# Stored data for newform 2175.2.a.r, downloaded from the LMFDB on 12 January 2026.
{"Nk2": 8700, "analytic_conductor": 17.367462439628483, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [5, 1], [29, -1]], "atkin_lehner_string": "++-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [2175, 1, [1451, 2002, 901], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 21, "field_disc_factorization": [[3, 1], [7, 1]], "field_poly": [-5, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-5, -1, 1]], [7, [1, 1]]], "hecke_orbit": 18, "hecke_orbit_code": 76561193698855039, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "2175.2.a.r", "level": 2175, "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": [3, 5, 29], "level_radical": 435, "minimal_twist": "435.2.a.f", "nf_label": "2.2.21.1", "prim_orbit_index": 1, "qexp_display": "q+\\beta q^{2}-q^{3}+(3+\\beta )q^{4}-\\beta q^{6}-q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "2175.2.a", "trace_display": [1, -2, 0, -2], "trace_hash": 1216888275797813433, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.902", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.159", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.932", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "traces": [0, 2, 1, -2, 7, 0, -1, -2, 12, 2, 0, 10, -7, 0, -1, 0, 13, 6, 1, -2, 0, 2, 5, 8, -12, 0, -21, -2, -7, 2, 0, 8, 35, -10, 3, 0, 7, 8, -22, 0, 0, 0, 1, 10, 35, 0, 4, -12, -13, -12, 0, -6, -21, -10, -1, 0, -12, 2, 1, -6, 0, -2, 4, -2, 44, 0, -5, -10, 21, -8, 0, -10, 12, -8, 4, 0, -28, -10, 21, 6, 0, 2, 42, 14, 7, 0, -16, -2, 60, 12, 0, 0, 28, -8, 15, 0, -35, -14, -6, 10, 0, 8, -3, -12, -42, 0, -26, 8, -7, 10, 0, -8, -13, 10, 22, 0, 7, 0, 18, -6, 0, 28, -64, 0, 28, 0, -1, -4, 57, -10, 0, -30, -35, 2, -47, 0, 36, 4, -4, -28, 0, 12, 16, 0, 13, 0, -4, 12, 28, 6, 0, -4, -54, 6, -5, 0, 21, 6, -18, 10, 0, -8, 1, -6, 42, 0, -14, 0, 12, 16, 0, -2, 14, -12, -1, 0, 65, 6, 27, -18, 0, 14, 21, 2, 48, 0, -4, 30, -21, 2, 0, -8, -44, 4, 14, 0, -42, -4, 5, 36, 0, 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