# Stored data for newform 336.6.q.f, downloaded from the LMFDB on 09 December 2024. {"Nk2": 12096, "analytic_conductor": 53.888963457161495, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 17, "char_orbit_label": "q", "char_order": 3, "char_parity": 1, "char_values": [336, 3, [127, 85, 113, 241], [3, 3, 3, 2]], "cm_discs": [], "conrey_index": 193, "dim": 4, "field_disc": 829612809, "field_disc_factorization": [[3, 2], [9601, 2]], "field_poly": [5760000, 2400, 2401, -1, 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": [[5, [2883204, 89994, 4507, -53, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22519097749143888, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 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": "336.6.q.f", "level": 336, "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, 7], "level_radical": 42, "minimal_twist": "42.6.e.c", "nf_label": "4.0.829612809.1", "prim_orbit_index": 3, "qexp_display": "q+(-9+9\\beta _{2})q^{3}+(\\beta _{1}+26\\beta _{2})q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "5.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "336.6.q", "trace_display": [0, -18, 53, -6], "trace_hash": 884079271850032922, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.717", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "49.837", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1066.623", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 4, 0, -18, 0, 53, 0, -6, 0, -162, 0, 191, 0, -758, 0, -954, 0, 340, 0, -1769, 0, -27, 0, 3236, 0, 45, 0, 2916, 0, 8918, 0, 1994, 0, 1719, 0, 4562, 0, -20587, 0, 3411, 0, 17628, 0, -31706, 0, 4293, 0, 33912, 0, 9598, 0, 3060, 0, -49239, 0, -37882, 0, 31842, 0, -56735, 0, -67508, 0, 729, 0, 42762, 0, 75723, 0, -58248, 0, 17984, 0, 3201, 0, 405, 0, 120299, 0, 26612, 0, -13122, 0, 1898, 0, 210040, 0, -40131, 0, -176562, 0, -210085, 0, 17946, 0, 234098, 0, -258846, 0, -30942, 0, 34508, 0, 229531, 0, 174249, 0, -142677, 0, 70197, 0, 370566, 0, 7844, 0, -104956, 0, 30699, 0, -479540, 0, 183849, 0, -79326, 0, -175218, 0, 12176, 0, 142677, 0, 139567, 0, -179259, 0, 38637, 0, -77170, 0, 136086, 0, -610416, 0, -300222, 0, -174667, 0, -561483, 0, 96942, 0, -154881, 0, -55080, 0, 1680246, 0, 322994, 0, -443151, 0, 4640, 0, -161552, 0, 170469, 0, -1897376, 0, -179810, 0, -143289, 0, 427538, 0, 1272200, 0, -510615, 0, 493962, 0, 1341682, 0, 1215144, 0, 300730, 0, 447580, 0, -4374, 0, -222042, 0, 1161944, 0, -769716, 0, -2432348, 0, 753964, 0, 681507, 0, 1157945, 0, 550404, 0, 262116, 0, 1534316, 0, -764108, 0, -80928, 0, -837748, 0, -3933419, 0, 28809, 0, 991680, 0, -2329946, 0, -7290, 0, -1507287, 0, -847605, 0, -223758, 0, 594670, 0, -1647546, 0, -479016, 0, 2791428, 0, -1735933, 0, -118098, 0, -1326901, 0, -1724189, 0, -8541, 0, 2190198, 0, 426056, 0, -945180, 0, 2302836, 0, 337467, 0, -361179, 0, -615450, 0, -449442, 0, 3178116, 0, 1980047, 0, 3187475, 0, 2381364, 0, -1276430, 0, 3596351, 0, -323028, 0, -1753220, 0, 3293997, 0, 2106882, 0, -1293774, 0, 861714, 0, 1164807, 0, -7000626, 0, -2613314, 0, 139239, 0, -402000, 0, 1718133, 0, 310572, 0, 1942578, 0, -3471930, 0, -4131558, 0, -889178, 0, -3490440, 0, -1937763, 0, -695271, 0, 1889987, 0, 2568186, 0, -8090240, 0, -2807219, 0, 631773, 0, 596274, 0, 781021, 0, -1667547, 0, 7248856, 0, 3016396, 0, -35298, 0, 3745983, 0, -388800, 0, -944604, 0, 6089292, 0, 3185016, 0, -552582, 0, 1025862, 0, 6670958, 0, 850320, 0, 2917342, 0, -3914043, 0, -3309282, 0, 8570528, 0, 1593802, 0, -713934, 0, -5474421, 0, 44637, 0, 788481, 0, -8132232, 0, -16414698, 0, -54792, 0, 2578250, 0, 767297, 0, 1284093, 0, -5129488, 0, 1868320, 0, -2512206, 0, -5438511, 0, 1612345, 0, -6787665, 0, -2961924, 0, 8282239, 0, -695466, 0, -6380372, 0, 1942748, 0, -694530, 0, -1069205, 0, 8517233, 0, -612387, 0, 6697308, 0, -4828346, 0, 2746872, 0, 5080880, 0, 150170, 0, -2701998, 0, 4544718, 0, 6970730, 0, 3144006, 0, 3611120, 0, -1335517, 0, 4275909, 0, -794707, 0, 5686998, 0, -1744956, 0, 3868748, 0, -742428, 0, -1393929, 0, 297222, 0, -2021484, 0, 247860, 0, 2261324, 0, -19311834, 0, -7561107, 0, -697994, 0, -7975258, 0, 2906946, 0, 574256, 0, 19765662, 0, 7976718, 0, -2931766, 0, 6594317, 0, 778644, 0, 6080081, 0, 581446, 0, 2907936, 0, -8785098, 0, -5098580, 0, 1534221, 0, -25757656, 0, 738021, 0, 8538192, 0, 17750748, 0, -7695268, 0, 809145, 0, -5735373, 0, -20997386, 0, -1289601, 0, -4570414, 0, -1011588, 0, -7695684, 0, -12311034, 0, -5100431, 0, -2291661, 0, -16084620, 0, 7560030, 0, 9191070, 0, 3629820, 0, 11024895, 0, 4445658, 0, 5741936, 0, -7873991, 0, -6037569, 0, 32283416, 0, 13704368, 0, -5468148, 0, 7476404, 0, 4613539, 0, 2706570, 0, 15959693, 0, -3179870, 0, -8056440, 0, -1175437, 0, 19296332, 0, -19683, 0, 18667794, 0, -4086475, 0, 3996756, 0, -1889792, 0, -7395966, 0, 10457496, 0, -33971185, 0, 10102887, 0, 3463722, 0, -1004038, 0, -64935382, 0, 10945566, 0, 1402122, 0, -13756460, 0, 6785676, 0, 14795790, 0, 42073748, 0, -12267126, 0, -9456476, 0, -12183682, 0, -13237569, 0, 1811334, 0, 14749690, 0, -9907272, 0, -14325848, 0, -22076745, 0, 2359044, 0, -213576, 0, 5905008, 0, -6904422, 0, 2793440, 0, 23477182, 0, 3438486, 0, 3147243, 0, -551489, 0, -728352, 0, 4295662, 0, 20474686, 0, 15079464, 0, -22465452, 0, 6402295, 0, 7004781, 0, 18100233, 0, 4198297, 0, -518562, 0, -15789736, 0, -28149, 0, 8925120, 0, -45685648, 0, 6043340, 0, 10484757, 0, -11357868, 0, -58993192, 0, 32805, 0, 9321555, 0, -37650893, 0, -13565583, 0, 19890891, 0, 7181564, 0, 15256890, 0, 21212028, 0, -19150955, 0, -7730397, 0, 15018916, 0, 7835040, 0, -10704060, 0, 26873966, 0, -8661007, 0, -14827914, 0, 23862242, 0, -2266852, 0, 2155572, 0, 12750840, 0, 3271032, 0, -12561426, 0, 10732740, 0, -2545047, 0, -15623397, 0, 15620344, 0, 36181560, 0, 2125764, 0, -11047880, 0, 21136801, 0, -3326031, 0, 857296, 0, 37393265, 0, 31035402, 0, -38528136, 0, 28048626, 0, -76869, 0, -6601908, 0, 28166720, 0, -9855891, 0, 61676986, 0, 7728520, 0, -1917252, 0, -20040944, 0, -71302142, 0, -8506620, 0, 12916308, 0, 15605352, 0, -41451048, 0, -4318624, 0, 41681081, 0, 8257869, 0, -20152470, 0, -31304614, 0, 6501222, 0, -51490064, 0, -30597346, 0, -5539050, 0, -76781362, 0, 11102990, 0, 2022489, 0, -25479246, 0, 41485200, 0, -14301522, 0, 20696492, 0, 41222876, 0, 17820423, 0, 9819962, 0, -3588420, 0, -57374550, 0, -12424612, 0, 30310075, 0, -4415391, 0, 7734283, 0, 29624472, 0, 22975740, 0, -39374862, 0, 18527499, 0, 32367159, 0, 11469880, 0, -30535994, 0, 1453626, 0, -12693184, 0, -26436594, 0, 7889490, 0, -22395767, 0, 3757157, 0, 29645973, 0, 32330464, 0, -63831334, 0, -37923876, 0, -3215862, 0, 76556326, 0, 14138496, 0, 2902840, 0, 12931970, 0, -15510852, 0, -42250038, 0, 3445945, 0, 10483263, 0, -33206259, 0, 16243398, 0, 31502817, 0, 2383452, 0, -70572602, 0, 11759913, 0, 16007718, 0, -11961908, 0, 1253151, 0, 59201406, 0, -70770912, 0, 7236000, 0, -43578579, 0, -13231620, 0, -18579942, 0, 21113634, 0, 22631993, 0, -5590296, 0, 20721396, 0, -42369793, 0, 17483202, 0, -8524874, 0, -57816195, 0, 15623685, 0, 138110772, 0, -26877918, 0, 18592011, 0, 20498472, 0, 43883578, 0, -8002602, 0, -6772340, 0, 23728388, 0, 62827920, 0, -8300533, 0, 15528384, 0, 3325698, 0, 17990602, 0, 45598223, 0, 12514878, 0, 76280092, 0, 42550332, 0, 17009883, 0, -28294690, 0, -73843964, 0, -11556837, 0, 12560326, 0, -85688672, 0, 36406080, 0, -30366429, 0, -53067235, 0, -25264971, 0, -5017968, 0, -23642292, 0, -11371914, 0, 59254440, 0, 11484742, 0, 27875232, 0, -27320728, 0, -37632386, 0, -14058378, 0, -23060872, 0, 12321107, 0, -15007923, 0], "weight": 6, "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], [-9, 0, 9, 0], [0, 0, 0, 0], [0, 1, 26, 0], [0, 0, 0, 0], [-3, -2, 3, 1], [0, 0, 0, 0], [0, 0, -81, 0], [0, 0, 0, 0], [93, 5, -98, 5], [0, 0, 0, 0], [-184, 0, 0, -11], [0, 0, 0, 0], [-243, 0, 0, 9], [0, 0, 0, 0], [180, -20, -160, -20], [0, 0, 0, 0], [0, -39, -865, 0], [0, 0, 0, 0], [18, -9, -18, -27], [0, 0, 0, 0], [0, 4, 1616, 0], [0, 0, 0, 0], [-4, 53, -49, 53], [0, 0, 0, 0], [729, 0, 0, 0], [0, 0, 0, 0], [2199, 0, 0, 61], [0, 0, 0, 0], [1079, -164, -915, -164], [0, 0, 0, 0], [0, -45, 882, 0], [0, 0, 0, 0], [4773, -80, -7174, -51], [0, 0, 0, 0], [0, 51, -10319, 0], [0, 0, 0, 0], [1656, 99, -1755, 99], [0, 0, 0, 0], [4440, 0, 0, -66], [0, 0, 0, 0], [-7970, 0, 0, 87], [0, 0, 0, 0], [2187, -81, -2106, -81], [0, 0, 0, 0], [0, 156, 16878, 0], [0, 0, 0, 0], [-7192, -2, 19197, -13], [0, 0, 0, 0], [0, 180, 1440, 0], [0, 0, 0, 0], [-24507, -225, 24732, -225], [0, 0, 0, 0], [-9489, 0, 0, 37], [0, 0, 0, 0], [8136, 0, 0, -351], [0, 0, 0, 0], [-28347, -41, 28388, -41], [0, 0, 0, 0], [0, -32, -33738, 0], [0, 0, 0, 0], [81, 243, -81, 162], [0, 0, 0, 0], [0, 102, 21330, 0], [0, 0, 0, 0], [38030, -337, -37693, -337], [0, 0, 0, 0], [-14580, 0, 0, 36], [0, 0, 0, 0], [5166, 0, 0, -1340], [0, 0, 0, 0], [2038, -875, -1163, -875], [0, 0, 0, 0], [0, -477, 441, 0], [0, 0, 0, 0], [35814, 83, -11804, 284], [0, 0, 0, 0], [0, 986, 12813, 0], [0, 0, 0, 0], [-6561, 0, 6561, 0], [0, 0, 0, 0], [1359, 0, 0, -1769], [0, 0, 0, 0], [52860, 0, 0, -700], [0, 0, 0, 0], [-19791, -549, 20340, -549], [0, 0, 0, 0], [0, -210, -88176, 0], [0, 0, 0, 0], [-25848, 401, -53385, -162], [0, 0, 0, 0], [0, 1476, 8235, 0], [0, 0, 0, 0], [118008, -1918, -116090, -1918], [0, 0, 0, 0], [-63721, 0, 0, -1981], [0, 0, 0, 0], [-7533, 0, 0, -405], [0, 0, 0, 0]]}