Newform orbit 43.9.f.a

• Label: 43.9.f.a
• Level: $43$
• Weight: $9$
• Character orbit: 43.f
• Analytic conductor: $17.517$
• Analytic rank: $0$
• Dimension: $174$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.f (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(17.5172802326\)
Analytic rank:	\(0\)
Dimension:	\(174\)
Relative dimension:	\(29\) over \(\Q(\zeta_{14})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 174 q - 7 q^{2} - 7 q^{3} + 4021 q^{4} - 7 q^{5} + 1780 q^{6} - 5383 q^{8} + 56490 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−13.4582	−	27.9461i	−47.5652	+	98.7701i	−440.252	+	552.058i	167.318	+	38.1893i	3400.38				−	4550.37i	13611.4	+	3106.71i	−3402.37	−	4266.43i	−1184.55	−	5189.85i
2.2	−13.1485	−	27.3031i	64.2865	−	133.492i	−412.962	+	517.838i	−972.457	−	221.957i	−4490.02				−	292.786i	12005.0	+	2740.07i	−9596.72	−	12033.9i	6726.21	+	29469.4i
2.3	−12.3921	−	25.7324i	27.0409	−	56.1510i	−348.980	+	437.608i	1129.38	+	257.774i	−1780.00				−	11.8724i	8457.04	+	1930.26i	1668.99	+	2092.85i	−7362.24	−	32256.1i
2.4	−11.5206	−	23.9228i	−29.0150	+	60.2502i	−279.962	+	351.061i	−438.800	−	100.153i	1775.62					3131.86i	4996.73	+	1140.47i	1302.50	+	1633.28i	2659.29	+	11651.1i
2.5	−10.2670	−	21.3197i	22.6641	−	47.0626i	−189.504	+	237.631i	67.6603	+	15.4430i	−1236.05					643.549i	1106.00	+	252.436i	2389.49	+	2996.33i	−365.429	−	1601.05i
2.6	−9.26628	−	19.2416i	5.00685	−	10.3968i	−124.763	+	156.448i	−758.071	−	173.025i	−246.447				−	4635.90i	−1163.81	−	265.632i	4007.69	+	5025.49i	3695.22	+	16189.8i
2.7	−7.83493	−	16.2694i	−45.2846	+	94.0344i	−43.6938	+	54.7902i	843.199	+	192.455i	1884.69					324.806i	−3273.12	−	747.068i	−2701.06	−	3387.03i	−3475.28	−	15226.2i
2.8	−6.10369	−	12.6745i	64.4015	−	133.731i	36.2267	−	45.4269i	363.007	+	82.8539i	−2088.06					1931.33i	−4307.89	−	983.247i	−9645.74	−	12095.4i	−1165.55	−	5106.63i
2.9	−5.86394	−	12.1766i	−67.7996	+	140.787i	45.7298	−	57.3434i	−958.314	−	218.729i	2111.88				−	747.870i	−4339.50	−	990.462i	−11133.6	−	13961.0i	2956.12	+	12951.6i
2.10	−5.51717	−	11.4565i	38.3400	−	79.6139i	58.8006	−	73.7336i	121.203	+	27.6637i	−1123.63				−	1965.00i	−4342.77	−	991.209i	−777.697	−	975.201i	−351.766	−	1541.19i
2.11	−5.04009	−	10.4659i	−24.0340	+	49.9071i	75.4818	−	94.6511i	11.0383	+	2.51943i	643.453				−	674.726i	−4270.24	−	974.653i	2177.63	+	2730.67i	−29.2663	−	128.224i
2.12	−3.74733	−	7.78141i	23.1343	−	48.0389i	113.106	−	141.830i	−1134.95	−	259.044i	−460.503					3469.08i	−3683.04	−	840.631i	2318.17	+	2906.90i	2237.29	+	9802.22i
2.13	−1.08134	−	2.24542i	−24.6440	+	51.1739i	155.741	−	195.293i	−234.966	−	53.6295i	141.556				−	271.708i	−1228.94	−	280.497i	2079.28	+	2607.33i	133.657	+	585.590i
2.14	−0.911670	−	1.89310i	5.18580	−	10.7684i	156.861	−	196.697i	618.914	+	141.263i	−25.1134					3955.82i	−1039.79	−	237.325i	4001.65	+	5017.91i	−296.820	−	1300.45i
2.15	−0.397118	−	0.824624i	14.6893	−	30.5027i	159.091	−	199.494i	1129.77	+	257.863i	−30.9866				−	4070.52i	−456.118	−	104.106i	3376.08	+	4233.47i	−236.012	−	1034.04i
2.16	1.53552	+	3.18853i	57.5019	−	119.404i	151.804	−	190.357i	−620.261	−	141.571i	469.018				−	2752.04i	1723.33	+	393.338i	−6860.10	−	8602.29i	−501.019	−	2195.11i
2.17	3.22586	+	6.69857i	−59.4708	+	123.492i	125.149	−	156.932i	267.347	+	61.0203i	−1019.07					4439.62i	3310.53	+	755.607i	−7622.86	−	9558.77i	453.677	+	1987.69i
2.18	3.66053	+	7.60117i	−21.3391	+	44.3111i	115.235	−	144.500i	−661.934	−	151.082i	−414.929				−	1496.55i	3625.83	+	827.571i	2582.60	+	3238.48i	−1274.63	−	5584.51i
2.19	3.66094	+	7.60201i	−55.7168	+	115.697i	115.225	−	144.488i	474.386	+	108.275i	−1083.51				−	3609.61i	3626.10	+	827.633i	−6190.76	−	7762.96i	913.584	+	4002.67i
2.20	4.47023	+	9.28252i	45.7755	−	95.0539i	93.4311	−	117.159i	498.592	+	113.800i	1086.97					1744.42i	4076.58	+	930.453i	−2849.12	−	3572.69i	1172.46	+	5136.90i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
43.f	odd	14	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	43.9.f.a	✓	174
43.f	odd	14	1	inner	43.9.f.a	✓	174

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
43.9.f.a	✓	174	1.a	even	1	1	trivial
43.9.f.a	✓	174	43.f	odd	14	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{9}^{\mathrm{new}}(43, [\chi])\).