Embedded newform 43.4.e.a.11.10

• Label: 43.4.e.a.11.10
• Level: $43$
• Weight: $4$
• Character: 43.11
• Analytic conductor: $2.537$
• Analytic rank: $0$
• Dimension: $60$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.53708213025\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Relative dimension:	\(10\) over \(\Q(\zeta_{7})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			11.10
Character	\(\chi\)	\(=\)	43.11
Dual form			43.4.e.a.4.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.96047 + 3.71232i) q^{2} +(4.10366 - 5.14583i) q^{3} +(-3.23672 + 14.1810i) q^{4} +(-6.52318 + 3.14140i) q^{5} +31.2517 q^{6} +6.49418 q^{7} +(-28.0025 + 13.4853i) q^{8} +(-3.63147 - 15.9105i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 3 q^{3} - 31 q^{4} - 23 q^{5} + 16 q^{6} + 96 q^{7} + 61 q^{8} - 177 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{7}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

(See \(a_n\) instead)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.96047	+	3.71232i	1.04669	+	1.31250i	0.948308	+	0.317353i	\(0.102794\pi\)
							0.0983775	+	0.995149i	\(0.468635\pi\)
\(3\)	4.10366	−	5.14583i	0.789751	−	0.990316i	−0.210169	−	0.977665i	\(-0.567402\pi\)
							0.999920	−	0.0126510i	\(-0.00402704\pi\)
\(5\)	−6.52318	+	3.14140i	−0.583451	+	0.280975i	−0.702235	−	0.711945i	\(-0.747814\pi\)
							0.118785	+	0.992920i	\(0.462100\pi\)
\(7\)	6.49418			0.350653			0.175326	−	0.984510i	\(-0.443902\pi\)
							0.175326	+	0.984510i	\(0.443902\pi\)
\(11\)	−14.2157	−	62.2832i	−0.389655	−	1.70719i	−0.665848	−	0.746087i	\(-0.731930\pi\)
							0.276194	−	0.961102i	\(-0.410927\pi\)
\(13\)	−60.9667	+	29.3600i	−1.30070	+	0.626385i	−0.950627	−	0.310336i	\(-0.899558\pi\)
							−0.350076	+	0.936721i	\(0.613844\pi\)
\(17\)	3.84960	+	1.85387i	0.0549214	+	0.0264488i	0.461143	−	0.887326i	\(-0.347440\pi\)
							−0.406221	+	0.913775i	\(0.633154\pi\)
\(19\)	25.0832	−	109.897i	0.302867	−	1.32695i	−0.562910	−	0.826518i	\(-0.690318\pi\)
							0.865777	−	0.500429i	\(-0.166825\pi\)
\(23\)	21.8573	+	95.7630i	0.198155	+	0.868172i	0.972034	+	0.234839i	\(0.0754564\pi\)
							−0.773879	+	0.633333i	\(0.781686\pi\)
\(29\)	179.507	+	225.095i	1.14944	+	1.44135i	0.877852	+	0.478933i	\(0.158976\pi\)
							0.271584	+	0.962415i	\(0.412452\pi\)
\(31\)	−56.8270	−	71.2588i	−0.329239	−	0.412853i	0.589468	−	0.807792i	\(-0.299337\pi\)
							−0.918708	+	0.394938i	\(0.870766\pi\)
\(37\)	−207.629			−0.922542			−0.461271	−	0.887259i	\(-0.652606\pi\)
							−0.461271	+	0.887259i	\(0.652606\pi\)
\(41\)	151.751	+	190.290i	0.578039	+	0.724837i	0.981777	−	0.190037i	\(-0.0608608\pi\)
							−0.403738	+	0.914874i	\(0.632289\pi\)
\(43\)	101.435	−	263.093i	0.359737	−	0.933054i
							\(47\)	16.8156	−	73.6740i	0.0521874	−	0.228648i	−0.942108	−	0.335310i	\(-0.891159\pi\)
0.994295	+	0.106662i	\(0.0340162\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.e.a.11.10	yes	60
43.2	odd	14		1849.4.a.g.1.4		30
43.4	even	7	inner	43.4.e.a.4.10	✓	60
43.41	even	7		1849.4.a.h.1.27		30

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.4.10	✓	60	43.4	even	7	inner
43.4.e.a.11.10	yes	60	1.1	even	1	trivial
1849.4.a.g.1.4		30	43.2	odd	14
1849.4.a.h.1.27		30	43.41	even	7