# Stored data for newform 7225.2.a.bt, downloaded from the LMFDB on 17 May 2024.
{"label": "7225.2.a.bt", "space_label": "7225.2.a", "level": 7225, "weight": 2, "hecke_orbit": 46, "hecke_orbit_code": 202661983265233977, "dim": 15, "is_polredabs": true, "trace_hash": 332416264885987270, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [3, -81, 18, 555, -183, -1284, 301, 1350, -153, -678, 30, 171, -2, -21, 0, 1]], [3, [-1, 0, 171, -883, 501, 2463, -1340, -3093, 369, 1623, 258, -312, -105, 12, 9, 1]], [7, [3043, -8847, -39129, 59781, 167592, -11424, -158103, -65919, 25560, 21566, 2058, -1539, -385, 12, 12, 1]], [11, [2049, 15345, 1170, -64425, -44547, 72996, 78989, -10377, -30498, -2597, 4698, 666, -297, -48, 6, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(-1+\\beta _{12})q^{3}+(1+\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 28900, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 57.69191546037508, "hecke_ring_index": 1, "level_radical": 85, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, "analytic_rank_proved": true, "char_values": [7225, 1, [2602, 2026], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [5, 17], "conrey_indexes": [1], "field_disc": 19882633229457582677208741, "field_disc_factorization": [[3, 21], [1900761173509447, 1]], "field_poly": [3, -81, 18, 555, -183, -1284, 301, 1350, -153, -678, 30, 171, -2, -21, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.598", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "534.986", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "33359.945", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 15, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [17, -1]], "trace_display": [0, -9, 0, -12], "traces": [0, 15, 0, -9, 12, 0, -9, -12, 6, 12, 0, -6, -24, 0, 0, 0, 6, 0, 12, 6, 0, 30, -12, -36, -18, 0, 36, -36, -24, 18, 0, 0, 12, 12, 0, 0, -9, -12, -6, -9, 0, 18, 36, -3, 12, 0, -21, -3, 12, 15, 0, 0, -27, 0, -21, 0, 6, -39, -18, -12, 0, 15, -54, -60, -36, 0, 18, -24, 0, 42, 0, -6, 66, 9, 36, 0, -18, 30, -30, 9, 0, 51, 36, 15, 9, 0, -36, -51, -30, -24, 0, -27, -15, -42, -57, 0, -42, -48, 0, -12, 0, -6, 0, -6, 108, 0, -15, -48, -36, -24, 0, 12, -75, -51, 144, 0, 30, 84, -18, 0, 0, -33, -60, -6, 12, 0, -108, 0, -39, 18, 0, -48, 48, 6, 21, 0, 0, -39, -93, 33, 0, 18, -87, -84, 12, 0, -99, -123, 9, 18, 0, 6, 3, 0, 78, 0, -84, 48, 0, 96, 0, 24, 114, -18, 117, 0, 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