# Stored data for newform 117.4.q.f, downloaded from the LMFDB on 24 April 2024.
{"label": "117.4.q.f", "space_label": "117.4.q", "level": 117, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22519097715589237, "dim": 12, "is_polredabs": true, "trace_hash": 1208840804874265689, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [54756, 0, -47034, 0, 32913, 0, -5964, 0, 823, 0, -32, 0, 1]]], "qexp_display": "q+(\\beta _{1}+\\beta _{2})q^{2}+(-3\\beta _{3}-\\beta _{8})q^{4}+(\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "q", "char_is_real": false, "Nk2": 1872, "analytic_conductor": 6.9032234706716515, "hecke_ring_index": 3888, "level_radical": 39, "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": "0.589", "prec": 17}, "analytic_rank_proved": true, "char_values": [117, 6, [92, 28], [6, 5]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [3, 13], "conrey_indexes": [10, 82], "field_disc": 12477885786210605398769664, "field_disc_factorization": [[2, 14], [3, 6], [13, 2], [8867, 4]], "field_poly": [54756, 0, -47034, 0, 32913, 0, -5964, 0, 823, 0, -32, 0, 1], "hecke_ring_index_factorization": [[2, 4], [3, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.595", "prec": 20}, {"__RealLiteral__": 0, "data": "5.919", "prec": 17}, {"__RealLiteral__": 0, "data": "1082.014", "prec": 27}, {"__RealLiteral__": 0, "data": "1583.987", "prec": 27}, {"__RealLiteral__": 0, "data": "162224.628", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "3.2.3.c6", "trace_display": [0, 0, 0, -18], "traces": [0, 12, 0, 0, 16, 0, 0, -18, 0, 0, -56, 0, 0, -154, 0, 0, -92, 0, 0, -48, 0, 0, 292, 0, 0, -92, 0, 0, 552, 0, 0, 0, 0, 0, 0, 0, 0, -360, 0, 0, -448, 0, 0, -810, 0, 0, 996, 0, 0, -1068, 0, 0, -700, 0, 0, 460, 0, 0, 3048, 0, 0, 1294, 0, 0, -184, 0, 0, 2658, 0, 0, 0, 0, 0, 0, 0, 0, 1188, 0, 0, -6380, 0, 0, -1268, 0, 0, -3768, 0, 0, -5140, 0, 0, 342, 0, 0, 1660, 0, 0, 1686, 0, 0, 5084, 0, 0, -5484, 0, 0, 15264, 0, 0, 0, 0, 0, 0, 0, 0, 3396, 0, 0, -2240, 0, 0, -1802, 0, 0, -17892, 0, 0, -6578, 0, 0, -260, 0, 0, 4308, 0, 0, 14748, 0, 0, 2550, 0, 0, -21752, 0, 0, 22836, 0, 0, 0, 0, 0, 0, 0, 0, 4008, 0, 0, -8484, 0, 0, -5112, 0, 0, -12426, 0, 0, -12164, 0, 0, 6138, 0, 0, 10232, 0, 0, 14802, 0, 0, 7144, 0, 0, -9480, 0, 0, 41028, 0, 0, 0, 0, 0, 0, 0, 0, 19518, 0, 0, -20600, 0, 0, -10970, 0, 0, -38568, 0, 0, -19712, 0, 0, 1056, 0, 0, 14230, 0, 0, 7332, 0, 0, 9162, 0, 0, -29832, 0, 0, 26076, 0, 0, 0, 0, 0, 0, 0, 0, 11328, 0, 0, -25544, 0, 0, -5892, 0, 0, -10116, 0, 0, -27452, 0, 0, 5100, 0, 0, -2320, 0, 0, 39624, 0, 0, 24284, 0, 0, -15624, 0, 0, 67032, 0, 0, 0, 0, 0, 0, 0, 0, -5394, 0, 0, -12200, 0, 0, -2100, 0, 0, -30372, 0, 0, -21830, 0, 0, -19304, 0, 0, 5778, 0, 0, 18816, 0, 0, 5248, 0, 0, -29696, 0, 0, 14274, 0, 0, 0, 0, 0, 0, 0, 0, -8424, 0, 0, -33260, 0, 0, -17780, 0, 0, -5412, 0, 0, -408, 0, 0, 8726, 0, 0, 15980, 0, 0, 9306, 0, 0, 29824, 0, 0, 21556, 0, 0, 54000, 0, 0, 0, 0, 0, 0, 0, 0, 31326, 0, 0, 25848, 0, 0, -16460, 0, 0, 3948, 0, 0, -21042, 0, 0, -32652, 0, 0, 1146, 0, 0, 20460, 0, 0, -530, 0, 0, 1880, 0, 0, -28254, 0, 0, 0, 0, 0, 0, 0, 0, -56460, 0, 0, -72456, 0, 0, 26248, 0, 0, 16734, 0, 0, 4000, 0, 0, 28422, 0, 0, -13692, 0, 0, -10638, 0, 0, 1688, 0, 0, -18344, 0, 0, 1992, 0, 0, 0, 0, 0, 0, 0, 0, 46794, 0, 0, 71096, 0, 0, -17846, 0, 0, -10572, 0, 0, -13002, 0, 0, -11880, 0, 0, -2192, 0, 0, -16980, 0, 0, -38228, 0, 0, 10936, 0, 0, -58146, 0, 0, 0, 0, 0, 0, 0, 0, 16848, 0, 0, -19020, 0, 0, 29744, 0, 0, 58068, 0, 0, 61060, 0, 0, 31308, 0, 0, -25624, 0, 0, -41160, 0, 0, -7808, 0, 0, 56496, 0, 0, -33984, 0, 0, 0, 0, 0, 0, 0, 0, -31884, 0, 0, 110440, 0, 0, -9978, 0, 0, -36516, 0, 0, 17032, 0, 0, -18148, 0, 0, 19308, 0, 0, -98436, 0, 0, -47502, 0, 0, -42912, 0, 0, -135996, 0, 0, 0, 0, 0, 0, 0, 0, -54108, 0, 0, -52788, 0, 0, 50784, 0, 0, 81546, 0, 0, 112532, 0, 0, 102586, 0, 0, -35636, 0, 0, -10104, 0, 0, -66844, 0, 0, 177784, 0, 0, -70548, 0, 0, 0, 0, 0, 0, 0, 0, 68436, 0, 0, 245152, 0, 0, 28548, 0, 0, 60528, 0, 0, 60708, 0, 0, -148800, 0, 0, 3904, 0, 0, -48252, 0, 0, -27456, 0, 0, -18808, 0, 0, -172914, 0, 0, 0, 0, 0, 0, 0, 0, -155844, 0, 0, -28916, 0, 0, 79820, 0, 0, 87918, 0, 0, 84760, 0, 0, 39800, 0, 0, -93104, 0, 0, -57246, 0, 0, -12588, 0, 0, 44512, 0, 0, -197364, 0, 0, 0, 0, 0, 0, 0, 0, 51270, 0, 0, 108152, 0, 0, -38532, 0, 0, 31404, 0, 0, 11190, 0, 0, 35284, 0, 0, 25122, 0, 0, -206496, 0, 0, -112496, 0, 0, 152936, 0, 0, -145758, 0, 0, 0, 0, 0, 0, 0, 0, -61932, 0, 0, -38184, 0, 0, 61132, 0, 0, 175854, 0, 0, 117272, 0, 0, 71188, 0, 0, -101660, 0, 0, 51966, 0, 0, 37400, 0, 0, 169948, 0, 0, 8352, 0, 0, 0, 0, 0, 0, 0, 0, -10116, 0, 0, 114552, 0, 0, 7132, 0, 0, 96012, 0, 0, -15036, 0, 0, -137568, 0, 0, -42740, 0, 0, -123756, 0, 0, -42258, 0, 0, -59456, 0, 0, -312744, 0, 0, 0, 0, 0, 0, 0, 0, -131904, 0, 0, -144272, 0, 0, -19508, 0, 0, 232866, 0, 0, 120296, 0, 0, 58974, 0, 0, -3632, 0, 0, -89412, 0, 0, 14860, 0, 0, 170736, 0, 0, -182496, 0, 0, 0, 0, 0, 0, 0, 0, 89916, 0, 0, 281328, 0, 0, 35472, 0, 0, -25824, 0, 0, -2774, 0, 0, -174744, 0, 0, 5008, 0, 0, 122784, 0, 0, -83574, 0, 0, 92584, 0, 0, -21210, 0, 0, 0, 0, 0, 0, 0, 0, -143292, 0, 0, -135188, 0, 0, 43660, 0, 0, 190848, 0, 0, 25020, 0, 0, 66588, 0, 0, -46056, 0, 0, -23280, 0, 0, 10892, 0, 0, -55556, 0, 0, 94896, 0, 0, 0, 0, 0, 0, 0, 0, 167196, 0, 0, 289840, 0, 0, -79920, 0, 0, -61788, 0, 0, -14984, 0, 0, 34164, 0, 0, 38920, 0, 0, -164256, 0, 0, -20888, 0, 0, 66544, 0, 0, -199344, 0, 0, 0, 0, 0, 0, 0, 0, -202644, 0, 0, -117056, 0, 0, 79020, 0, 0, -61860, 0, 0, 156200, 0, 0, -33690, 0, 0, -39900, 0, 0, 70608, 0, 0, 122368, 0, 0, -34584, 0, 0, 363108, 0, 0, 0, 0, 0, 0, 0, 0, -121554, 0, 0, -76992, 0, 0, -105176, 0, 0, -92316, 0, 0, -152144, 0, 0, -93492, 0, 0, 996, 0, 0, -48504, 0, 0, -49062, 0, 0, -399824], "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, 3, 2, -1, 2, 0], [1, 1, 13, 5, 1, 6, 0], [1, 1, 39, 8, -1, 6, 0]], "char_orbit_index": 17, "prim_orbit_index": 5, "minimal_twist": "117.4.q.f", "char_is_minimal": true, "conrey_index": 10, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1], [0, 0, 3, 0, 1, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-10, 0, 0, -10, 0, 1, 0, -1, -2, 0, 0, -2], [0, 4, 4, 0, 0, 0, 0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-16, 0, 0, -4, 0, 1, 0, -1, -1, 0, 0, -4], [0, 4, 2, 0, 0, 0, -1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-17, 0, 0, -17, 0, 3, 0, -2, -5, 0, 0, -4], [0, -3, -6, 0, -1, 0, -2, 0, 0, 4, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, -3, 0, -3, 0, 0, -1, 0, 0, -5], [0, -9, 0, 0, 2, 0, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -53, 0, 1, 0, -2, -13, 0, 0, -1], [0, 4, -4, 0, -6, 0, 2, 0, 0, -1, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, 0, -13, 0, 4, 0, 0, 0, -4], [0, -27, -30, 0, 1, 0, -5, 0, 0, -2, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [31, 0, 0, -31, 0, 4, 0, -5, -1, 0, 0, 0], [0, 17, -17, 0, 0, 0, 18, 0, 0, -9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-10, 0, 0, -20, 0, 9, 0, 4, -18, 0, 0, 4], [0, -15, 0, 0, -3, 0, -6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [43, 0, 0, 86, 0, -11, 0, 0, 22, 0, 0, 0], [0, -12, -24, 0, 3, 0, 7, 0, 0, -14, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-24, 0, 0, 24, 0, 13, 0, -1, 12, 0, 0, 0], [0, 8, 4, 0, 1, 0, -5, 0, 0, -5, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-40, 0, 0, 0, 0, 26, 0, -9, 0, 0, 0, 9], [0, -15, -15, 0, 0, 0, 0, 0, 0, 28, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 143, 0, -9, 0, 18, 24, 0, 0, 9], [0, 0, 116, 0, 5, 0, -11, 0, 0, 11, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [134, 0, 0, 67, 0, -49, 0, 0, 35, 0, 0, 21], [0, 0, -24, 0, 1, 0, -19, 0, 0, 19, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-181, 0, 0, -181, 0, 13, 0, 4, -9, 0, 0, 8], [0, 70, 70, 0, 0, 0, 0, 0, 0, -12, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [62, 0, 0, 256, 0, 14, 0, -1, 38, 0, 0, 9], [0, 158, 79, 0, 2, 0, -11, 0, 0, -11, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [71, 0, 0, 71, 0, 28, 0, 11, -17, 0, 0, 22], [0, 8, 16, 0, 1, 0, -13, 0, 0, 26, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [356, 0, 0, 178, 0, -25, 0, 0, 26, 0, 0, 27], [0, -20, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -226, 0, -11, 0, 22, -31, 0, 0, 11], [0, -94, 94, 0, 18, 0, 8, 0, 0, -4, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, -17, 0, -16, 0, 0, 0, 16], [0, -65, -117, 0, 0, 0, 0, 0, 0, -26, -13, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [139, 0, 0, -139, 0, 17, 0, 9, 26, 0, 0, 0], [0, 107, -107, 0, -6, 0, 32, 0, 0, -16, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [101, 0, 0, 202, 0, 11, 0, 3, -22, 0, 0, 3], [0, -168, 0, 0, 7, 0, -9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [39, 0, 0, 78, 0, -8, 0, -6, 16, 0, 0, -6], [0, -123, -246, 0, -12, 0, -1, 0, 0, 2, 24, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [65, 0, 0, -65, 0, 22, 0, -19, 3, 0, 0, 0], [0, 48, 24, 0, 2, 0, 18, 0, 0, 18, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-550, 0, 0, 0, 0, -17, 0, 36, 0, 0, 0, -36], [0, -113, -113, 0, 0, 0, 0, 0, 0, -13, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 217, 0, 22, 0, -44, 17, 0, 0, -22], [0, 0, 200, 0, -23, 0, 1, 0, 0, -1, 23, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-404, 0, 0, -202, 0, -89, 0, 0, 22, 0, 0, -45], [0, 0, -254, 0, -24, 0, 27, 0, 0, -27, 24, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-881, 0, 0, -881, 0, 60, 0, -13, -73, 0, 0, -26], [0, 126, 126, 0, 0, 0, 0, 0, 0, -4, 34, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [267, 0, 0, 486, 0, 28, 0, 11, -41, 0, 0, 5], [0, 504, 252, 0, -11, 0, 13, 0, 0, 13, -11, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [275, 0, 0, 275, 0, -16, 0, -21, -5, 0, 0, -42], [0, -64, -128, 0, 13, 0, 25, 0, 0, -50, -26, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [148, 0, 0, 74, 0, 54, 0, 0, -59, 0, 0, -64], [0, -289, 0, 0, 9, 0, 12, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -870, 0, 30, 0, -60, -68, 0, 0, -30]]}