# Stored data for newform 380.2.u.b, downloaded from the LMFDB on 19 April 2024.
{"label": "380.2.u.b", "space_label": "380.2.u", "level": 380, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504974050460028, "dim": 18, "is_polredabs": true, "trace_hash": 669173912569363823, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [5329, 219, 2901, -1309, 1386, -6228, 4117, -33, 1344, 1403, 45, 0, 113, -111, 60, 6, -3, -3, 1]]], "qexp_display": "q+\\beta _{13}q^{3}+(\\beta _{2}-\\beta _{11})q^{5}+(-\\beta _{1}-\\beta _{4}+\\cdots)q^{7}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 19, "char_orbit_label": "u", "char_is_real": false, "Nk2": 1520, "analytic_conductor": 3.0343152768086545, "hecke_ring_index": 1, "level_radical": 190, "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": "0.014", "prec": 17}, "analytic_rank_proved": true, "char_values": [380, 9, [191, 77, 21], [9, 9, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 5, 19], "conrey_indexes": [61, 81, 101, 161, 301, 321], "field_disc": -1107204545652479697239573067, "field_disc_factorization": [[-1, 1], [3, 27], [719, 2], [16759, 2]], "field_poly": [5329, -3285, 13851, -5266, 21573, -7125, 19237, -4101, 11430, -2224, 4413, -705, 1178, -207, 192, -30, 21, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "17.026", "prec": 20}, {"__RealLiteral__": 0, "data": "1.103", "prec": 17}, {"__RealLiteral__": 0, "data": "867.842", "prec": 24}, {"__RealLiteral__": 0, "data": "1255.630", "prec": 27}, {"__RealLiteral__": 0, "data": "75833.214", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c9", "trace_display": [0, 3, 0, 0], "traces": [0, 18, 0, 3, 0, 0, 0, 0, 0, 15, 0, 0, 0, 9, 0, 3, 0, 12, 0, -18, 0, -9, 0, 21, 0, 0, 0, 18, 0, -9, 0, 6, 0, -21, 0, -6, 0, -36, 0, -12, 0, 6, 0, -12, 0, -6, 0, 21, 0, -3, 0, -9, 0, 36, 0, -3, 0, -24, 0, 0, 0, -6, 0, 36, 0, 15, 0, 60, 0, 27, 0, -36, 0, -60, 0, -6, 0, -36, 0, -3, 0, 3, 0, -6, 0, 12, 0, 21, 0, 6, 0, -30, 0, -48, 0, -21, 0, -57, 0, 3, 0, 48, 0, 18, 0, -9, 0, -3, 0, -78, 0, -93, 0, -90, 0, 12, 0, -51, 0, -18, 0, 27, 0, 48, 0, -9, 0, 0, 0, 12, 0, -18, 0, -57, 0, -9, 0, 24, 0, 90, 0, 42, 0, 33, 0, 15, 0, 15, 0, -60, 0, 30, 0, 18, 0, 33, 0, -54, 0, 57, 0, 120, 0, 9, 0, 15, 0, -6, 0, -3, 0, -135, 0, -42, 0, 3, 0, 153, 0, 39, 0, 108, 0, 93, 0, 15, 0, -33, 0, 30, 0, 96, 0, 12, 0, 0, 0, 51, 0, 18, 0, 51, 0, -3, 0, 15, 0, -3, 0, -15, 0, -111, 0, 45, 0, 6, 0, 84, 0, 108, 0, 0, 0, 30, 0, -3, 0, -90, 0, -48, 0, -69, 0, 39, 0, 15, 0, 84, 0, 15, 0, -15, 0, 51, 0, -36, 0, -105, 0, -51, 0, -54, 0, 18, 0, -18, 0, 66, 0, 0, 0, -117, 0, -12, 0, -66, 0, -12, 0, -39, 0, -21, 0, -15, 0, -3, 0, -27, 0, -81, 0, 54, 0, -72, 0, -57, 0, -99, 0, 48, 0, 0, 0, 78, 0, 0, 0, 72, 0, 15, 0, -57, 0, -144, 0, 0, 0, 48, 0, 93, 0, 60, 0, -51, 0, 15, 0, -42, 0, -81, 0, 102, 0, -168, 0, 0, 0, -15, 0, -45, 0, -6, 0, -108, 0, 12, 0, -96, 0, -144, 0, 114, 0, 168, 0, -9, 0, 15, 0, 12, 0, 51, 0, 0, 0, 72, 0, 9, 0, -168, 0, -78, 0, -72, 0, 12, 0, 0, 0, 81, 0, 189, 0, 75, 0, 3, 0, -171, 0, -42, 0, -144, 0, 15, 0, 6, 0, 75, 0, 66, 0, 33, 0, 174, 0, 24, 0, -9, 0, -132, 0, -30, 0, 111, 0, -33, 0, 48, 0, 60, 0, -96, 0, -12, 0, 36, 0, 144, 0, 198, 0, -30, 0, 123, 0, -3, 0, -90, 0, 21, 0, -54, 0, 24, 0, -30, 0, 12, 0, -186, 0, -90, 0, -57, 0, 3, 0, 0, 0, 39, 0, 0, 0, -102, 0, -66, 0, -60, 0, 96, 0, -102, 0, 117, 0, -48, 0, 27, 0, 69, 0, -24, 0, -228, 0, -3, 0, -93, 0, -39, 0, 192, 0, 18, 0, -57, 0, 30, 0, -66, 0, -102, 0, -228, 0, 84, 0, 63, 0, -120, 0, 18, 0, -15, 0, -30, 0, -195, 0, 78, 0, 171, 0, -81, 0, 60, 0, 75, 0, 12, 0, 21, 0, 39, 0, 12, 0, 0, 0, 45, 0, 108, 0, -96, 0, 6, 0, -12, 0, 60, 0, -21, 0, -33, 0, 66, 0, -117, 0, 108, 0, -21, 0, 120, 0, 51, 0, 51, 0, 42, 0, 60, 0, 105, 0, -3, 0, 87, 0, 48, 0, 30, 0, 132, 0, 21, 0, 90, 0, 63, 0, 66, 0, 126, 0, 75, 0, -42, 0, 111, 0, -33, 0, 99, 0, -27, 0, 33, 0, 42, 0, -114, 0, 237, 0, -84, 0, 192, 0, -270, 0, 45, 0, -45, 0, -45, 0, 171, 0, 69, 0, 33, 0, 177, 0, 0, 0, 108, 0, 132, 0, -87, 0, -30, 0, 3, 0, 132, 0, 84, 0, -159, 0, -63, 0, -36, 0, -12, 0, -42, 0, 21, 0, -144, 0, -18, 0, 72, 0, 3, 0, -102, 0, -207, 0, -54, 0, -72, 0, 51, 0, -21, 0, 60, 0, -9, 0, 60, 0, 24, 0, -129, 0, -144, 0, 6, 0, -201, 0, 3, 0, 144, 0, 18, 0, -15, 0, 78, 0, -39, 0, 225, 0, -84, 0, 18, 0, -123, 0, 66, 0, -15, 0, -252, 0, 27, 0, -198, 0, 15, 0, -6, 0, -84, 0, 18, 0, 9, 0, -66, 0, -30, 0, -180, 0, 33, 0, 6, 0, 81, 0, 159, 0, -45, 0, 66, 0, -105, 0, -45, 0, 81, 0, 102, 0, 42, 0, -153, 0, -66, 0, -72, 0, 108, 0, 24, 0, -72, 0, -63, 0, 135, 0, 48, 0, -3, 0, 57, 0, -174, 0, 27, 0, 147, 0, -27, 0, -105, 0, -219, 0, -105, 0, 42, 0, 27, 0, 66, 0, -30, 0, -234, 0, 51, 0, -6, 0, 33, 0, -96, 0, -42, 0, 207, 0, -93, 0, 69, 0, -90, 0, -183, 0, -54, 0, 9, 0, 21, 0, -24, 0, -207, 0, 57, 0, -54, 0, -252, 0, -186, 0, -213, 0, -108, 0, -3, 0, -48, 0, -78, 0, -102, 0, -21, 0, 39, 0, 63, 0, -15, 0, 123, 0, -33, 0, -42, 0, -168, 0, 9, 0, 237, 0, -198, 0, 0, 0, 0, 0, 150, 0, -27, 0, -162, 0, -18, 0, -168, 0, -21, 0, 99, 0, 75, 0, 36, 0, -51, 0, 69, 0, 3, 0, -261, 0, 12, 0, 129, 0, 78, 0, 282, 0, 90, 0, 0, 0, 99, 0, 96, 0, 168, 0, -6, 0, -12, 0, -102, 0, 60, 0, 72, 0, 270, 0, 12, 0, 36, 0, -21, 0, 81, 0, 174, 0, 12, 0, 174, 0, -54, 0, 240, 0, 138, 0, 3, 0, -105, 0, 48, 0, -39, 0, 168, 0, 57, 0, 171, 0, 117, 0, -42, 0, 270, 0, 18, 0, 57, 0, 207, 0, -120, 0, 72, 0, -3, 0, 216, 0, -78, 0, -111, 0, -69, 0, -63, 0, -30, 0, -48, 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, 19, 5, 1, 9, 0]], "char_orbit_index": 21, "prim_orbit_index": 5, "minimal_twist": "380.2.u.b", "char_is_minimal": true, "conrey_index": 61, "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, 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, 1, 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, -1, 0, 0, -1, 0, 0, 0, -1, 1, 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], [1, 0, 1, 0, 0, 0, -1, 0, 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], [-1, 0, -1, 0, -1, 0, 1, -1, -1, 0, 0, 1, 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, -1, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 2, -1, 0, 0, -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, 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, -2, 1, 0, 1, 0, -1, 0, 1, 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, 0], [-2, 1, 1, -2, -1, -1, 1, 0, -1, 0, 1, 0, -1, 0, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, 1, -2, 0, -2, -1, 0, 0, -1, 0, 1, 1, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, 2, -1, -1, 0, 0, 1, -1, -1, 2, 0, 2, 0, 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, 0, 1, 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], [3, 0, 2, 2, 3, 0, -2, 0, 2, 0, -1, -3, -1, 1, -1, 2, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 2, -1, -2, -2, -1, 4, -1, -1, 0, 2, 3, 0, 0, 1, -3, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -2, 0, 0, 0, -1, 0, 1, -2, 1, 1, 2, 0, -1, 1, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -2, 0, -1, 1, -1, 0, -1, 1, 0, 2, 2, 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, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, 0, 2, 0, 1, -2, -1, -1, -1, -1, -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], [-2, 2, 2, -2, 0, -2, 3, -1, 0, 0, -1, 1, -1, 1, 1, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 0, 0, 1, 0, -2, 2, 0, 2, 0, -3, 1, -1, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -3, -1, -2, 2, 0, 0, -1, 1, 3, 3, 2, 0, -1, -3, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 0, 0, -1, 0, -1, -1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, 0, -2, 0, 3, -3, -2, 0, -1, 1, 0, 1, 3, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 0, 2, 0, -1, 2, 2, -2, -1, -3, -2, -1, -1, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 4, -1, 3, 0, 0, 1, 0, 4, -3, 0, 2, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 1, 1, 0, 1, -2, 0, 3, 2, -2, -1, 2, -5, 0, 0, 2, 1, 1], [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, 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], [-1, -1, 3, 0, 1, -1, 0, -1, 0, 0, -2, -5, -3, 0, -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, -2, -1, 1, -1, 2, 0, 1, 2, 0, 0, -2, 1, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 2, -2, 2, 2, 0, 4, -2, 0, 1, -1, -1, -2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, -2, 0, -1, -1, 0, -1, 1, -2, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 0, 2, 0, -1, 1, 0, 1, 0, -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], [6, 2, 2, 0, 4, 3, 0, 1, 2, 0, 2, -6, 0, -2, -1, 2, -2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, -2, 0, -4, 3, 2, -1, -1, 4, 0, 3, -2, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 2, 2, -1, -1, -1, 3, 2, 0, -2, -2, 2, 0, -1, 1, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, -2, 0, 2, 3, 0, 1, -1, 0, 1, 0, -2, 2, 2, -1, 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, -3, 1, 3, 0, 2, 1, -1, 1, 1, -1, 0, 0, -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, 0, -1, 2, 0, 0, 1, 0, -3, 0, 2, 2, 2, 1, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -3, 0, 2, 0, -1, -1, 2, 0, 2, 3, -1, 0, 1, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 2, -2, 5, 1, 1, -2, 0, -5, -2, 1, -1, 1, 0, 2], [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, 1, 0, -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], [2, 0, -3, 1, 2, 0, 3, 2, -1, 3, -2, -1, -4, 0, -2, -1, 3, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 4, -1, 0, 0, 1, -4, 0, 4, 0, 0, 1, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -2, -2, -2, 0, 0, -1, 0, -1, 1, 0, -1, -2, 0, 1, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 4, 4, -2, 5, -3, 5, 2, 0, -3, 0, 0, -8, 0, 2, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -2, 0, -1, 1, 1, 0, -1, 1, 2, 1, 0, -1, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 3, 1, -1, 1, -1, -1, 0, 1, 4, 0, -2, -4, 1, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -4, 1, -4, 0, 0, 1, 0, 1, -2, 2, 4, 1, 0, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}