# Stored data for newform 320.6.c.h, downloaded from the LMFDB on 19 April 2024. {"label": "320.6.c.h", "space_label": "320.6.c", "level": 320, "weight": 6, "hecke_orbit": 8, "hecke_orbit_code": 31525334931210560, "dim": 4, "is_polredabs": true, "nf_label": "4.0.400.1", "trace_hash": 1672621414180163876, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [55696, 0, 972, 0, 1]], [11, [0, 1]]], "qexp_display": "q+(5\\beta _{1}+\\beta _{2})q^{3}-5\\beta _{3}q^{5}+(-46\\beta _{1}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "c", "char_is_real": true, "Nk2": 11520, "analytic_conductor": 51.322822340153806, "hecke_ring_index": 400, "level_radical": 10, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.881", "prec": 17}, "analytic_rank_proved": true, "char_values": [320, 2, [191, 261, 257], [2, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 5], "conrey_indexes": [129], "field_disc": 400, "field_disc_factorization": [[2, 4], [5, 2]], "field_poly": [1, 0, 3, 0, 1], "hecke_ring_index_factorization": [[2, 4], [5, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.782", "prec": 17}, {"__RealLiteral__": 0, "data": "1.738", "prec": 17}, {"__RealLiteral__": 0, "data": "178.714", "prec": 24}, {"__RealLiteral__": 0, "data": "136.242", "prec": 24}, {"__RealLiteral__": 0, "data": "9394.484", "prec": 27}], "related_objects": [], "self_twist_discs": [-20], "cm_discs": [-20], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "5.2.1.d2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, -972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14408, 0, 0, 0, 12500, 0, 0, 0, -6744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -95000, 0, 0, 0, -67228, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 302344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 485804, 0, 0, 0, 0, 0, 0, 0, -597144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -550008, 0, 0, 0, 505000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -644204, 0, 0, 0, 0, 0, 0, 0, 268744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 665192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1889208, 0, 0, 0, 0, 0, 0, 0, 1485172, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1281608, 0, 0, 0, 0, 0, 0, 0, -3838000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4413992, 0, 0, 0, 4705000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3037500, 0, 0, 0, -4267256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -915000, 0, 0, 0, -7762456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1638792, 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, 5679428, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3621992, 0, 0, 0, 11685000, 0, 0, 0, 3770056, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4070408, 0, 0, 0, 0, 0, 0, 0, -11598744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17305000, 0, 0, 0, -11818456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9904396, 0, 0, 0, 0, 0, 0, 0, -35758000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9138392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18673992, 0, 0, 0, 23085000, 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, 23290404, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18191208, 0, 0, 0, 0, 0, 0, 0, -37356344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9960008, 0, 0, 0, 0, 0, 0, 0, -28921944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21221592, 0, 0, 0, 45025000, 0, 0, 0, -25745372, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54336808, 0, 0, 0, 18885000, 0, 0, 0, -88806000, 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, 61312392, 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, -24291888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -131518000, 0, 0, 0, 39062500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53525000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45090344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 77957608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15475000, 0, 0, 0, 93906056, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20678408, 0, 0, 0, -21075000, 0, 0, 0, -118050372, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96505000, 0, 0, 0, -83730456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -118392792, 0, 0, 0, 0, 0, 0, 0, -125529656, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15161144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145105992, 0, 0, 0, -114475000, 0, 0, 0, 4267944, 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, -70674212, 0, 0, 0, 0, 0, 0, 0, 165776456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 190082000, 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, 145991144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133651944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15423592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -127767192, 0, 0, 0, -342190000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -114516604, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -143526000, 0, 0, 0, 0, 0, 0, 0, -113133144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 20, 4, -1, 2, -20], [1, 1, 4, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "160.6.c.b", "char_is_minimal": false, "conrey_index": 129, "id": 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], [1, 0, 0, 0], [0, 0, 0, 0], [0, 5, 1, 0], [0, 0, 0, 0], [0, 0, 0, -5], [0, 0, 0, 0], [0, -46, -1, 0], [0, 0, 0, 0], [-243, 0, 0, 38], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 180, 95, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [3602, 0, 0, -202], [0, 0, 0, 0], [0, -664, -237, 0], [0, 0, 0, 0], [3125, 0, 0, 0], [0, 0, 0, 0], [0, -1368, -722, 0], [0, 0, 0, 0], [-1686, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -385, -915, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1882], [0, 0, 0, 0], [0, 1123, -1439, 0], [0, 0, 0, 0], [-23750, 0, 0, 1215], [0, 0, 0, 0], [0, -3866, 1203, 0], [0, 0, 0, 0], [-16807, 0, 0, 366], [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, -4674], [0, 0, 0, 0], [0, 14104, 7197, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -12853, -1195, 0], [0, 0, 0, 0], [75586, 0, 0, -6922], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 15625, 3125, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [121451, 0, 0, -9234], [0, 0, 0, 0], [0, 21187, 3117, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -8430, -1686, 0], [0, 0, 0, 0], [-149286, 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]]}