# Stored data for newform 693.4.a.h, downloaded from the LMFDB on 13 March 2026.
{"Nk2": 11088, "analytic_conductor": 40.888323633978246, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [7, -1], [11, -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": [693, 1, [155, 199, 442], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 37, "field_disc_factorization": [[37, 1]], "field_poly": [-9, -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, [-7, 3, 1]], [5, [-147, 2, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525197458703029, "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": "693.4.a.h", "level": 693, "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, 7, 11], "level_radical": 231, "minimal_twist": "231.4.a.i", "nf_label": "2.2.37.1", "prim_orbit_index": 1, "qexp_display": "q+(-1-\\beta )q^{2}+(2+3\\beta )q^{4}+(1-4\\beta )q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "693.4.a", "trace_display": [-3, 0, -2, 14], "trace_hash": 43587073584404632, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.955", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.568", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "67.108", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 2, -3, 0, 7, -2, 0, 14, -42, 0, 77, 22, 0, -134, -21, 0, 7, 26, 0, 152, -229, 0, -33, -178, 0, 48, 127, 0, 49, -190, 0, 346, 381, 0, -446, -14, 0, -206, 105, 0, 42, -244, 0, 242, 77, 0, 452, -920, 0, 98, -220, 0, -247, 550, 0, -22, -294, 0, -825, 412, 0, 252, -630, 0, -646, -162, 0, 16, 1312, 0, 539, 572, 0, -1026, -875, 0, -467, 154, 0, -52, 215, 0, -744, -138, 0, -1654, 1672, 0, -462, -1512, 0, -938, -1178, 0, 1121, 1180, 0, -1106, -147, 0, 612, -1622, 0, 1232, 2814, 0, -1676, 592, 0, -1794, 847, 0, 49, -2376, 0, 918, 2665, 0, -1543, 182, 0, 242, -2746, 0, 1544, -390, 0, -1670, 1029, 0, -4641, -2280, 0, 1064, 679, 0, -546, -1222, 0, -2436, -1603, 0, -3448, -1474, 0, -4250, -2383, 0, 2831, 434, 0, -530, -3192, 0, -231, -790, 0, -3388, -144, 0, 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