# Stored data for newform 144.11.g.e, downloaded from the LMFDB on 29 May 2024.
{"Nk2": 17424, "analytic_conductor": 91.49144438501627, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 4, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 2, "char_parity": -1, "char_values": [144, 2, [127, 37, 65], [1, 2, 2]], "cm_discs": [], "conrey_index": 127, "dim": 4, "field_disc": 58293225, "field_disc_factorization": [[3, 2], [5, 2], [509, 2]], "field_poly": [404496, 636, 637, -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, [-903420, 1500, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014811010891920, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 36864, "hecke_ring_index_factorization": [[2, 12], [3, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 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": "144.11.g.e", "level": 144, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2, 3], "level_radical": 6, "minimal_twist": "48.11.g.c", "nf_label": "4.0.58293225.4", "prim_orbit_index": 2, "qexp_display": "q+(-750-\\beta _{2})q^{5}+(107\\beta _{1}-13\\beta _{3})q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "10.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "144.11.g", "trace_display": [0, 0, -3000, 0], "trace_hash": 340432428416211718, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.660", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "68.970", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1856.499", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.505", "prec": 17}, "traces": [0, 4, 0, 0, 0, -3000, 0, 0, 0, 0, 0, 0, 0, 864136, 0, 0, 0, 55128, 0, 0, 0, 0, 0, 0, 0, -30948820, 0, 0, 0, 80790312, 0, 0, 0, 0, 0, 0, 0, -212511640, 0, 0, 0, 544453272, 0, 0, 0, 0, 0, 0, 0, -1845182972, 0, 0, 0, 888804072, 0, 0, 0, 0, 0, 0, 0, -208335256, 0, 0, 0, 1075819920, 0, 0, 0, 0, 0, 0, 0, 4881669448, 0, 0, 0, -18371224512, 0, 0, 0, 0, 0, 0, 0, 10313912880, 0, 0, 0, -21540382536, 0, 0, 0, 0, 0, 0, 0, 14965768456, 0, 0, 0, -12126464280, 0, 0, 0, 0, 0, 0, 0, -69925309496, 0, 0, 0, -57169105224, 0, 0, 0, 0, 0, 0, 0, -80507565404, 0, 0, 0, 43712970000, 0, 0, 0, 0, 0, 0, 0, -152555483328, 0, 0, 0, 71382892632, 0, 0, 0, 0, 0, 0, 0, -103380006960, 0, 0, 0, -259072511928, 0, 0, 0, 0, 0, 0, 0, 37810607528, 0, 0, 0, -442115179776, 0, 0, 0, 0, 0, 0, 0, 142081833708, 0, 0, 0, -847729730040, 0, 0, 0, 0, 0, 0, 0, 826541661064, 0, 0, 0, 56159507280, 0, 0, 0, 0, 0, 0, 0, 92884699016, 0, 0, 0, 143460959016, 0, 0, 0, 0, 0, 0, 0, -779334987600, 0, 0, 0, -95774127552, 0, 0, 0, 0, 0, 0, 0, -841908796992, 0, 0, 0, 3056355633072, 0, 0, 0, 0, 0, 0, 0, -250770017720, 0, 0, 0, 3185152486584, 0, 0, 0, 0, 0, 0, 0, 1110838347592, 0, 0, 0, 1579640322120, 0, 0, 0, 0, 0, 0, 0, -2488747555584, 0, 0, 0, 2079583185912, 0, 0, 0, 0, 0, 0, 0, 1480717607760, 0, 0, 0, -1120691588952, 0, 0, 0, 0, 0, 0, 0, 5569402062856, 0, 0, 0, 1517871096696, 0, 0, 0, 0, 0, 0, 0, 10224171354380, 0, 0, 0, -11094651784344, 0, 0, 0, 0, 0, 0, 0, 6015948014016, 0, 0, 0, 2860064654160, 0, 0, 0, 0, 0, 0, 0, -1428845055352, 0, 0, 0, -448642267032, 0, 0, 0, 0, 0, 0, 0, -9271880259880, 0, 0, 0, 6520396111488, 0, 0, 0, 0, 0, 0, 0, -14759069373368, 0, 0, 0, -1182072702528, 0, 0, 0, 0, 0, 0, 0, -19400540838424, 0, 0, 0, 9288605252664, 0, 0, 0, 0, 0, 0, 0, 6588433241956, 0, 0, 0, -11927774331120, 0, 0, 0, 0, 0, 0, 0, -21518334408664, 0, 0, 0, 4873996012368, 0, 0, 0, 0, 0, 0, 0, -2560632117120, 0, 0, 0, -28244573229240, 0, 0, 0, 0, 0, 0, 0, -22804663980952, 0, 0, 0, -2474336806248, 0, 0, 0, 0, 0, 0, 0, 36169392536200, 0, 0, 0, -73875423590208, 0, 0, 0, 0, 0, 0, 0, 25318743824392, 0, 0, 0, -15959424957240, 0, 0, 0, 0, 0, 0, 0, 34759471608008, 0, 0, 0, -25554588362496, 0, 0, 0, 0, 0, 0, 0, 29592894720240, 0, 0, 0, 20470591117656, 0, 0, 0, 0, 0, 0, 0, 13198924835464, 0, 0, 0, -88173580186872, 0, 0, 0, 0, 0, 0, 0, -43498135473216, 0, 0, 0, 124137550551744, 0, 0, 0, 0, 0, 0, 0, -76257661115440, 0, 0, 0, 33107697931920, 0, 0, 0, 0, 0, 0, 0, -74448871967376, 0, 0, 0, 252729078395904, 0, 0, 0, 0, 0, 0, 0, 76607377488720, 0, 0, 0, -16677352494360, 0, 0, 0, 0, 0, 0, 0, -93333520487808, 0, 0, 0, 157595026309272, 0, 0, 0, 0, 0, 0, 0, 99182694308164, 0, 0, 0, 8547878284848, 0, 0, 0, 0, 0, 0, 0, -3268943590712, 0, 0, 0, 71924405364240, 0, 0, 0, 0, 0, 0, 0, 198001925031360, 0, 0, 0, -110180550243768, 0, 0, 0, 0, 0, 0, 0, -50969422740240, 0, 0, 0, 122019858014232, 0, 0, 0, 0, 0, 0, 0, 180959804547656, 0, 0, 0, -398061229935168, 0, 0, 0, 0, 0, 0, 0, -91172716091712, 0, 0, 0, 43219093807032, 0, 0, 0, 0, 0, 0, 0, 226926323093192, 0, 0, 0, -153531157109880, 0, 0, 0, 0, 0, 0, 0, 217410373489064, 0, 0, 0, 98544223709304, 0, 0, 0, 0, 0, 0, 0, 173415488598100, 0, 0, 0, -185222812746000, 0, 0, 0, 0, 0, 0, 0, -341070848795768, 0, 0, 0, -86827929870504, 0, 0, 0, 0, 0, 0, 0, -501518808747072, 0, 0, 0, -19947472608312, 0, 0, 0, 0, 0, 0, 0, -375299201475352, 0, 0, 0, 334157762494080, 0, 0, 0, 0, 0, 0, 0, -312486099978040, 0, 0, 0, -350862124577400, 0, 0, 0, 0, 0, 0, 0, 57093010086960, 0, 0, 0, 823324173447888, 0, 0, 0, 0, 0, 0, 0, -647673574342896, 0, 0, 0, -376969160744472, 0, 0, 0, 0, 0, 0, 0, -177921189372728, 0, 0, 0, -138801133004544, 0, 0, 0, 0, 0, 0, 0, 813991462846656, 0, 0, 0, -560910296517960, 0, 0, 0, 0, 0, 0, 0, -631424763632504, 0, 0, 0, -463124377191744, 0, 0, 0, 0, 0, 0, 0, 374592800935440, 0, 0, 0, -440039879703360, 0, 0, 0, 0, 0, 0, 0, 215461890795208, 0, 0, 0, -974042286174120, 0, 0, 0, 0, 0, 0, 0, 243192221791496, 0, 0, 0, 227774880692904, 0, 0, 0, 0, 0, 0, 0, 1294817926887936, 0, 0, 0, -648912077870640, 0, 0, 0, 0, 0, 0, 0, 749913585680336, 0, 0, 0, 860463342920136, 0, 0, 0, 0, 0, 0, 0, 420477005975040, 0, 0, 0, 244607562119256, 0, 0, 0, 0, 0, 0, 0, -731067127193664, 0, 0, 0, 728520451995048, 0, 0, 0, 0, 0, 0, 0, -162186072464696, 0, 0, 0, 320269650729816, 0, 0, 0, 0, 0, 0, 0, 261158425852652, 0, 0, 0, 638290120849560, 0, 0, 0, 0, 0, 0, 0, -1487566981204504, 0, 0, 0, 2371251419940120, 0, 0, 0, 0, 0, 0, 0, 249208539930000, 0, 0, 0, 1146990048315840, 0, 0, 0, 0, 0, 0, 0, -1273699396857880, 0, 0, 0, -88045357215240, 0, 0, 0, 0, 0, 0, 0, -1748661657142464, 0, 0, 0, 1930888583710848, 0, 0, 0, 0, 0, 0, 0, 3804417786388464, 0, 0, 0, -441947439554160, 0, 0, 0, 0, 0, 0, 0, -2704395284949312, 0, 0, 0, 4609359743547456, 0, 0, 0, 0, 0, 0, 0, 1799082457646200, 0, 0, 0, 1261107136641432, 0, 0, 0, 0, 0, 0, 0, 268377617567624, 0, 0, 0, -3378604165964664, 0, 0, 0, 0, 0, 0, 0, -1375750962536048, 0, 0, 0, -5542616288106984, 0, 0, 0, 0, 0, 0, 0, 2812426927470916, 0, 0, 0, -1690696577128560, 0, 0, 0, 0, 0, 0, 0, 4114319125881408, 0, 0, 0, -288137775890664, 0, 0, 0, 0, 0, 0, 0, -400035295767600, 0, 0, 0, 597559677242112, 0, 0, 0, 0, 0, 0, 0, -1010193988567000, 0, 0, 0], "weight": 11, "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], [0, 0, 0, 0], [0, 0, 0, 0], [-750, 0, -1, 0], [0, 0, 0, 0], [0, 107, 0, -13], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -18537, 0, -82], [0, 0, 0, 0], [216034, 0, -294, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [13782, 0, -1766, 0], [0, 0, 0, 0], [0, 234907, 0, -646], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 81324, 0, -1926], [0, 0, 0, 0], [-7737205, 0, 1500, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [20197578, 0, 7297, 0], [0, 0, 0, 0], [0, 1119213, 0, -3581], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4844490, 0, 10178], [0, 0, 0, 0], [-53127910, 0, 17604, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [136113318, 0, 63270, 0], [0, 0, 0, 0], [0, 23366241, 0, 28406], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -36452562, 0, 25238], [0, 0, 0, 0], [-461295743, 0, -33384, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [222201018, 0, -366207, 0], [0, 0, 0, 0], [0, -16148610, 0, -12648], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -9633603, 0, -323912], [0, 0, 0, 0], [-52083814, 0, -461112, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [268954980, 0, 4466, 0], [0, 0, 0, 0], [0, -51170351, 0, -194808], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -81145176, 0, 1097858], [0, 0, 0, 0], [1220417362, 0, 1409784, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-4592806128, 0, 2786484, 0], [0, 0, 0, 0], [0, -27637235, 0, 863351], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -52470543, 0, -1745378], [0, 0, 0, 0], [2578478220, 0, 1310718, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-5385095634, 0, -2291668, 0], [0, 0, 0, 0], [0, -1377570922, 0, -2682610], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -412926330, 0, 1424128], [0, 0, 0, 0], [3741442114, 0, -7560444, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}