# Stored data for newform 961.2.g.m, downloaded from the LMFDB on 04 September 2025.
{"Nk2": 3844, "analytic_conductor": 7.673623634245045, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 31, "char_degree": 8, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 15, "char_parity": 1, "char_values": [961, 15, [3], [13]], "cm_discs": [], "conrey_index": 235, "dim": 16, "field_disc": 4208972802978515625, "field_disc_factorization": [[3, 8], [5, 12], [1621, 2]], "field_poly": [1, 0, 44, 0, 410, 0, 956, 0, 979, 0, 511, 0, 140, 0, 19, 0, 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": [[2, [81, -81, 729, 189, 1521, -18, 561, 132, 292, -282, 221, -22, 6, -4, 9, -4, 1]], [3, [961, 3162, 7574, 15771, 20442, 14157, 4258, -219, -244, 129, 118, 108, 72, 9, -1, 3, 1]]], "hecke_orbit": 13, "hecke_orbit_code": 54043607878861761, "hecke_ring_generator_nbound": 3, "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, 31, 7, 1, 15, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "961.2.g.m", "level": 961, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": true, "level_is_square": true, "level_is_squarefree": false, "level_primes": [31], "level_radical": 31, "minimal_twist": "31.2.g.a", "prim_orbit_index": 7, "qexp_display": "q+(\\beta _{2}-\\beta _{3}-\\beta _{9}-\\beta _{10}+\\beta _{12}+\\beta _{13}+\\cdots)q^{2}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c15", "self_twist_discs": [], "self_twist_type": 0, "space_label": "961.2.g", "trace_display": [4, -3, -3, -3], "trace_hash": 806568765471253122, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.880", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "572.522", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "39198.053", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.008", "prec": 17}, "traces": [0, 16, 4, -3, 6, -3, -11, -3, -8, 5, 18, 2, 20, 27, -6, -4, -2, 16, 22, -4, -18, -29, -4, -21, 25, -13, -9, -9, -40, -26, 22, 0, -42, 7, -28, 21, 1, 8, -27, 2, -16, -3, 51, -8, -4, 25, 16, 4, 86, 27, -27, 13, -24, -66, -39, 52, -30, 17, -10, -51, -35, 60, 0, -46, -32, -18, 20, 13, -30, 48, 27, -24, 2, -27, -28, 32, 18, 42, 15, -8, -39, -7, 29, -4, 27, 63, -34, 15, 17, -26, 57, -8, 64, 0, 44, 28, 62, -37, -10, -6, -38, -60, 23, 45, -63, -39, -72, 22, -43, -53, -54, 8, 11, -123, 35, -7, 21, 34, -14, -57, 65, -14, 49, -92, 0, -24, 12, 32, 0, -51, 21, -3, 48, 47, -116, 7, 95, 78, -49, -90, 30, -88, -46, 63, 85, 73, 75, 50, -122, 52, 24, 51, 91, 57, -120, 0, 128, -3, -54, 6, 31, -27, 6, 9, -50, 34, 49, -9, -51, -3, 1, -19, -59, -81, -48, 12, 6, 64, -71, -28, 46, -27, -60, -3, 3, 44, 0, -14, 38, 13, -76, -12, 128, 86, -57, 9, 13, 0, 18, -69, -141, 38, 118, -15, 56, 62, 30, -25, 1, 22, -84, 13, 45, 18, 117, 56, -186, 0, 74, -115, 66, 6, 106, 37, 27, 10, 54, -44, -37, -71, -38, 75, 142, -47, 33, 103, -16, 74, 48, -51, -42, -3, -15, 48, 12, 37, 8, -18, 0, -132, -51, -45, -63, -32, -30, -57, 72, -3, 65, -37, -54, 4, 46, -58, -74, 39, -45, 92, 4, 63, 7, 2, 93, -5, -32, -99, -85, 20, 50, 0, 30, 67, 63, 7, -34, -48, 33, 3, 22, 0, 15, 24, -53, -130, -16, 17, -159, -35, -37, 3, 50, 29, -2, -36, 38, -5, -34, 1, 48, 0, 0, 60, 66, -42, 39, 48, 31, -110, 36, -61, -154, -197, -24, -69, 120, 21, -60, -58, -55, -78, -45, -100, 51, 130, 10, 53, -47, 127, -16, -72, -50, 0, -88, -52, -58, 14, -17, -9, -69, 29, -111, -60, 169, 49, 53, 31, -122, 21, 155, 19, 2, 4, -200, 5, 28, 78, -64, 11, -3, -12, -29, 156, 0, 0, 110, -73, 91, 39, -33, 3, -81, 95, 9, 165, 4, 114, -16, 7, 36, 64, 0, 19, -64, 64, -21, -174, 45, -75, 5, 70, -164, -21, 30, 0, -26, 44, 42, -81, -58, -80, 29, -14, 125, 24, -22, 146, 54, -10, -48, -32, 102, 26, 31, -97, 45, -24, 46, 22, 4, 12, -52, 113, -97, -6, 0, 50, -100, 79, 111, -40, -63, 41, -60, -48, 295, -97, -36, 52, -12, 93, 66, -6, -30, -81, 85, -21, -199, 20, 10, -86, 48, -62, -144, -103, 192, 0, -84, -8, 30, 23, -62, 7, 93, -81, 0, 96, 36, -114, 93, 44, 71, -1, 19, 54, -101, -144, 88, -32, -21, -30, -55, -66, 31, 25, -18, 32, 0, 78, -144, 117, -84, -55, 61, 15, -51, -70, 104, 61, -67, 16, 128, 25, 12, 60, 255, -55, -44, 5, -159, -89, 12, 25, -31, -122, 61, 28, 184, 0, 6, 103, -192, 55, -17, 24, 43, 146, -142, -155, -146, 71, 94, -21, 2, 120, 141, -131, 96, 126, -229, 39, 33, -83, -85, 74, -5, -172, -110, 114, 0, -116, 48, -20, -22, 93, -58, 27, -15, -81, -33, 138, 150, -3, 51, -32, -117, 63, 49, -14, 8, -184, 92, -57, 246, 3, -96, 132, -114, 151, 132, 0, -192, -72, -236, 130, 17, 63, -38, 80, 144, 15, 135, -60, 165, -34, -97, 48, 107, -111, 52, 48, 53, 60, -74, 133, 132, 26, 36, 25, -110, -204, 0, 44, 6, 12, 86, 42, -75, 76, -70, -61, -6, 112, -48, -166, -13, 21, 12, 56, 86, -65, -95, 39, 22, -54, -15, -31, 50, -106, 110, -23, -72, 0, -34, 128, 92, -29, -9, 94, -222, -96, 71, -112, -132, 60, 2, 27, 29, -9, -211, 6, 19, 96, 60, -60, 147, -88, 5, 13, 18, -16, 60, -140, 0, 206, -75, 83, 60, 45, -149, -192, 148, 84, -190, -33, -12, -275, -173, 4, -223, 123, -55, -225, -123, 19, -48, 1, 61, -66, -120, -71, -106, -48, -284, 0, 24, -6, -37, -249, 33, -83, -105, 10, -90, 116, -178, -72, -141, 164, 21, -61, -255, 37, 256, 61, -81, 35, 62, -38, 109, 37, -76, 16, 66, 150, 0, -44, 110, -25, 34, -57, 34, -119, 27, 184, 126, 52, 43, 142, -36, -57, -77, -95, -152, 47, -36, 104, 3, -93, -134, 15, 75, -30, -34, -43, 4, 0, -108, -28, 186, -19, -24, 26, 168, -22, -9, -51, -125, 23, 57, -308, 93, 93, -80, 136, 26, 237, 109, 124, 114, -69, -24, 63, 225, 9, 272, -156, 0, 188, 123, 38, -137, 138, 66, 26, 52, 138, -6, 54, -176, -143, 95, 125, 179, -80, 80, 54, -132, 91, 209, -11, 39, 65, 97, 50, 290, -17, -26, 0, 62, -77, -36, 130, -11, 69, 95, -64, -70, -10, -93, 95, -48, 22, 70, 21, -129, 22, 38, -77, 63, 157, 158, -36, 34, -43, -125, 254, 82, -204, 0, 114, -89, -88, -160, -109, 72, 282, -12, -158, -135, -31, -24, 4, 36, -103, 54, -111, -210, 132, 270, -140, -102, -82, -110, -30, -36, 121, 189, 3, 34, 0, 98, -102, -100, -20, 15, 138, 190, -11, -56, 23, 75, 95, 6, -89, -136, 61, 146, -216, -169, 5, 121, -47, -83, -144, 78, -152, 27, -15, 256, -96, 0, 154, -80, 58, -37, 7, 30, -1, 60, 0, -54, 75, -63, -92, -123, -141, -1, 117, 21, -61, 3, 18, 147, 8, -282, 98, 45, -43, 75, -84, 104, 0, -168, -49, 335, 83, 9, 77, 108, 80, -39, 123, 196, 25, 95, 14, -60, 63, -198, -20, 68, -34, 270, -25, 42, -150, 96, 87, 19, -92, -26, -4, 0, -234, 6, -164, -105, -29, 93, -152, -193], "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], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, 0, 0, 0, -1, -1, 0, 1, 1, -1, 0], [-1, 1, 0, 1, 1, 0, 2, 0, -1, 0, 1, 0, -2, 0, 0, 0], [-1, -1, 0, 0, 1, 0, 1, -1, -1, 0, -1, 0, 0, 1, -1, 0], [1, 0, 0, -1, 1, 0, -1, 1, 1, 1, 0, -1, 0, -2, 1, 0], [1, -2, 0, 2, -5, 1, 0, -2, 1, 1, -1, 1, 2, 0, 1, 0], [0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 1, -2, 0, 0, 0, 0], [0, -3, 0, 0, 0, 1, 1, 1, 0, 0, -1, -2, 0, 1, -2, 1], [-1, 2, 0, 1, 1, 0, 2, 1, -2, -1, 1, 0, -2, 0, 1, 0], [1, 1, 1, -1, 3, 0, 0, 2, -1, -1, 1, 0, 0, 0, -2, 2], [2, -2, 0, -1, -2, 0, 0, 0, 3, -1, 0, 0, 3, 1, -1, 0], [3, 1, -2, 0, -1, 0, 0, 1, 2, -1, 3, -1, -2, -3, 2, 0], [1, 0, 0, 0, 0, 1, 1, 0, 1, -1, -1, -2, 0, 1, -2, 1], [-2, -1, 3, 1, 4, -1, 0, 1, -3, 1, 1, 2, 0, 1, 0, 1], [0, -2, -2, -2, 0, -2, -5, 0, 6, 0, 0, -2, 1, 0, 0, -2], [0, -3, 0, 0, 2, 0, 1, 2, 2, 0, 0, -2, 1, 1, -3, 3], [-2, -1, 2, 1, 0, -2, 0, -1, 0, 0, -1, 0, 0, 2, 1, 0], [0, 3, 1, -1, 1, -1, -1, 1, 1, -1, 0, -1, 0, 1, 0, 0], [-1, 2, 2, 0, 2, 0, 2, -1, -1, 1, 0, 2, 0, 0, 1, 0], [-2, 2, 2, -1, 2, -1, -2, 0, 2, 1, -1, -1, 3, 0, 1, -1], [1, 1, -2, -1, -2, 0, -1, 0, 2, 1, 0, -1, 1, -2, 1, -3], [-3, 3, 1, 1, 5, -3, 2, 1, -3, 1, 2, 2, -4, -2, 3, -1], [0, -1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 2, -1, 0, -1, 0], [0, 4, 1, 0, 0, -1, -2, 0, -2, -2, 1, 2, -1, 0, 2, -2], [1, 0, 1, -3, 2, 0, 3, 2, -2, -2, 0, 3, 1, 1, -3, 1], [-5, -1, 0, 1, 0, -1, 3, -2, -1, -1, -2, -2, 0, 3, -1, 1], [-1, 1, -1, 0, -2, 1, 1, -1, -3, 0, -2, 0, 1, 2, -2, 0], [1, -3, 1, 1, -4, 0, -1, -1, 5, 1, 0, 0, 6, 0, 0, -1], [-2, -1, 1, 1, -2, -2, 0, 0, 1, -1, 1, 1, 1, 1, 1, 0], [0, -1, 4, 3, 2, -1, 5, -3, -5, 4, -1, 6, -2, 0, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -3, 0, 1, -2, -1, 2, 1, 8, 0, 1, -4, 2, 0, 0, 1], [3, 0, -1, 1, -5, 4, 2, -1, 2, -1, -1, -3, 2, 1, -2, 0], [-1, -1, 3, 1, -5, -2, 1, -3, 2, 3, -2, -1, 2, 0, 2, -1], [3, -2, -1, 0, -5, 2, -3, 1, 5, -1, -1, -5, -1, 1, -1, 1], [-3, 5, 4, 1, 3, -1, 6, -2, -3, -1, 1, 2, -1, 1, 1, -2], [1, 0, 0, -6, 6, -1, -1, 5, 2, -4, 1, -1, -1, 2, -5, 1], [0, -2, 2, 2, -4, -1, -1, -4, -2, 3, -2, 5, 3, -2, 3, -3], [2, 0, 1, 1, -3, 1, 2, 0, 0, -1, 1, 0, -2, 0, -1, 0], [2, -2, 3, -1, -2, -4, -3, -2, 1, 4, -1, 3, 6, -2, 1, -2], [0, 2, -1, -1, 1, 0, -1, 2, 0, -1, 1, -1, 1, 0, 1, -1], [0, 2, -1, 3, 5, 1, 6, -1, -9, 1, 1, 7, -6, -1, 1, 2], [0, -4, 0, 0, -5, -2, -6, -2, -1, 4, -3, 0, 4, 1, 3, -2], [3, -2, 2, -1, -4, 0, -1, 1, 4, -2, 0, 1, 1, 1, -2, 1], [8, -9, -3, -2, -6, 1, -4, 1, 9, -2, 1, -3, 3, -1, -3, 1], [4, -3, -6, 2, -6, 2, -2, 0, 4, 0, 0, -2, 0, -3, 3, -1], [-2, 4, 1, 1, 1, -1, 2, -2, -2, 0, 0, 3, 1, 1, 3, -4], [6, 2, 1, -2, 2, 1, 0, 0, -1, -1, 0, 2, -4, -1, -1, -1], [4, -3, -1, -1, -3, 2, 2, 1, 4, -2, -1, -2, -1, 2, -4, 2], [-5, 2, -3, 0, 6, 3, 4, 3, -2, -4, 0, -3, -5, 1, -5, 3], [0, 0, -3, 3, -1, 4, 6, -2, -4, -2, 1, 2, -4, 0, -2, 3], [-4, -5, 0, 4, -2, 0, 2, -2, 1, 2, -1, -4, 0, 2, -2, 4], [-1, -1, 5, -1, -3, 2, 1, -1, -1, 0, -1, 0, 4, 1, -2, 1], [-7, -2, -4, 1, 2, 2, 4, -1, -2, -2, -1, -3, -3, 3, -3, 3], [5, -1, 1, 1, -2, 1, -4, -2, 0, 4, -2, 0, 4, -1, -1, 1], [-1, 1, -3, 3, -5, -3, -4, 0, 3, 3, 3, -2, -4, -3, 6, -3], [5, -2, -8, -1, -4, 2, -5, 3, 5, 1, 1, -6, -3, -2, -1, 1], [1, 6, -1, 1, -1, -4, -2, 1, 4, 3, 5, 0, -4, -5, 7, -3], [-4, -2, 1, 0, -2, -1, -2, -4, 1, 2, -4, 4, 4, 1, 1, -1], [6, -10, -7, -1, -13, 3, -8, -2, 9, 2, -5, -1, 4, -2, -1, 0], [6, -1, 0, -3, 1, 2, 1, 3, 5, -5, 2, -4, -1, 0, -4, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -1, -2, -1, 1, -4, 1, 0, -1, 0, -2, 1, 0, 0, 0], [-1, -2, 2, 4, -2, -6, -1, -1, 0, 6, 2, 4, 0, -6, 8, 0], [-1, 3, -1, -3, 8, -1, -2, 6, 1, 0, 3, -1, -6, -3, 1, 1], [-5, 1, -2, 2, 5, -3, 3, -2, -7, 1, 1, 3, -3, -1, 5, -1], [1, -1, 2, 1, 1, 3, 3, 2, -2, -1, 0, -2, -1, 4, -6, 3], [0, -2, -3, 4, -7, -2, -1, -3, 2, 4, 2, 1, -3, -4, 6, -1], [2, 3, 3, -4, 5, -1, -3, 5, 0, -3, 1, -3, 0, 1, -3, 3], [-1, 2, 1, -2, 2, -4, 0, -2, 0, 1, 1, -1, 2, -2, 6, -2], [-2, 1, 2, -1, 3, 3, 4, 0, -3, -1, 0, 0, -2, 1, -2, 2], [0, 0, 2, 4, -4, 0, 2, -6, -6, 4, -3, 8, 4, 0, 4, -4], [3, -3, -1, -5, -6, -2, -10, 0, 6, 2, -5, 0, 8, 0, 2, -5], [-8, 1, 4, 0, 11, 2, 9, 0, -4, -2, -3, 0, -1, 5, -7, 2], [1, 2, 1, 3, -4, -2, -4, -3, -1, 6, -2, 1, 3, -1, 8, -4], [3, 0, -1, 2, -4, 3, 0, -2, -5, 1, -2, 4, -1, -3, 3, -1], [0, 1, 3, 2, 1, 2, 5, -2, -7, 0, 0, 5, -2, 4, -2, 4], [4, 1, -3, 0, -6, 2, 0, -3, 0, 0, 0, 2, 1, -3, 4, -2], [1, 2, 0, 2, 7, 4, 3, 4, -1, 2, 4, -4, -5, -4, -2, 4], [-3, 7, -3, 1, 3, -1, 1, -1, -4, 3, 3, 3, -2, -4, 4, -2], [1, -1, 5, 0, -3, -3, -5, 0, 1, 2, -3, 3, 4, 1, 1, -3], [-3, 6, 4, -2, 12, -4, 1, 3, -3, 0, 2, 3, -2, 1, 0, -1], [-4, 10, 1, -2, 3, 0, 4, 2, -9, -3, 1, 3, -11, 1, 2, -1], [6, -3, -1, -3, -7, 7, -1, 2, 3, -6, -4, -5, 5, 4, -7, 3], [7, -2, 7, -4, 2, -5, -6, 1, 2, 5, -2, 2, 10, -3, 6, -3], [2, -3, 2, -4, 3, 1, 0, 3, 1, 1, 1, -2, 2, -1, -3, 3], [-2, 0, 3, 2, 0, 4, 7, -4, -8, -1, -4, 4, 4, 4, -2, 2], [4, 6, 0, -1, 2, 1, 1, 2, 1, 1, 3, -1, -4, -5, 3, -2], [-3, 0, 3, -3, 5, 4, 6, 1, -4, -5, -3, 0, 0, 3, -9, 5], [4, 3, -1, -3, 7, 1, 0, 8, -1, -4, 5, -4, -6, -2, -1, 3], [2, 2, -1, 0, 6, 1, 0, 3, -1, 3, 6, -1, -2, -3, 1, 0], [1, 6, -2, -4, 8, 0, -1, 8, -1, -6, 4, -4, -8, 0, -2, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 5, 3, 1, -2, 4, -6, -10, 5, -5, 12, -1, 0, 4, -5], [2, 3, 0, -5, 4, -2, 2, 4, 1, -3, 3, -1, -2, 3, -3, 0], [8, -2, -4, -4, -9, 8, -2, 0, 3, -8, -4, -7, 4, 4, -8, 0], [0, 5, -1, -2, 6, -2, 2, 1, -2, 3, 3, 3, 0, -3, -1, -3], [-5, -2, -2, 2, -2, 0, 4, -2, -1, -2, -2, -4, -1, 0, 2, 2], [-1, 3, 2, 3, -2, 2, 1, -1, -4, 1, -2, 0, 3, 1, 1, -2], [-6, -2, 1, -1, 6, 1, 7, 6, -1, -5, 1, -6, -4, 5, -6, 6]]}