# Stored data for newform 100.2.e.d, downloaded from the LMFDB on 26 December 2025.
{"Nk2": 400, "analytic_conductor": 0.7985040202128039, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 20, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 4, "char_parity": 1, "char_values": [100, 4, [51, 77], [2, 1]], "cm_discs": [], "conrey_index": 7, "dim": 8, "field_disc": 3317760000, "field_disc_factorization": [[2, 16], [3, 4], [5, 4]], "field_poly": [16, 0, 0, 0, -7, 0, 0, 0, 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": [[3, [25, 0, 0, 0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13511073793572964, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 8, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 2, 5, 3, -1, 4, 0], [1, 1, 20, 4, -1, 2, 0], [1, 2, 20, 5, 1, 4, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "100.2.e.d", "level": 100, "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, 5], "level_radical": 10, "minimal_twist": "100.2.e.d", "nf_label": "8.0.3317760000.5", "prim_orbit_index": 5, "qexp_display": "q+\\beta _{1}q^{2}+(-\\beta _{4}+\\beta _{6})q^{3}+\\beta _{2}q^{4}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "100.2.e", "trace_display": [0, 0, 0, 0], "trace_hash": 2242134098990557697, "trace_moments": [{"__RealLiteral__": 0, "data": "0.055", "prec": 17}, {"__RealLiteral__": 0, "data": "7.412", "prec": 17}, {"__RealLiteral__": 0, "data": "8.143", "prec": 17}, {"__RealLiteral__": 0, "data": "906.438", "prec": 24}, {"__RealLiteral__": 0, "data": "1476.018", "prec": 27}, {"__RealLiteral__": 0, "data": "137419.993", "prec": 34}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.880", "prec": 17}, "traces": [0, 8, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -24, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 0, 0, 96, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, -80, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 16, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, -120, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, -48, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 136, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, -144, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 200, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, -32, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, -240, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, -264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, -64, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -112, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 96, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 80, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 120, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 136, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, -144, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 16, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 336, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, -240, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, -240, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, -56, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156, 0, 0, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 336, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 600, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, -232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, -64, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0], "weight": 2, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 1, 0], [0, 0, 0, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, -2], [0, -3, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, -2, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, -2, 0], [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, 1, 0, 0, 0, -4, 0, 0], [0, 0, 0, 0, 2, 0, -2, 0], [0, 0, -3, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 0, 0, -2], [0, -1, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 4], [0, 3, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 5, 0, 5, 0], [0, 0, 1, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2], [0, -4, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, -4, 0, -1, 0], [0, 0, 4, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 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, 1, -8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, -2], [0, 2, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, -6, 0, 1, 0], [0, 0, 0, -7, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 2], [0, -2, 0, 0, 0, -4, 0, 0], [0, 0, 0, 0, -2, 0, -2, 0], [0, 0, -1, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, -5, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0], [0, 0, 4, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [10, 0, 0, 0, 0, 0, 0, 5], [0, 3, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 2, 0, -1, 0], [0, 0, 0, 10, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, -4], [0, 2, 0, 0, 0, -4, 0, 0], [0, 0, 0, 0, 3, 0, 3, 0], [0, 0, -4, 8, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 8, 0, 2, 0], [0, 0, -8, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [11, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 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, -6, 0, 0, 0, -6, 0, 0], [0, 0, 0, 0, 2, 0, -7, 0], [0, 0, 0, -9, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, -4, 0, 0], [0, 0, 0, 0, -10, 0, -10, 0], [0, 0, 2, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-12, 0, 0, 0, 0, 0, 0, 1], [0, -4, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, -7, 0], [0, 0, -4, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}