# Stored data for newform 108.2.i.a, downloaded from the LMFDB on 23 April 2024.
{"label": "108.2.i.a", "space_label": "108.2.i", "level": 108, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 549789368428, "dim": 18, "is_polredabs": true, "trace_hash": 1837339998080358926, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\beta _{12}q^{3}+(-1+\\beta _{1}-\\beta _{4}-\\beta _{6}-\\beta _{7}+\\cdots)q^{5}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 27, "char_orbit_label": "i", "char_is_real": false, "Nk2": 432, "analytic_conductor": 0.8623843418298281, "hecke_ring_index": 27, "level_radical": 6, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.026", "prec": 17}, "analytic_rank_proved": true, "char_values": [108, 9, [55, 29], [9, 4]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [13, 25, 49, 61, 85, 97], "field_disc": -1399963599251637393713067, "field_disc_factorization": [[-1, 1], [3, 27], [428471, 2]], "field_poly": [19683, -39366, 52488, -48114, 37179, -25515, 17577, -12150, 8100, -4941, 2700, -1350, 651, -315, 153, -66, 24, -6, 1], "hecke_ring_index_factorization": [[3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "17.733", "prec": 20}, {"__RealLiteral__": 0, "data": "4.165", "prec": 17}, {"__RealLiteral__": 0, "data": "928.197", "prec": 24}, {"__RealLiteral__": 0, "data": "968.478", "prec": 24}, {"__RealLiteral__": 0, "data": "77378.412", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c9", "trace_display": [0, 0, 3, 0], "traces": [0, 18, 0, 0, 0, 3, 0, 0, 0, 6, 0, 3, 0, 0, 0, -9, 0, -12, 0, 0, 0, -30, 0, -30, 0, 9, 0, -27, 0, -24, 0, 9, 0, -18, 0, -21, 0, 0, 0, 3, 0, 21, 0, -9, 0, 45, 0, 45, 0, -18, 0, 63, 0, 66, 0, 0, 0, 54, 0, 60, 0, -18, 0, 57, 0, 33, 0, -27, 0, -9, 0, -12, 0, 9, 0, -33, 0, -75, 0, -36, 0, -54, 0, -45, 0, -36, 0, -63, 0, -48, 0, 9, 0, -33, 0, 6, 0, -27, 0, 27, 0, 15, 0, -18, 0, 54, 0, 30, 0, 0, 0, 54, 0, 36, 0, -9, 0, -42, 0, -15, 0, 9, 0, -27, 0, -57, 0, 0, 0, -75, 0, -33, 0, 27, 0, -54, 0, -78, 0, 45, 0, -9, 0, -3, 0, 0, 0, 18, 0, 15, 0, 90, 0, 45, 0, 114, 0, 81, 0, 63, 0, 138, 0, -54, 0, 99, 0, 36, 0, 90, 0, 48, 0, 0, 0, 99, 0, 18, 0, -33, 0, 0, 0, -21, 0, -30, 0, 45, 0, -81, 0, -93, 0, 18, 0, -117, 0, -12, 0, 0, 0, -15, 0, -66, 0, 9, 0, -54, 0, -21, 0, 18, 0, 0, 0, -84, 0, -18, 0, -45, 0, 3, 0, -54, 0, -39, 0, -18, 0, -72, 0, -81, 0, -24, 0, -27, 0, -3, 0, -36, 0, -81, 0, -45, 0, -9, 0, -90, 0, 54, 0, -6, 0, -27, 0, 36, 0, 45, 0, -108, 0, 72, 0, 33, 0, -99, 0, 90, 0, 120, 0, -18, 0, 72, 0, 84, 0, -27, 0, 66, 0, 3, 0, -27, 0, 63, 0, 78, 0, -9, 0, 33, 0, 78, 0, 45, 0, 27, 0, 84, 0, 63, 0, 90, 0, -30, 0, -18, 0, -15, 0, -6, 0, 45, 0, -18, 0, -57, 0, 117, 0, -126, 0, -42, 0, 0, 0, -63, 0, -126, 0, 108, 0, 12, 0, 33, 0, 63, 0, 9, 0, -21, 0, -18, 0, 9, 0, 27, 0, 36, 0, 45, 0, 66, 0, 18, 0, 18, 0, 54, 0, -9, 0, 141, 0, 78, 0, -27, 0, -18, 0, 24, 0, -99, 0, 45, 0, -30, 0, 54, 0, -9, 0, 39, 0, -144, 0, -15, 0, 33, 0, -126, 0, 45, 0, 51, 0, 0, 0, -15, 0, 21, 0, -144, 0, 126, 0, -21, 0, -135, 0, -45, 0, 3, 0, 0, 0, -96, 0, -144, 0, -72, 0, -144, 0, -147, 0, -63, 0, -207, 0, -192, 0, 54, 0, -216, 0, -132, 0, -18, 0, -135, 0, -171, 0, 45, 0, -72, 0, 0, 0, 27, 0, 42, 0, -24, 0, 135, 0, 90, 0, 57, 0, 144, 0, 36, 0, 93, 0, 54, 0, -51, 0, -3, 0, 198, 0, 81, 0, 9, 0, 171, 0, -72, 0, -138, 0, 108, 0, -27, 0, 6, 0, 180, 0, 0, 0, 147, 0, 162, 0, 27, 0, 63, 0, 54, 0, 189, 0, 120, 0, 117, 0, 18, 0, 141, 0, 135, 0, 216, 0, 6, 0, 36, 0, -150, 0, 93, 0, -18, 0, -108, 0, -147, 0, -99, 0, -36, 0, -72, 0, 0, 0, -54, 0, -201, 0, -108, 0, 21, 0, -48, 0, -135, 0, 81, 0, 6, 0, 63, 0, 90, 0, 171, 0, -216, 0, 216, 0, 258, 0, -225, 0, -9, 0, 141, 0, 63, 0, 93, 0, 72, 0, -153, 0, 36, 0, -66, 0, -108, 0, -63, 0, 24, 0, 0, 0, -54, 0, -66, 0, -99, 0, -24, 0, 84, 0, -63, 0, 144, 0, 63, 0, 9, 0, 54, 0, 21, 0, -18, 0, 117, 0, -6, 0, 54, 0, -144, 0, -87, 0, 0, 0, 21, 0, -147, 0, 144, 0, -216, 0, -150, 0, 81, 0, -144, 0, -270, 0, -54, 0, -225, 0, 6, 0, 63, 0, -168, 0, -228, 0, 90, 0, -117, 0, 93, 0, 0, 0, -30, 0, 33, 0, 90, 0, 81, 0, 33, 0, -36, 0, 171, 0, 0, 0, -27, 0, -78, 0, -57, 0, -117, 0, 36, 0, -30, 0, -63, 0, 0, 0, -60, 0, -126, 0, 27, 0, 21, 0, -135, 0, 102, 0, 75, 0, -225, 0, 36, 0, 126, 0, -54, 0, 150, 0, 111, 0, -189, 0, -45, 0, 120, 0, -135, 0, 117, 0, 96, 0, -54, 0, 159, 0, -54, 0, -171, 0, 117, 0, 33, 0, -135, 0, -162, 0, 78, 0, -126, 0, 27, 0, -117, 0, 54, 0, -126, 0, 174, 0, 90, 0, 54, 0, -27, 0, -81, 0, 183, 0, 150, 0, 126, 0, 162, 0, -12, 0, 198, 0, 198, 0, 135, 0, -108, 0, 126, 0, 225, 0, 216, 0, -126, 0, 78, 0, 333, 0, 54, 0, 60, 0, 0, 0, 18, 0, -3, 0, 288, 0, 87, 0, -129, 0, 270, 0, 90, 0, 33, 0, -108, 0, -48, 0, 90, 0, 243, 0, 81, 0, 63, 0, 144, 0, -9, 0, 9, 0, -54, 0, -42, 0, -159, 0, 99, 0, -126, 0, -90, 0, 45, 0, -153, 0, -12, 0, 108, 0, -234, 0, -75, 0, -81, 0, -6, 0, -213, 0, -162, 0, -90, 0, -96, 0, 0, 0, -54, 0, -105, 0, -180, 0, -189, 0, -45, 0, -180, 0, -18, 0, -111, 0, 0, 0, 60, 0, -3, 0, -162, 0, -225, 0, 18, 0, -135, 0, 63, 0, -300, 0, 144, 0, 0, 0, -33, 0, -108, 0, -60, 0, 18, 0, 9, 0, -135, 0, 63, 0, 27, 0, -66, 0, 42, 0, 72, 0, -54, 0, -63, 0, 9, 0, -36, 0, -9, 0, 54, 0, -162, 0, -75, 0, 171, 0, 72, 0, -183, 0, 126, 0, -36, 0, 108, 0, 36, 0, 126, 0, -66, 0, 180, 0, 30, 0, 24, 0, 180, 0, 108, 0, -105, 0, 63, 0, -84, 0, 15, 0, -72, 0, -108, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 27, 5, 1, 9, 0]], "char_orbit_index": 9, "prim_orbit_index": 5, "minimal_twist": "108.2.i.a", "char_is_minimal": true, "conrey_index": 13, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": 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, 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], [-1, 1, 0, 0, -1, 0, -1, -1, 1, 0, 0, 1, 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, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 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, 0, 1, -1, 0, 0, 0, -1, -1, 0, 0, -1, 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, 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], [0, -1, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, -2, 0, -2, 1, 0, -1, -1, -1, -2, 1, -1, -2, 0, 1, 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, -2, -1, 1, 2, 1, 2, -1, 0, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 0, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 1, -2, 0, -1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 0, -3, -1, -1, 1, 1, -1, 0, 0, 1, -1, -1, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 2, 0, 0, -2, 0, 0, -2, -1, 1, -2, -2, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 0, 1, 0, -2, -1, 0, -4, 2, 1, 1, -1, 2, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -1, 1, 1, 3, 1, -2, 2, -3, -1, -1, 0, 0, 0, -2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 1, 0, 1, 2, 1, 0, 0, -1, 2, -1, 1, -1, 0, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -2, 2, 1, 2, 2, 1, 5, -3, -3, 0, 2, -1, -2, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 1, 4, 0, -4, -2, 1, -2, 0, 0, -1, -1, 1, 1, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, -1, 0, -1, -3, 0, 0, 1, 2, 1, 0, 0, 1, 1, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 2, -1, 0, 1, 0, 0, -2, -3, 2, 2, 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, 1, 1, -2, -2, 3, 1, 0, 0, 2, -2, -2, 2, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 2, 1, -2, -1, -1, -3, 0, 1, 2, -1, -1, 1, 2, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -3, -2, -1, -1, 0, 1, 4, 1, 4, -2, 2, 1, 1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -3, -1, -1, 2, -1, 1, 1, 2, 1, 0, -4, 2, 0, 1, -2, 2, -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, 1, 1, 0, -2, 0, 2, 2, -1, -2, -1, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 0, -1, -1, 0, -1, -2, 0, 3, -3, 1, 1, -1, -2, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 1, -2, 0, -1, -1, 0, -4, 2, 1, 1, 1, 1, 1, 3, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, 0, 2, -1, -2, 4, -1, -2, 0, 4, -2, -1, 0, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 2, 1, 4, 1, -2, -2, 0, 3, 1, 2, -1, -1, 0, 3, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -1, 0, 0, 0, 1, 0, 2, 2, -5, 0, 2, 1, 0, -1, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, -1, -1, -2, 1, 0, -1, -2, -1, -2, 2, -1, -2, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 1, 0, 3, 1, 4, -1, 0, 0, -3, 2, -2, -2, 1, 1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 5, 1, 1, 4, 3, -5, -1, 0, 3, 0, 2, 0, -1, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, -1, 2, -2, -1, -1, -3, -1, -2, -1, 3, -1, 1, -1, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, -2, 1, -4, 1, 0, 0, -1, -1, -4, 0, -1, 1, -2, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, -1, 0, 1, 0, 0, 2, 5, 0, 1, -2, 2, 1, 1, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, 2, -2, -2, 0, -1, -2, -1, 1, 1, -2, 0, 0, 1, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, -6, 0, 6, 0, 0, 6, 6, -1, 0, 2, 0, 0, -3, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 1, 2, -4, -2, -5, -2, 0, -5, 3, -1, 1, 0, 3, 2, 1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 3, 0, 1, -1, 2, -3, 0, 2, 2, 2, 2, -1, 2, 2, 2, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 2, 1, 4, -2, -2, 1, 1, -3, 1, 0, 2, -3, 0, 0, 1, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 2, 4, 2, 3, 1, -5, 1, -6, 0, -2, 0, 1, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, -2, 2, 0, 0, -2, 0, -2, 3, -2, 0, -3, 0, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 3, 1, -1, -1, -3, -1, 1, -2, 2, 6, -2, 0, 0, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -4, -2, 1, 1, -2, 1, 1, 1, -2, -4, -6, 3, -1, -2, -1, 3, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 0, 1, 3, 0, 2, -1, 0, -2, 0, -3, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, -3, 0, 3, 0, 0, 1, -3, 0, -1, 6, 2, 0, 0, 0, 2, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, -2, 4, 0, 3, -1, -3, 1, 3, -2, -5, -1, -1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 0, -1, 2, -3, 2, 4, -2, -1, 0, 0, 0, 0, -2, -1, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -3, -1, -1, 2, -1, 0, -2, 3, -1, -1, 4, -1, 0, 0, -1, 3, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}