# Stored data for newform 144.7.e.b, downloaded from the LMFDB on 24 April 2024.
{"label": "144.7.e.b", "space_label": "144.7.e", "level": 144, "weight": 7, "hecke_orbit": 2, "hecke_orbit_code": 4503874622718096, "dim": 2, "is_polredabs": true, "nf_label": "2.0.8.1", "trace_hash": 1786025995256062336, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [50, 0, 1]], [7, [60, 1]]], "qexp_display": "q+5\\beta q^{5}-60q^{7}-236\\beta q^{11}+1192q^{13}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "e", "char_is_real": true, "Nk2": 7056, "analytic_conductor": 33.12778804125854, "hecke_ring_index": 1, "level_radical": 6, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [144, 2, [127, 37, 65], [2, 2, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [17], "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.995", "prec": 17}, {"__RealLiteral__": 0, "data": "0.254", "prec": 17}, {"__RealLiteral__": 0, "data": "15.621", "prec": 20}, {"__RealLiteral__": 0, "data": "4.071", "prec": 17}, {"__RealLiteral__": 0, "data": "152.035", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "6.2.3.c2", "trace_display": [0, 0, 0, -120], "traces": [0, 2, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 2384, 0, 0, 0, 0, 0, -16864, 0, 0, 0, 0, 0, 31150, 0, 0, 0, 0, 0, -93784, 0, 0, 0, 0, 0, 21852, 0, 0, 0, 0, 0, -118832, 0, 0, 0, 0, 0, -228098, 0, 0, 0, 0, 0, 4720, 0, 0, 0, 0, 0, -679804, 0, 0, 0, 0, 0, 296048, 0, 0, 0, 0, 0, -803104, 0, 0, 0, 0, 0, -158312, 0, 0, 0, 0, 0, -58700, 0, 0, 0, 0, 0, -143040, 0, 0, 0, 0, 0, 1327840, 0, 0, 0, 0, 0, -1606472, 0, 0, 0, 0, 0, 3024944, 0, 0, 0, 0, 0, 90640, 0, 0, 0, 0, 0, 3320338, 0, 0, 0, 0, 0, -583352, 0, 0, 0, 0, 0, 1011840, 0, 0, 0, 0, 0, 6388560, 0, 0, 0, 0, 0, -475740, 0, 0, 0, 0, 0, 1754024, 0, 0, 0, 0, 0, -2970052, 0, 0, 0, 0, 0, 12489744, 0, 0, 0, 0, 0, -6811890, 0, 0, 0, 0, 0, -1869000, 0, 0, 0, 0, 0, -5075472, 0, 0, 0, 0, 0, 2770640, 0, 0, 0, 0, 0, -1177700, 0, 0, 0, 0, 0, -22162856, 0, 0, 0, 0, 0, -1038420, 0, 0, 0, 0, 0, -908240, 0, 0, 0, 0, 0, 5627040, 0, 0, 0, 0, 0, -39549080, 0, 0, 0, 0, 0, 14328656, 0, 0, 0, 0, 0, -1660080, 0, 0, 0, 0, 0, -6353472, 0, 0, 0, 0, 0, -20101888, 0, 0, 0, 0, 0, -4278208, 0, 0, 0, 0, 0, -1311120, 0, 0, 0, 0, 0, -1165180, 0, 0, 0, 0, 0, 10194440, 0, 0, 0, 0, 0, -41638864, 0, 0, 0, 0, 0, 74472608, 0, 0, 0, 0, 0, 13818238, 0, 0, 0, 0, 0, -3986720, 0, 0, 0, 0, 0, 7129920, 0, 0, 0, 0, 0, 78932880, 0, 0, 0, 0, 0, -59670012, 0, 0, 0, 0, 0, 22454928, 0, 0, 0, 0, 0, 37130800, 0, 0, 0, 0, 0, -1892272, 0, 0, 0, 0, 0, 71891040, 0, 0, 0, 0, 0, 27803760, 0, 0, 0, 0, 0, 48510276, 0, 0, 0, 0, 0, -5820880, 0, 0, 0, 0, 0, 48105486, 0, 0, 0, 0, 0, -108921656, 0, 0, 0, 0, 0, 42898276, 0, 0, 0, 0, 0, -83051968, 0, 0, 0, 0, 0, -283200, 0, 0, 0, 0, 0, 53205680, 0, 0, 0, 0, 0, 67849156, 0, 0, 0, 0, 0, -111790528, 0, 0, 0, 0, 0, 109950816, 0, 0, 0, 0, 0, -1419760, 0, 0, 0, 0, 0, -244371344, 0, 0, 0, 0, 0, 40788240, 0, 0, 0, 0, 0, -140106052, 0, 0, 0, 0, 0, -144492408, 0, 0, 0, 0, 0, -5315700, 0, 0, 0, 0, 0, 49013424, 0, 0, 0, 0, 0, -327340448, 0, 0, 0, 0, 0, 347125688, 0, 0, 0, 0, 0, -17762880, 0, 0, 0, 0, 0, -262656800, 0, 0, 0, 0, 0, 26047584, 0, 0, 0, 0, 0, 224373208, 0, 0, 0, 0, 0, -279259380, 0, 0, 0, 0, 0, -202654656, 0, 0, 0, 0, 0, 687420, 0, 0, 0, 0, 0, 48186240, 0, 0, 0, 0, 0, 78355776, 0, 0, 0, 0, 0, 35937472, 0, 0, 0, 0, 0, 213915682, 0, 0, 0, 0, 0, 32378880, 0, 0, 0, 0, 0, 385882992, 0, 0, 0, 0, 0, -350594992, 0, 0, 0, 0, 0, 9498720, 0, 0, 0, 0, 0, -141647744, 0, 0, 0, 0, 0, 5180460, 0, 0, 0, 0, 0, 173552160, 0, 0, 0, 0, 0, 574056676, 0, 0, 0, 0, 0, 54996496, 0, 0, 0, 0, 0, 790786688, 0, 0, 0, 0, 0, 3522000, 0, 0, 0, 0, 0, -425969284, 0, 0, 0, 0, 0, 444411752, 0, 0, 0, 0, 0, -512895260, 0, 0, 0, 0, 0, -786783488, 0, 0, 0, 0, 0, 483598750, 0, 0, 0, 0, 0, 679227736, 0, 0, 0, 0, 0, -271892816, 0, 0, 0, 0, 0, 665302224, 0, 0, 0, 0, 0, 188173184, 0, 0, 0, 0, 0, 33890720, 0, 0, 0, 0, 0, -247302500, 0, 0, 0, 0, 0, 431210736, 0, 0, 0, 0, 0, -949599292, 0, 0, 0, 0, 0, -79670400, 0, 0, 0, 0, 0, 41317140, 0, 0, 0, 0, 0, 70967504, 0, 0, 0, 0, 0, -609552540, 0, 0, 0, 0, 0, -184256064, 0, 0, 0, 0, 0, 49787344, 0, 0, 0, 0, 0, 5626240, 0, 0, 0, 0, 0, 96388320, 0, 0, 0, 0, 0, -291255432, 0, 0, 0, 0, 0, -193954736, 0, 0, 0, 0, 0, -521112736, 0, 0, 0, 0, 0, 46423780, 0, 0, 0, 0, 0, -363786360, 0, 0, 0, 0, 0, -504276848, 0, 0, 0, 0, 0, -181496640, 0, 0, 0, 0, 0, 1134902500, 0, 0, 0, 0, 0, -1460685800, 0, 0, 0, 0, 0, 274745536, 0, 0, 0, 0, 0, -724206944, 0, 0, 0, 0, 0, -810326368, 0, 0, 0, 0, 0, -974466960, 0, 0, 0, 0, 0, -5438400, 0, 0, 0, 0, 0, 1009184320, 0, 0, 0, 0, 0, 1001991424, 0, 0, 0, 0, 0, 202227176, 0, 0, 0, 0, 0, 2001518768, 0, 0, 0, 0, 0, -100791840, 0, 0, 0, 0, 0, -1073638834, 0, 0, 0, 0, 0, -199220280, 0, 0, 0, 0, 0, -1962646628, 0, 0, 0, 0, 0, -11305008, 0, 0, 0, 0, 0, 66195900, 0, 0, 0, 0, 0, 352889216, 0, 0, 0, 0, 0, 777581700, 0, 0, 0, 0, 0, 2351150384, 0, 0, 0, 0, 0, 35001120, 0, 0, 0, 0, 0, 114567360, 0, 0, 0, 0, 0, -683960660, 0, 0, 0, 0, 0, 2382334288, 0, 0, 0, 0, 0, 67012672, 0, 0, 0, 0, 0, -1257623672, 0, 0, 0, 0, 0, 340344900, 0, 0, 0, 0, 0, 1923322336, 0, 0, 0, 0, 0, -1221811620, 0, 0, 0, 0, 0, 941223888, 0, 0, 0, 0, 0, -957299968, 0, 0, 0, 0, 0, -184097760, 0, 0, 0, 0, 0, 2622711966, 0, 0, 0, 0, 0, 873972536, 0, 0, 0, 0, 0, -383313600, 0, 0, 0, 0, 0, 250901040, 0, 0, 0, 0, 0, -181153860, 0, 0, 0, 0, 0, -66417656, 0, 0, 0, 0, 0, 2523134948, 0, 0, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "72.7.e.a", "char_is_minimal": false, "conrey_index": 17, "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], [1, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [-60, 0], [0, 0], [0, 0], [0, 0], [0, -236], [0, 0], [1192, 0], [0, 0], [0, 0], [0, 0], [0, 2935], [0, 0], [-8432, 0], [0, 0], [0, 0], [0, 0], [0, -4532], [0, 0], [15575, 0], [0, 0], [0, 0], [0, 0], [0, 23787], [0, 0], [-46892, 0], [0, 0], [0, 0], [0, 0], [0, -300], [0, 0], [10926, 0], [0, 0], [0, 0], [0, 0], [0, 51921], [0, 0], [-59416, 0], [0, 0], [0, 0], [0, 0], [0, 83004], [0, 0], [-114049, 0], [0, 0], [0, 0], [0, 0], [0, 58259], [0, 0], [2360, 0], [0, 0], [0, 0], [0, 0], [0, 199336], [0, 0], [-339902, 0], [0, 0], [0, 0], [0, 0], [0, 5960], [0, 0], [148024, 0], [0, 0], [0, 0], [0, 0], [0, 291044], [0, 0], [-401552, 0], [0, 0], [0, 0], [0, 0], [0, 14160], [0, 0], [-79156, 0], [0, 0], [0, 0], [0, 0], [0, 70988], [0, 0], [-29350, 0], [0, 0], [0, 0], [0, 0], [0, 265785], [0, 0], [-71520, 0], [0, 0], [0, 0], [0, 0], [0, -42160], [0, 0], [663920, 0], [0, 0], [0, 0], [0, 0]]}