# Stored data for newform 2700.3.u.b, downloaded from the LMFDB on 24 April 2024.
{"label": "2700.3.u.b", "space_label": "2700.3.u", "level": 2700, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4504974067239564, "dim": 8, "is_polredabs": true, "nf_label": "8.0.303595776.1", "trace_hash": 1909401652612825786, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [29986576, 0, -815924, 0, 16725, 0, -149, 0, 1]]], "qexp_display": "q+(-\\beta _{3}+\\beta _{4}-2\\beta _{7})q^{7}+(12-5\\beta _{2}+\\cdots)q^{11}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 45, "char_orbit_label": "u", "char_is_real": false, "Nk2": 24300, "analytic_conductor": 73.56967137728016, "hecke_ring_index": 81, "level_radical": 30, "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": "0.593", "prec": 17}, "analytic_rank_proved": true, "char_values": [2700, 6, [1351, 1001, 2377], [6, 5, 3]], "hecke_ring_generator_nbound": 17, "inner_twist_count": 4, "level_primes": [2, 3, 5], "conrey_indexes": [449, 2249], "field_disc": 303595776, "field_disc_factorization": [[2, 8], [3, 4], [11, 4]], "field_poly": [81, 0, 45, 0, 16, 0, 5, 0, 1], "hecke_ring_index_factorization": [[3, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.069", "prec": 17}, {"__RealLiteral__": 0, "data": "7.124", "prec": 17}, {"__RealLiteral__": 0, "data": "7.958", "prec": 17}, {"__RealLiteral__": 0, "data": "399.561", "prec": 24}, {"__RealLiteral__": 0, "data": "915.889", "prec": 24}, {"__RealLiteral__": 0, "data": "36245.878", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -126, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -604, 0, 0, 0, 0, 0, 0, 0, 0, 0, -882, 0, 0, 0, 0, 0, 0, 0, -664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 344, 0, 0, 0, 0, 0, 0, 0, 0, 0, -126, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, 0, 0, 0, 0, -234, 0, -710, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -354, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 808, 0, 0, 0, 0, 0, 0, 0, 0, 0, -234, 0, 0, 0, 0, 0, 0, 0, 1040, 0, 0, 0, 0, 0, 0, 0, 0, 0, -630, 0, -962, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -670, 0, 0, 0, 0, 0, 0, 0, 0, 0, -810, 0, 196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 280, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1278, 0, 0, 0, 0, 0, 0, 0, -764, 0, 0, 0, 0, 0, 0, 0, 0, 0, 198, 0, -46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2574, 0, 0, 0, 0, 0, 0, 0, 630, 0, 0, 0, 0, 0, 0, 0, 0, 0, -810, 0, -626, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2292, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2448, 0, 0, 0, 0, 0, 0, 0, -1924, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1098, 0, 1584, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -616, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1458, 0, -506, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2736, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1710, 0, 0, 0, 0, 0, 0, 0, 3796, 0, 0, 0, 0, 0, 0, 0, 0, 0, 378, 0, 1028, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1584, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4014, 0, 848, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1250, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1456, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2016, 0, 0, 0, 0, 0, 0, 0, 460, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2628, 0, -248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 810, 0, 0, 0, 0, 0, 0, 0, -884, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2502, 0, 1528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4480, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1206, 0, -4322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3258, 0, 0, 0, 0, 0, 0, 0, 790, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2736, 0, 2662, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2070, 0, 0, 0, 0, 0, 0, 0, -4588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3204, 0, 598, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8370, 0, 0, 0, 0, 0, 0, 0, 2906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2358, 0, -1476, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2108, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4122, 0, 0, 0, 0, 0, 0, 0, -3568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2862, 0, 2810, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4356, 0, 0, 0, 0, 0, 0, 0, -2092, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5958, 0, -2362, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5404, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, -486, 0, 0, 0, 0, 0, 0, 0, 9848, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2754, 0, 246, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1062, 0, 0, 0, 0, 0, 0, 0, 676, 0, 0, 0, 0, 0, 0, 0, 0, 0, -990, 0, 1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5904, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2584, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3654, 0, 0, 0, 0, 0, 0, 0, -2800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5652, 0, 1246, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6174, 0, 0, 0, 0, 0, 0, 0, -766, 0, 0, 0, 0, 0, 0, 0, 0, 0, 414, 0, 304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1150, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5940, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2124, 0, 0, 0, 0, 0, 0, 0, 12028, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10242, 0, -5094, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2250, 0, 0, 0, 0, 0, 0, 0, -7372, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3438, 0, -1444, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -932, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14380, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7002, 0, 0, 0, 0, 0, 0, 0, -11844, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2412, 0, -2168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5778, 0, 0, 0, 0, 0, 0, 0, 1584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4698, 0, 2290, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2368, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3148, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7254, 0, 0, 0, 0, 0, 0, 0, 1760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6768, 0, 3964, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12330, 0, 0, 0, 0, 0, 0, 0, 5868, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3186, 0, 136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1886, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12204, 0, 0, 0, 0, 0, 0, 0, -600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19152, 0, 298, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2952, 0, 0, 0, 0, 0, 0, 0, 3290, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3420, 0, 1512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12996, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10782, 0, 0, 0, 0, 0, 0, 0, -9232, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7722, 0, 3190, 0, 0, 0, 0, 0, 0, 0, 0, 0, 468, 0, 0, 0, 0, 0, 0, 0, -2278, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7128, 0, 1568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2240, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9702, 0, 0, 0, 0, 0, 0, 0, 11528, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12978, 0, -4402, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10224, 0, 0, 0, 0, 0, 0, 0, -3982, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6210, 0, 1472, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2618, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6904, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6516, 0, 0, 0, 0, 0, 0, 0, -11916, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8226, 0, 5636, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18126, 0, 0, 0, 0, 0, 0, 0, 2198, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5148, 0, -280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6640, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16380, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3024, 0, 0, 0, 0, 0, 0, 0, -1480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6156, 0, 4738, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8064, 0, 0, 0, 0, 0, 0, 0, 11954, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3654, 0, -10890, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5978, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3708, 0, 0, 0, 0, 0, 0, 0, 4068, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8010, 0, -9446, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6606, 0, 0, 0, 0, 0, 0, 0, -5280, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9342, 0, -6614, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1862, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4772, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4374, 0, 0, 0, 0, 0, 0, 0, 5940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, -2376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7668, 0, 0, 0, 0, 0, 0, 0, -6830, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16830, 0, -1166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3244, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15588, 0, 0, 0, 0, 0, 0, 0, -11536, 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, 9, 4, -1, 6, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 45, 8, -1, 6, 0]], "char_orbit_index": 21, "prim_orbit_index": 8, "minimal_twist": "36.3.g.a", "char_is_minimal": false, "conrey_index": 449, "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, 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, 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, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [12, 0, -5, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 1, -2, 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, -15, 0, 7, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 2, -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, -17, 0, 33, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-21, 0, 14, 0, 0, -7, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 5, 0, 0, -3, -3, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, -18, 4, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [7, 0, -1, 0, 0, 8, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -23, 0, 23, 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, 12, 0, 15, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [25, 0, -26, 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, -24, 0, 16, -8, 0, 0, 8], [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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [25, 0, 17, 0, 0, 8, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 22, 0, 0, -3, 6, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 61, 0, -6, 12, 0, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [16, 0, -30, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, -23, 3, 0, 0, 3], [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, -55, 0, 93, 0, 0, 0, -17], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, -44, 0, 0, 5, -10, 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, -12, 0, -15, 3, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-64, 0, 120, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-77, 0, 3, 0, 0, -6, 3, 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, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 97, 0, -99, 2, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}