# Stored data for newform 152.2.q.c, downloaded from the LMFDB on 08 September 2025.
{"Nk2": 608, "analytic_conductor": 1.2137261107234618, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 19, "char_degree": 6, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 17, "char_orbit_label": "q", "char_order": 9, "char_parity": 1, "char_values": [152, 9, [39, 77, 97], [9, 9, 4]], "cm_discs": [], "conrey_index": 9, "dim": 18, "field_disc": -53647621209188234304330111003, "field_disc_factorization": [[-1, 1], [3, 27], [17, 2], [4933889, 2]], "field_poly": [1, 6, 132, -686, 8769, -6729, 14457, -2403, 12945, -2547, 4890, -972, 1304, -267, 204, -34, 21, -3, 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, [1, 33, 480, 3158, 8205, 2886, 11304, 1902, -912, -2523, 1638, -387, 200, 33, -21, 10, 3, 0, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9008298799923352, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 5, 1, 9, 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": "152.2.q.c", "level": 152, "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": [2, 19], "level_radical": 38, "minimal_twist": "152.2.q.c", "prim_orbit_index": 5, "qexp_display": "q+(\\beta _{2}-\\beta _{4})q^{3}+(-\\beta _{6}+\\beta _{7}-\\beta _{10}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c9", "self_twist_discs": [], "self_twist_type": 0, "space_label": "152.2.q", "trace_display": [0, 0, 0, -9], "trace_hash": 1842541272590902724, "trace_moments": [{"__RealLiteral__": 0, "data": "0.038", "prec": 17}, {"__RealLiteral__": 0, "data": "16.960", "prec": 20}, {"__RealLiteral__": 0, "data": "3.193", "prec": 17}, {"__RealLiteral__": 0, "data": "917.758", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "87515.442", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.012", "prec": 17}, "traces": [0, 18, 0, 0, 0, 0, 0, -9, 0, -6, 0, -3, 0, 3, 0, 33, 0, 9, 0, -24, 0, -15, 0, 6, 0, 6, 0, -12, 0, -3, 0, -6, 0, -45, 0, -15, 0, 48, 0, 12, 0, -18, 0, -39, 0, -42, 0, -27, 0, -18, 0, 48, 0, 39, 0, -27, 0, -6, 0, 9, 0, -24, 0, 3, 0, 27, 0, 39, 0, -3, 0, 0, 0, 12, 0, 90, 0, 60, 0, 63, 0, -6, 0, -27, 0, -30, 0, 18, 0, 66, 0, 108, 0, 60, 0, -75, 0, -81, 0, 15, 0, -3, 0, -3, 0, -18, 0, -66, 0, -72, 0, -57, 0, 18, 0, 48, 0, -93, 0, -72, 0, -48, 0, -102, 0, -45, 0, 27, 0, 48, 0, -6, 0, -12, 0, -6, 0, 30, 0, -42, 0, 36, 0, 36, 0, 54, 0, -18, 0, 51, 0, 48, 0, 126, 0, 30, 0, 30, 0, -24, 0, 3, 0, -33, 0, 66, 0, 54, 0, -9, 0, -87, 0, -30, 0, -54, 0, -3, 0, -66, 0, -72, 0, -48, 0, -123, 0, -6, 0, 36, 0, -6, 0, -39, 0, -153, 0, -33, 0, -12, 0, -36, 0, 57, 0, 12, 0, 51, 0, -24, 0, 33, 0, 66, 0, 87, 0, 33, 0, 123, 0, 54, 0, 114, 0, 21, 0, 60, 0, 78, 0, 156, 0, 6, 0, -6, 0, -39, 0, 72, 0, -6, 0, 93, 0, 81, 0, -21, 0, -69, 0, 87, 0, 3, 0, -15, 0, 3, 0, -39, 0, -126, 0, -84, 0, 102, 0, -36, 0, -114, 0, 33, 0, -12, 0, -66, 0, -36, 0, -87, 0, -30, 0, -99, 0, 81, 0, 12, 0, -57, 0, 0, 0, 30, 0, -9, 0, -6, 0, 24, 0, 39, 0, -198, 0, -6, 0, 60, 0, -24, 0, 6, 0, 39, 0, -3, 0, 18, 0, -78, 0, 9, 0, 9, 0, -18, 0, -36, 0, -21, 0, -72, 0, 15, 0, -15, 0, 57, 0, -3, 0, -156, 0, -120, 0, -129, 0, -45, 0, 15, 0, 84, 0, 0, 0, 24, 0, -150, 0, -27, 0, -30, 0, 156, 0, -84, 0, -60, 0, 54, 0, -84, 0, 39, 0, 156, 0, 81, 0, 138, 0, -72, 0, 66, 0, 189, 0, 102, 0, 21, 0, 21, 0, -30, 0, 54, 0, -120, 0, 150, 0, 27, 0, 18, 0, 84, 0, 57, 0, -57, 0, -24, 0, 0, 0, -36, 0, -24, 0, 12, 0, 48, 0, 48, 0, 66, 0, -9, 0, 105, 0, -132, 0, -81, 0, -45, 0, 162, 0, -78, 0, -45, 0, -57, 0, -3, 0, 30, 0, 54, 0, 0, 0, 39, 0, -258, 0, -12, 0, -81, 0, 87, 0, 24, 0, 183, 0, -24, 0, -75, 0, -135, 0, 144, 0, -141, 0, -15, 0, 21, 0, -42, 0, -75, 0, 27, 0, 72, 0, 36, 0, 75, 0, 54, 0, -228, 0, -99, 0, 171, 0, 102, 0, 51, 0, -6, 0, -27, 0, -9, 0, -9, 0, 81, 0, 195, 0, 114, 0, 42, 0, -27, 0, -21, 0, -24, 0, 117, 0, -90, 0, 90, 0, -162, 0, 219, 0, -3, 0, 15, 0, 309, 0, 75, 0, -135, 0, -90, 0, 24, 0, 147, 0, -30, 0, -36, 0, -51, 0, 30, 0, -108, 0, -84, 0, 90, 0, -72, 0, -222, 0, -24, 0, -18, 0, 6, 0, -48, 0, -81, 0, 36, 0, -162, 0, -153, 0, -18, 0, -138, 0, 63, 0, -27, 0, -165, 0, -27, 0, -18, 0, 120, 0, -54, 0, -117, 0, -96, 0, -96, 0, -75, 0, 0, 0, 78, 0, -156, 0, -84, 0, -90, 0, -201, 0, -186, 0, 6, 0, 9, 0, -258, 0, 117, 0, -63, 0, -120, 0, 27, 0, 45, 0, 12, 0, -300, 0, 78, 0, 174, 0, 24, 0, 78, 0, 291, 0, 18, 0, 72, 0, -132, 0, 120, 0, 237, 0, -78, 0, 129, 0, 297, 0, 12, 0, 0, 0, 9, 0, 306, 0, 99, 0, 42, 0, 30, 0, -111, 0, 36, 0, 66, 0, -135, 0, 162, 0, -75, 0, 33, 0, -63, 0, 135, 0, 231, 0, 303, 0, -117, 0, 24, 0, 111, 0, 120, 0, 138, 0, 60, 0, 192, 0, -96, 0, 48, 0, 189, 0, 144, 0, 42, 0, -12, 0, -102, 0, -93, 0, -144, 0, 3, 0, -54, 0, -12, 0, -9, 0, 27, 0, -159, 0, -129, 0, -291, 0, 135, 0, -402, 0, -390, 0, -72, 0, 30, 0, 33, 0, 147, 0, 12, 0, 21, 0, -315, 0, 81, 0, 60, 0, 51, 0, -21, 0, -90, 0, 105, 0, 177, 0, 48, 0, 186, 0, 162, 0, -102, 0, -180, 0, 126, 0, -204, 0, 66, 0, 54, 0, 18, 0, 9, 0, 99, 0, 111, 0, -42, 0, 156, 0, -261, 0, -96, 0, -132, 0, 141, 0, -60, 0, -174, 0, -39, 0, 222, 0, 156, 0, -138, 0, 27, 0, 30, 0, -24, 0, -54, 0, -3, 0, 162, 0, -39, 0, 228, 0, 138, 0, -66, 0, 138, 0, 87, 0, -168, 0, 15, 0, 159, 0, -54, 0, -192, 0, 228, 0, 75, 0, 90, 0, 0, 0, 63, 0, -18, 0, -159, 0, -126, 0, -51, 0, -24, 0, -372, 0, 99, 0, 0, 0, -9, 0, -12, 0, -27, 0, 48, 0, -225, 0, -132, 0, 54, 0, -363, 0, -30, 0, -18, 0, -162, 0, -99, 0, -57, 0, -171, 0, -81, 0, -69, 0, 90, 0, 93, 0, -78, 0, -45, 0, 54, 0, 153, 0, -39, 0, -6, 0, 276, 0, -42, 0, 75, 0, 207, 0, -111, 0, -48, 0, 63, 0, 138, 0, 105, 0, 78, 0, -81, 0, 12, 0, -141, 0, 27, 0, -84, 0, -57, 0, 21, 0, -9, 0, 33, 0, -66, 0, -168, 0, 267, 0, -174, 0, -3, 0, -39, 0, 45, 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, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 1, 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, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, -1, -1, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, 1, 0, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, -1, 2, 0, 1, 1, 0, 0, 0, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 1, 0, -1, -1, 0, -1, 1, 0, -1, -1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, 0, -1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 2, 1, -1, 0, 0, 1, 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], [-1, -1, 0, 1, 1, 0, 0, 0, -1, -3, 1, -3, 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, -2, -2, -1, 0, 0, 0, 0, -1, 2, 2, 0, -1, 0, 0, 2, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, -1, 0, 1, -1, 0, -1, -1, -1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, 1, -1, 1, -1, 0, -1, 0, -1, -2, 2, 2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 0, -1, -1, 0, 1, -3, 2, 0, -1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, -2, 1, 1, 2, -1, 1, 3, -3, 0, -2, -2, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, -1, -1, 1, 3, 0, -3, 2, 3, 0, 1, -3, -2, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 1, -2, 2, -1, -1, -1, 1, -1, 0, 0, 1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 1, -1, 2, -2, -1, -1, 1, 1, 0, 2, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 0, 1, -1, 2, 1, -1, 1, 0, -1, -1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 2, 0, 0, 0, -1, 1, -1, -1, 0, 2, 2, 0, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 2, 1, 1, -2, -1, 1, -2, 2, 1, 0, 3, 5, -3, 1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -2, 0, 1, 1, -1, 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, 0, 0, -2, 0, 0, 1, 0, -3, -3, 1, 3, -3, -3, -1, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 2, 0, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 1, 0, -1, 0, 0, 1, 2, 3, 0, 3, 1, -3, -1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -3, -2, 0, -2, 0, -1, -2, 2, -3, 4, 1, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, -1, 1, 2, 1, 1, 2, -3, 1, -1, -2, -4, 1, -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, 1, 0, 0, 0, 0, 0, 0, -1, 1, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, 1, -1, 2, 1, 0, 1, -1, 0, -1, 0, 2, -1, -1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 2, 1, 0, -3, 1, 4, 4, -2, 0, 4, -1, 0, -2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 1, -1, -4, 1, 2, 0, 6, -4, 0, -6, 3, -4, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 1, -1, -3, -2, 2, 1, -3, 0, 0, 0, 2, 2, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 0, 0, -1, -1, 0, -3, -3, 3, -1, 0, -1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 2, -1, -1, -1, -1, 1, -1, -3, 0, -4, -4, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -3, 0, 1, 0, -1, -2, 1, 4, 2, 0, 2, -2, -4, 0, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 1, 0, 0, 1, -2, 4, -4, -4, -2, -6, 0, -2, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 3, 0, -2, 0, -3, 2, 2, 2, -1, 4, 0, 2, -1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 2, 1, -2, 1, 2, 0, -2, 1, 2, 0, 6, -2, -1, -2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, 0, 0, -1, 0, 0, 0, -2, 3, 0, 0, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, -1, 0, 2, -1, 1, 0, 1, 2, -1, -1, 1, 5, -1, 2, 0, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 1, -2, 2, 0, 0, 0, -1, 0, 1, 4, 4, 4, -3, 1, -3, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, -1, -2, 0, 1, 0, -5, 3, -1, 5, 1, 3, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 1, 1, -1, -1, 0, 0, -1, -5, -5, 2, 0, -5, 5, 0, 2, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -2, 0, 0, 1, -1, 0, 0, 8, 3, 0, 3, -2, -6, 1, -2, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 1, 0, 3, 0, 3, 0, -3, -1, -2, -1, -2, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 2, 0, -2, 0, -3, 1, 2, 1, 0, -5, -5, 2, -2, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, -1, 0, 2, -4, -1, 1, 0, 0, 5, -2, 3, 2, 3, 1, -1, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, -3, -2, -1, -1, 0, -3, 0, -6, -2, -6, 3, -3, 1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}