Embedded newform 43.4.e.a.11.7

• Label: 43.4.e.a.11.7
• 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			11.7
Character	\(\chi\)	\(=\)	43.11
Dual form			43.4.e.a.4.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.20289 + 1.50838i) q^{2} +(3.21845 - 4.03581i) q^{3} +(0.951908 - 4.17058i) q^{4} +(3.04073 - 1.46434i) q^{5} +9.95900 q^{6} -15.9770 q^{7} +(21.3417 - 10.2776i) q^{8} +(0.0787180 + 0.344886i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 3 q^{3} - 31 q^{4} - 23 q^{5} + 16 q^{6} + 96 q^{7} + 61 q^{8} - 177 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.20289	+	1.50838i	0.425287	+	0.533293i	0.947599	−	0.319461i	\(-0.103502\pi\)
							−0.522312	+	0.852754i	\(0.674930\pi\)
\(3\)	3.21845	−	4.03581i	0.619392	−	0.776693i	−0.368867	−	0.929482i	\(-0.620254\pi\)
							0.988259	+	0.152789i	\(0.0488256\pi\)
\(5\)	3.04073	−	1.46434i	0.271971	−	0.130974i	−0.292928	−	0.956135i	\(-0.594630\pi\)
							0.564899	+	0.825160i	\(0.308915\pi\)
\(7\)	−15.9770			−0.862680			−0.431340	−	0.902190i	\(-0.641959\pi\)
							−0.431340	+	0.902190i	\(0.641959\pi\)
\(11\)	15.5424	+	68.0956i	0.426019	+	1.86651i	0.495002	+	0.868892i	\(0.335167\pi\)
							−0.0689839	+	0.997618i	\(0.521976\pi\)
\(13\)	−7.36994	+	3.54918i	−0.157235	+	0.0757203i	−0.510846	−	0.859672i	\(-0.670668\pi\)
							0.353611	+	0.935392i	\(0.384954\pi\)
\(17\)	−60.7293	−	29.2457i	−0.866412	−	0.417242i	−0.0527690	−	0.998607i	\(-0.516805\pi\)
							−0.813643	+	0.581365i	\(0.802519\pi\)
\(19\)	2.53499	−	11.1065i	0.0306088	−	0.134106i	−0.957315	−	0.289047i	\(-0.906662\pi\)
							0.987924	+	0.154941i	\(0.0495188\pi\)
\(23\)	−31.2724	−	137.013i	−0.283511	−	1.24214i	−0.893257	−	0.449546i	\(-0.851586\pi\)
							0.609747	−	0.792596i	\(-0.291271\pi\)
\(29\)	104.008	+	130.421i	0.665990	+	0.835125i	0.993981	−	0.109556i	\(-0.0349428\pi\)
							−0.327990	+	0.944681i	\(0.606371\pi\)
\(31\)	−17.2487	−	21.6292i	−0.0999341	−	0.125313i	0.729350	−	0.684141i	\(-0.239823\pi\)
							−0.829284	+	0.558828i	\(0.811251\pi\)
\(37\)	−32.5950			−0.144827			−0.0724133	−	0.997375i	\(-0.523070\pi\)
							−0.0724133	+	0.997375i	\(0.523070\pi\)
\(41\)	−140.317	−	175.953i	−0.534486	−	0.670224i	0.439129	−	0.898424i	\(-0.355287\pi\)
							−0.973614	+	0.228200i	\(0.926716\pi\)
\(43\)	279.901	+	34.0958i	0.992662	+	0.120920i
							\(47\)	45.3127	−	198.528i	0.140628	−	0.616133i	−0.854661	−	0.519186i	\(-0.826235\pi\)
0.995290	−	0.0969471i	\(-0.0309078\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.e.a.11.7	yes	60
43.2	odd	14		1849.4.a.g.1.12		30
43.4	even	7	inner	43.4.e.a.4.7	✓	60
43.41	even	7		1849.4.a.h.1.19		30

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.4.7	✓	60	43.4	even	7	inner
43.4.e.a.11.7	yes	60	1.1	even	1	trivial
1849.4.a.g.1.12		30	43.2	odd	14
1849.4.a.h.1.19		30	43.41	even	7