Embedded newform 43.6.e.a.11.5

• Label: 43.6.e.a.11.5
• Level: $43$
• Weight: $6$
• Character: 43.11
• Analytic conductor: $6.897$
• Analytic rank: $0$
• Dimension: $108$
• CM: no
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89650425196\)
Analytic rank:	\(0\)
Dimension:	\(108\)
Relative dimension:	\(18\) over \(\Q(\zeta_{7})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			11.5
Character	\(\chi\)	\(=\)	43.11
Dual form			43.6.e.a.4.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-4.75577 - 5.96355i) q^{2} +(-3.77448 + 4.73304i) q^{3} +(-5.82590 + 25.5249i) q^{4} +(-49.8748 + 24.0184i) q^{5} +46.1763 q^{6} +187.876 q^{7} +(-39.9875 + 19.2570i) q^{8} +(45.9176 + 201.178i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−4.75577	−	5.96355i	−0.840710	−	1.05422i	−0.997778	−	0.0666293i	\(-0.978776\pi\)
							0.157068	−	0.987588i	\(-0.449796\pi\)
\(3\)	−3.77448	+	4.73304i	−0.242133	+	0.303625i	−0.888017	−	0.459810i	\(-0.847917\pi\)
							0.645884	+	0.763435i	\(0.276489\pi\)
\(5\)	−49.8748	+	24.0184i	−0.892187	+	0.429655i	−0.823061	−	0.567953i	\(-0.807735\pi\)
							−0.0691264	+	0.997608i	\(0.522021\pi\)
\(7\)	187.876			1.44920			0.724598	−	0.689172i	\(-0.242025\pi\)
							0.724598	+	0.689172i	\(0.242025\pi\)
\(11\)	−98.0027	−	429.378i	−0.244206	−	1.06994i	−0.937145	−	0.348940i	\(-0.886542\pi\)
							0.692939	−	0.720996i	\(-0.256315\pi\)
\(13\)	551.081	−	265.387i	0.904392	−	0.435532i	0.0769190	−	0.997037i	\(-0.475492\pi\)
							0.827473	+	0.561505i	\(0.189777\pi\)
\(17\)	1027.38	+	494.758i	0.862198	+	0.415213i	0.812091	−	0.583531i	\(-0.198329\pi\)
							0.0501072	+	0.998744i	\(0.484044\pi\)
\(19\)	459.522	−	2013.30i	0.292027	−	1.27945i	−0.589673	−	0.807642i	\(-0.700744\pi\)
							0.881700	−	0.471810i	\(-0.156399\pi\)
\(23\)	846.113	+	3707.06i	0.333510	+	1.46120i	0.812283	+	0.583263i	\(0.198224\pi\)
							−0.478773	+	0.877939i	\(0.658918\pi\)
\(29\)	5099.66	+	6394.78i	1.12602	+	1.41199i	0.898919	+	0.438115i	\(0.144354\pi\)
							0.227102	+	0.973871i	\(0.427075\pi\)
\(31\)	3394.40	+	4256.45i	0.634394	+	0.795505i	0.990289	−	0.139021i	\(-0.0443954\pi\)
							−0.355895	+	0.934526i	\(0.615824\pi\)
\(37\)	11002.2			1.32122			0.660608	−	0.750731i	\(-0.270299\pi\)
							0.660608	+	0.750731i	\(0.270299\pi\)
\(41\)	−974.921	−	1222.51i	−0.0905753	−	0.113578i	0.734479	−	0.678632i	\(-0.237427\pi\)
							−0.825054	+	0.565054i	\(0.808855\pi\)
\(43\)	−11269.3	−	4473.31i	−0.929452	−	0.368942i
							\(47\)	3175.91	−	13914.6i	0.209712	−	0.918808i	−0.755047	−	0.655671i	\(-0.772386\pi\)
0.964759	−	0.263137i	\(-0.0847570\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.11.5	yes	108
43.4	even	7	inner	43.6.e.a.4.5	✓	108

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.5	✓	108	43.4	even	7	inner
43.6.e.a.11.5	yes	108	1.1	even	1	trivial