# Stored data for newform 336.4.bc.c, downloaded from the LMFDB on 18 April 2024. {"label": "336.4.bc.c", "space_label": "336.4.bc", "level": 336, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9009123467198800, "dim": 12, "is_polredabs": true, "trace_hash": 1638331982358797794, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [16083058761, 0, 10590781509, 0, 6898376178, 0, 49602429, 0, 272898, 0, 597, 0, 1]], [13, [49422707712, 0, 42650496, 0, 11724, 0, 1]]], "qexp_display": "q+(-\\beta _{3}+\\beta _{4})q^{3}-\\beta _{11}q^{5}+(2-2\\beta _{1}+\\cdots)q^{7}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "bc", "char_is_real": false, "Nk2": 5376, "analytic_conductor": 19.824641761928845, "hecke_ring_index": 34992, "level_radical": 42, "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": "0.592", "prec": 17}, "analytic_rank_proved": true, "char_values": [336, 6, [127, 85, 113, 241], [6, 6, 3, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [17, 257], "field_disc": 12450305331302297847696, "field_disc_factorization": [[2, 4], [3, 6], [7, 6], [11, 2], [61, 2], [67, 4]], "field_poly": [531441, 0, -91854, -23328, 5670, 2016, -50, 224, 70, -32, -14, 0, 1], "hecke_ring_index_factorization": [[2, 4], [3, 7]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.104", "prec": 17}, {"__RealLiteral__": 0, "data": "10.984", "prec": 20}, {"__RealLiteral__": 0, "data": "9.002", "prec": 17}, {"__RealLiteral__": 0, "data": "921.448", "prec": 24}, {"__RealLiteral__": 0, "data": "912.100", "prec": 24}, {"__RealLiteral__": 0, "data": "118631.664", "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, 42], "traces": [0, 12, 0, 0, 0, 0, 0, 42, 0, -84, 0, 0, 0, 0, 0, -132, 0, 0, 0, -204, 0, -378, 0, 0, 0, -444, 0, 0, 0, 0, 0, -1458, 0, -108, 0, 0, 0, 240, 0, 432, 0, 0, 0, 0, 0, -342, 0, 0, 0, -1218, 0, 300, 0, 0, 0, 0, 0, 180, 0, 0, 0, 2148, 0, -1596, 0, 0, 0, -1980, 0, 0, 0, 0, 0, -3084, 0, 3384, 0, 0, 0, 438, 0, 1008, 0, 0, 0, -6144, 0, 2898, 0, 0, 0, -3780, 0, 882, 0, 0, 0, 0, 0, -9216, 0, 0, 0, 1380, 0, 3738, 0, 0, 0, 1296, 0, 0, 0, 0, 0, -3348, 0, -3636, 0, 0, 0, 3948, 0, 3552, 0, 0, 0, 13716, 0, -2736, 0, 0, 0, -9324, 0, 2898, 0, 0, 0, 0, 0, 20292, 0, 0, 0, 18018, 0, 504, 0, 0, 0, 198, 0, 0, 0, 0, 0, 12780, 0, 15138, 0, 0, 0, 5148, 0, -2610, 0, 0, 0, -20532, 0, 324, 0, 0, 0, 13524, 0, -1212, 0, 0, 0, 0, 0, -7848, 0, 0, 0, -22644, 0, 9576, 0, 0, 0, -30, 0, 0, 0, 0, 0, -16044, 0, -11466, 0, 0, 0, 4560, 0, 8604, 0, 0, 0, 11184, 0, -23364, 0, 0, 0, -9786, 0, 4968, 0, 0, 0, 0, 0, 29256, 0, 0, 0, 6804, 0, -6048, 0, 0, 0, -10776, 0, 0, 0, 0, 0, 12882, 0, 30240, 0, 0, 0, -18072, 0, -78, 0, 0, 0, -39024, 0, 10116, 0, 0, 0, -14784, 0, -4536, 0, 0, 0, 0, 0, -58824, 0, 0, 0, -29514, 0, 20664, 0, 0, 0, 8316, 0, 0, 0, 0, 0, 16704, 0, -46638, 0, 0, 0, -10326, 0, -792, 0, 0, 0, 68700, 0, -35154, 0, 0, 0, -336, 0, 4644, 0, 0, 0, 0, 0, 27612, 0, 0, 0, 17490, 0, 504, 0, 0, 0, -21294, 0, 0, 0, 0, 0, 26232, 0, -23364, 0, 0, 0, -20208, 0, -1146, 0, 0, 0, -34908, 0, -4896, 0, 0, 0, 19992, 0, 522, 0, 0, 0, 0, 0, -23040, 0, 0, 0, -16200, 0, 31458, 0, 0, 0, -10350, 0, 0, 0, 0, 0, 18822, 0, -38844, 0, 0, 0, -31620, 0, 26322, 0, 0, 0, 7968, 0, 17856, 0, 0, 0, -65142, 0, -11112, 0, 0, 0, 0, 0, 30600, 0, 0, 0, 40932, 0, 17640, 0, 0, 0, 9060, 0, 0, 0, 0, 0, 96474, 0, 12996, 0, 0, 0, 174, 0, 3204, 0, 0, 0, 27120, 0, -24228, 0, 0, 0, 1344, 0, -5292, 0, 0, 0, 0, 0, -30240, 0, 0, 0, -9702, 0, 15036, 0, 0, 0, -39384, 0, 0, 0, 0, 0, 42696, 0, -26190, 0, 0, 0, 36462, 0, 24444, 0, 0, 0, 50448, 0, -39780, 0, 0, 0, 7560, 0, 10692, 0, 0, 0, 0, 0, -29628, 0, 0, 0, -1320, 0, 28980, 0, 0, 0, -57750, 0, 0, 0, 0, 0, 8820, 0, -65718, 0, 0, 0, 28908, 0, 37500, 0, 0, 0, 60264, 0, 10944, 0, 0, 0, -53760, 0, -8676, 0, 0, 0, 0, 0, 32904, 0, 0, 0, 117348, 0, 8064, 0, 0, 0, -10326, 0, 0, 0, 0, 0, 32598, 0, 26982, 0, 0, 0, 7116, 0, -6696, 0, 0, 0, 5112, 0, -59814, 0, 0, 0, 53508, 0, 19236, 0, 0, 0, 0, 0, -86580, 0, 0, 0, 66888, 0, 61866, 0, 0, 0, -2256, 0, 0, 0, 0, 0, -32730, 0, 33480, 0, 0, 0, -37710, 0, 68040, 0, 0, 0, 97728, 0, -119196, 0, 0, 0, -96684, 0, 51066, 0, 0, 0, 0, 0, 24360, 0, 0, 0, 70026, 0, 46494, 0, 0, 0, -16536, 0, 0, 0, 0, 0, 108552, 0, 41580, 0, 0, 0, -24774, 0, 41364, 0, 0, 0, -103140, 0, -42192, 0, 0, 0, -149940, 0, -6840, 0, 0, 0, 0, 0, -185952, 0, 0, 0, -108450, 0, 29736, 0, 0, 0, -28026, 0, 0, 0, 0, 0, -1524, 0, -148680, 0, 0, 0, 10836, 0, -5796, 0, 0, 0, 71628, 0, -174096, 0, 0, 0, -147966, 0, 43452, 0, 0, 0, 0, 0, 70776, 0, 0, 0, 73656, 0, 54936, 0, 0, 0, -86808, 0, 0, 0, 0, 0, -46848, 0, 62766, 0, 0, 0, -40824, 0, 24558, 0, 0, 0, -235368, 0, -46440, 0, 0, 0, -98196, 0, 37872, 0, 0, 0, 0, 0, -80460, 0, 0, 0, -80820, 0, 190470, 0, 0, 0, 23916, 0, 0, 0, 0, 0, -64944, 0, -135144, 0, 0, 0, 116274, 0, 110346, 0, 0, 0, 29376, 0, -145260, 0, 0, 0, -17388, 0, 45882, 0, 0, 0, 0, 0, 143208, 0, 0, 0, 119484, 0, -21924, 0, 0, 0, -44208, 0, 0, 0, 0, 0, 136416, 0, 73098, 0, 0, 0, -42864, 0, 52200, 0, 0, 0, -140016, 0, -2754, 0, 0, 0, -20664, 0, -25158, 0, 0, 0, 0, 0, 19116, 0, 0, 0, 163392, 0, 114408, 0, 0, 0, 12744, 0, 0, 0, 0, 0, 178728, 0, -74052, 0, 0, 0, -177204, 0, 72036, 0, 0, 0, 71160, 0, -217620, 0, 0, 0, -190512, 0, -27378, 0, 0, 0, 0, 0, 198216, 0, 0, 0, 275928, 0, 37716, 0, 0, 0, -150516, 0, 0, 0, 0, 0, 330648, 0, 29934, 0, 0, 0, 28692, 0, 33666, 0, 0, 0, -95952, 0, -106686, 0, 0, 0, -12894, 0, 63936, 0, 0, 0, 0, 0, -203616, 0, 0, 0, -163008, 0, 38808, 0, 0, 0, -190356, 0, 0, 0, 0, 0, 270234, 0, -134568, 0, 0, 0, 56304, 0, 81540, 0, 0, 0, 118800, 0, 34632, 0, 0, 0, -185556, 0, 83274, 0, 0, 0, 0, 0, 137232, 0, 0, 0, -48816, 0, 143136, 0, 0, 0, 23616, 0, 0, 0, 0, 0, 203328, 0, 28728, 0, 0, 0, -8232, 0, 42984, 0, 0, 0, -71748, 0, -126594, 0, 0, 0, 7812, 0, -75168, 0, 0, 0, 0, 0, -122988, 0, 0, 0, -222012, 0, 161952, 0, 0, 0, -35862, 0, 0, 0, 0, 0, -245376, 0, 50760, 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, 21, 7, 1, 6, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 7, 4, -1, 6, 0]], "char_orbit_index": 29, "prim_orbit_index": 7, "minimal_twist": "84.4.k.c", "char_is_minimal": false, "conrey_index": 17, "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, 0, 0, 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, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 12, 1, 1, -1, -1, 1, -2, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, -2, 0, 1, -1, -2, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 32, 8, 0, 0, 0, -8, -2, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11, 0, 0, -2, 1, 0, 0, 8, 0, -8, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -4, 3, 6, -4, -4, 3, -5, -2, 1, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-27, -11, 4, 0, 0, 0, -5, -9, 0, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-34, -3, -8, -7, 8, 2, -2, 6, 3, -3, 4, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, 2, -6, 16, -4, -3, 1, 0, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-80, -74, 6, 0, 0, 0, 10, 10, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-38, -43, 7, 0, -2, -2, -7, 6, 2, 13, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -4, 4, 12, -6, -2, 4, -5, -2, 1, 5, 10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-73, 75, -2, 0, 0, 0, 11, -11, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, -18, -15, -3, -3, -18, -6, -6, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, -17, 10, 42, -38, -6, 15, -18, -2, -4, 9, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -48, 7, 0, 0, 0, 1, -8, 0, -8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [82, 72, -6, -8, -12, 0, 14, 10, -4, -6, 10, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8, 8, 4, 0, 28, 4, -4, 6, -4, 10, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 16, -16, 0, 0, 0, -16, -12, 0, 28, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 15, -13, 9, -8, -2, 19, -20, -1, 15, 21, 21], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-15, -15, 30, 90, 0, 0, 15, -15, 0, 15, 0, -14], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-119, 63, 21, 0, 0, 0, -35, 35, 0, 7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-61, -8, 19, -23, 52, -6, -61, 42, 0, 48, 10, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-24, 0, 24, 48, 48, 0, 0, 0, 0, 24, 13, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [119, 263, 35, 0, 0, 0, -35, -40, 0, -5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [14, 2, -2, 30, -15, 1, -2, 16, 1, -14, -14, -28], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 6, -2, -24, 26, -4, -7, 5, -2, 6, 31, 31], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [245, 138, -25, 0, 0, 0, -31, -6, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-77, 27, -11, 49, -52, 8, 52, 10, 12, -52, -12, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [54, -64, 10, 108, -196, -20, 54, -64, 0, -44, 28, 14], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-259, -330, -71, 0, 0, 0, 26, 26, 0, -71, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [98, 332, 32, 0, 45, -9, -32, 20, 9, 52, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 26, -26, -120, 60, -8, -26, 22, -8, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-147, 130, 17, 0, 0, 0, 45, -45, 0, -17, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [382, 156, 58, 112, -16, -16, 38, -52, -32, 36, 0, 30], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-30, 24, 4, -84, 150, -22, -36, 25, 2, 39, -16, -17], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-44, -30, 1, 0, 0, 0, -44, 43, 0, 43, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [141, 168, 42, 63, 48, 0, 42, 27, -15, 42, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, 12, -6, 0, -18, 18, 6, 3, -18, -3, -7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-512, -32, 32, 0, 0, 0, 32, -105, 0, 73, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [184, -125, -59, -12, 12, 0, 5, -5, 0, 59, -12, -12], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [49, 34, -71, -222, -6, -6, -31, 28, -12, -34, 0, -18], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-588, -546, 154, 0, 0, 0, 42, -70, 0, -42, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, -165, 24, 95, -181, -9, -6, -18, 0, -9, -30, -15], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [41, 0, -69, -138, -110, 0, -14, 14, 28, -69, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-387, -596, 108, 0, 0, 0, -108, -73, 0, 35, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-780, 105, -105, -78, 39, 12, -105, 123, 12, -18, -18, -36], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}