_hash": 1522036962802032156, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [96100, 0, 0, 0, 1]]], "qexp_display": "q-\\beta _{2}q^{3}+(55+10\\beta _{1})q^{5}-11\\beta _{3}q^{7}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 20, "char_orbit_label": "n", "char_is_real": false, "Nk2": 2880, "analytic_conductor": 12.830705585038451, "hecke_ring_index": 8, "level_radical": 10, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.625", "prec": 17}, "analytic_rank_proved": true, "char_values": [80, 4, [31, 21, 17], [2, 4, 1]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 4, "level_primes": [2, 5], "conrey_indexes": [47, 63], "field_disc": 384400, "field_disc_factorization": [[2, 4], [5, 2], [31, 2]], "field_poly": [1521, 0, -77, 0, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.864", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "87.161", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2792.902", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c4", "trace_display": [0, 0, 220, 0], "traces": [0, 4, 0, 0, 0, 220, 0, 0, 0, 0, 0, 0, 0, 660, 0, 0, 0, 5060, 0, 0, 0, 13640, 0, 0, 0, 11700, 0, 0, 0, 0, 0, 0, 0, 6200, 0, 0, 0, 5540, 0, 0, 0, 8712, 0, 0, 0, -2680, 0, 0, 0, 0, 0, 0, 0, -95660, 0, 0, 0, -136400, 0, 0, 0, -143528, 0, 0, 0, 42900, 0, 0, 0, 0, 0, 0, 0, -86460, 0, 0, 0, -68200, 0, 0, 0, 283364, 0, 0, 0, 227700, 0, 0, 0, 0, 0, 0, 0, -353400, 0, 0, 0, -2460, 0, 0, 0, 587928, 0, 0, 0, 750200, 0, 0, 0, 0, 0, 0, 0, 46820, 0, 0, 0, 44220, 0, 0, 0, 582204, 0, 0, 0, 599500, 0, 0, 0, 0, 0, 0, 0, -1500400, 0, 0, 0, -972220, 0, 0, 0, -492280, 0, 0, 0, -103840, 0, 0, 0, 0, 0, 0, 0, -339020, 0, 0, 0, -887740, 0, 0, 0, -586520, 0, 0, 0, 403000, 0, 0, 0, 0, 0, 0, 0, -66220, 0, 0, 0, -1351600, 0, 0, 0, -457512, 0, 0, 0, 249300, 0, 0, 0, 0, 0, 0, 0, -2089340, 0, 0, 0, 1205380, 0, 0, 0, 2672200, 0, 0, 0, 479160, 0, 0, 0, 0, 0, 0, 0, 3341800, 0, 0, 0, 3887400, 0, 0, 0, 1669800, 0, 0, 0, -294800, 0, 0, 0, 0, 0, 0, 0, 2812260, 0, 0, 0, 1091200, 0, 0, 0, -2682328, 0, 0, 0, 828120, 0, 0, 0, 0, 0, 0, 0, -266600, 0, 0, 0, -2399580, 0, 0, 0, -695728, 0, 0, 0, -6217900, 0, 0, 0, 0, 0, 0, 0, 2250600, 0, 0, 0, 3472260, 0, 0, 0, -860728, 0, 0, 0, -6138000, 0, 0, 0, 0, 0, 0, 0, 4270420, 0, 0, 0, -1091200, 0, 0, 0, -15154040, 0, 0, 0, -7894040, 0, 0, 0, 0, 0, 0, 0, 2832900, 0, 0, 0, -564700, 0, 0, 0, -6097080, 0, 0, 0, 2656500, 0, 0, 0, 0, 0, 0, 0, -371180, 0, 0, 0, -1888700, 0, 0, 0, 3534000, 0, 0, 0, 533200, 0, 0, 0, 0, 0, 0, 0, 9088900, 0, 0, 0, 17254600, 0, 0, 0, 20103604, 0, 0, 0, -5619900, 0, 0, 0, 0, 0, 0, 0, -1778700, 0, 0, 0, 1713360, 0, 0, 0, -6097080, 0, 0, 0, -3069000, 0, 0, 0, 0, 0, 0, 0, 11389400, 0, 0, 0, 3572100, 0, 0, 0, 7121928, 0, 0, 0, 15585020, 0, 0, 0, 0, 0, 0, 0, -14867600, 0, 0, 0, -15140400, 0, 0, 0, -1359688, 0, 0, 0, 9234500, 0, 0, 0, 0, 0, 0, 0, 5743140, 0, 0, 0, 5865200, 0, 0, 0, 5548404, 0, 0, 0, 4576960, 0, 0, 0, 0, 0, 0, 0, -25029400, 0, 0, 0, -14639900, 0, 0, 0, -24272072, 0, 0, 0, -22971000, 0, 0, 0, 0, 0, 0, 0, -6888200, 0, 0, 0, -6409220, 0, 0, 0, 1828200, 0, 0, 0, -110700, 0, 0, 0, 0, 0, 0, 0, -13135760, 0, 0, 0, -36759800, 0, 0, 0, -2496120, 0, 0, 0, 32336040, 0, 0, 0, 0, 0, 0, 0, -24006400, 0, 0, 0, 2461400, 0, 0, 0, 34579688, 0, 0, 0, 39897000, 0, 0, 0, 0, 0, 0, 0, 1437480, 0, 0, 0, 4228400, 0, 0, 0, -1839112, 0, 0, 0, -3768160, 0, 0, 0, 0, 0, 0, 0, 12003200, 0, 0, 0, 3759140, 0, 0, 0, 15686000, 0, 0, 0, 3043300, 0, 0, 0, 0, 0, 0, 0, -21334200, 0, 0, 0, 9203300, 0, 0, 0, 42461320, 0, 0, 0, 1989900, 0, 0, 0, 0, 0, 0, 0, -11871420, 0, 0, 0, 36679200, 0, 0, 0, 34275912, 0, 0, 0, 32021220, 0, 0, 0, 0, 0, 0, 0, 18000180, 0, 0, 0, -26906620, 0, 0, 0, -9384320, 0, 0, 0, 29382500, 0, 0, 0, 0, 0, 0, 0, -25711400, 0, 0, 0, -13663980, 0, 0, 0, -15435288, 0, 0, 0, 13776400, 0, 0, 0, 0, 0, 0, 0, 8832820, 0, 0, 0, -5792820, 0, 0, 0, -64234888, 0, 0, 0, -97526000, 0, 0, 0, 0, 0, 0, 0, 29416420, 0, 0, 0, -28728700, 0, 0, 0, -71459960, 0, 0, 0, -43749900, 0, 0, 0, 0, 0, 0, 0, 4569400, 0, 0, 0, 11020680, 0, 0, 0, 26418392, 0, 0, 0, -27075400, 0, 0, 0, 0, 0, 0, 0, 15196200, 0, 0, 0, 28916800, 0, 0, 0, -2114200, 0, 0, 0, -11422400, 0, 0, 0, 0, 0, 0, 0, -29401900, 0, 0, 0, -13361000, 0, 0, 0, -45012000, 0, 0, 0, 13955040, 0, 0, 0, 0, 0, 0, 0, 61311800, 0, 0, 0, 10291780, 0, 0, 0, 4085928, 0, 0, 0, -22036300, 0, 0, 0, 0, 0, 0, 0, 87556660, 0, 0, 0, 18891400, 0, 0, 0, -33418000, 0, 0, 0, -39948300, 0, 0, 0, 0, 0, 0, 0, -23682120, 0, 0, 0, 61646820, 0, 0, 0, 30665632, 0, 0, 0, -32258600, 0, 0, 0, 0, 0, 0, 0, 82181000, 0, 0, 0, 151540400, 0, 0, 0, 42386872, 0, 0, 0, 24955000, 0, 0, 0, 0, 0, 0, 0, 104757180, 0, 0, 0, 62198400, 0, 0, 0, 55087732, 0, 0, 0, -12673720, 0, 0, 0, 0, 0, 0, 0, -89257740, 0, 0, 0, -117379900, 0, 0, 0, 29707920, 0, 0, 0, -4304300, 0, 0, 0, 0, 0, 0, 0, 164820, 0, 0, 0, 29136580, 0, 0, 0, 22159272, 0, 0, 0, -60822000, 0, 0, 0, 0, 0, 0, 0, 54150800, 0, 0, 0, -8797800, 0, 0, 0, -242019800, 0, 0, 0, -25163160, 0, 0, 0, 0, 0, 0, 0, 19300600, 0, 0, 0, -125283400, 0, 0, 0, -143370040, 0, 0, 0, 10110500, 0, 0, 0, 0, 0, 0, 0, -46307800, 0, 0, 0, 9368260, 0, 0, 0, 210209208, 0, 0, 0, 24006400, 0, 0, 0, 0, 0, 0, 0, 25482820, 0, 0, 0, 16095200, 0, 0, 0, -86921396, 0, 0, 0, -135807100, 0, 0, 0, 0, 0, 0, 0, -166544400, 0, 0, 0, -45194780, 0, 0, 0, -25246672, 0, 0, 0, 54242100, 0, 0, 0, 0, 0, 0, 0, -92696200, 0, 0, 0, -75623900, 0, 0, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0], [1, 1, 5, 3, -1, 4, 0], [1, 1, 20, 5, 1, 4, 0]], "char_orbit_index": 14, "prim_orbit_index": 5, "minimal_twist": "80.6.n.c", "char_is_minimal": true, "conrey_index": 47, "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, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [55, 10, 0, 0], [0, 0, 0, 0], [0, 0, 0, -11], [0, 0, 0, 0], [0, 67, 0, 0], [0, 0, 0, 0], [0, 0, 5, -5], [0, 0, 0, 0], [165, -165, 0, 0], [0, 0, 0, 0], [0, 0, -55, 10], [0, 0, 0, 0], [1265, 1265, 0, 0], [0, 0, 0, 0], [0, 0, 110, 110], [0, 0, 0, 0], [3410, 0, 0, 0], [0, 0, 0, 0], [0, 0, 43, 0], [0, 0, 0, 0], [2925, 1100, 0, 0], [0, 0, 0, 0], [0, 0, 0, -176], [0, 0, 0, 0], [0, 2596, 0, 0], [0, 0, 0, 0], [0, 0, -285, 285], [0, 0, 0, 0], [1550, -1550, 0, 0], [0, 0, 0, 0], [0, 0, -110, -605], [0, 0, 0, 0], [1385, 1385, 0, 0], [0, 0, 0, 0], [0, 0, -165, -165], [0, 0, 0, 0], [2178, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1111, 0], [0, 0, 0, 0], [-670, 3685, 0, 0], [0, 0, 0, 0], [0, 0, 0, 397], [0, 0, 0, 0], [0, -20703, 0, 0], [0, 0, 0, 0], [0, 0, -1265, 1265], [0, 0, 0, 0], [-23915, 23915, 0, 0], [0, 0, 0, 0], [0, 0, 225, -325], [0, 0, 0, 0], [-34100, -34100, 0, 0], [0, 0, 0, 0], [0, 0, 1090, 1090], [0, 0, 0, 0], [-35882, 0, 0, 0], [0, 0, 0, 0], [0, 0, -737, 0], [0, 0, 0, 0], [10725, -7425, 0, 0], [0, 0, 0, 0], [0, 0, 0, -2155], [0, 0, 0, 0], [0, -13330, 0, 0], [0, 0, 0, 0], [0, 0, 2695, -2695], [0, 0, 0, 0], [-21615, 21615, 0, 0], [0, 0, 0, 0], [0, 0, -2925, 1100], [0, 0, 0, 0], [-17050, -17050, 0, 0], [0, 0, 0, 0], [0, 0, -880, -880], [0, 0, 0, 0], [70841, 0, 0, 0], [0, 0, 0, 0], [0, 0, -3113, 0], [0, 0, 0, 0], [56925, 82225, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2596], [0, 0, 0, 0], [0, -114424, 0, 0], [0, 0, 0, 0], [0, 0, 1815, -1815], [0, 0, 0, 0], [-88350, 88350, 0, 0], [0, 0, 0, 0], [0, 0, 7150, 4950], [0, 0, 0, 0], [-615, -615, 0, 0], [0, 0, 0, 0], [0, 0, -335, -335], [0, 0, 0, 0]]}