Embedded newform 43.6.c.a.6.15

• Label: 43.6.c.a.6.15
• Level: $43$
• Weight: $6$
• Character: 43.6
• Analytic conductor: $6.897$
• Analytic rank: $0$
• Dimension: $34$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89650425196\)
Analytic rank:	\(0\)
Dimension:	\(34\)
Relative dimension:	\(17\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.15
Character	\(\chi\)	\(=\)	43.6
Dual form			43.6.c.a.36.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+7.09985 q^{2} +(1.12246 - 1.94417i) q^{3} +18.4079 q^{4} +(51.2710 - 88.8039i) q^{5} +(7.96933 - 13.8033i) q^{6} +(-36.3371 - 62.9377i) q^{7} -96.5019 q^{8} +(118.980 + 206.080i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{2}{3}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	7.09985			1.25509			0.627544	−	0.778581i	\(-0.284060\pi\)
							0.627544	+	0.778581i	\(0.284060\pi\)
\(3\)	1.12246	−	1.94417i	0.0720062	−	0.124718i	−0.827774	−	0.561061i	\(-0.810393\pi\)
							0.899780	+	0.436343i	\(0.143727\pi\)
\(5\)	51.2710	−	88.8039i	0.917163	−	1.58857i	0.113459	−	0.993543i	\(-0.463807\pi\)
							0.803703	−	0.595030i	\(-0.202860\pi\)
\(7\)	−36.3371	−	62.9377i	−0.280289	−	0.485474i	0.691167	−	0.722695i	\(-0.257097\pi\)
							−0.971456	+	0.237221i	\(0.923764\pi\)
\(11\)	469.005			1.16868			0.584340	−	0.811509i	\(-0.301354\pi\)
							0.584340	+	0.811509i	\(0.301354\pi\)
\(13\)	235.694	+	408.234i	0.386803	+	0.669963i	0.992018	−	0.126100i	\(-0.0402460\pi\)
							−0.605214	+	0.796062i	\(0.706913\pi\)
\(17\)	−406.800	−	704.599i	−0.341396	−	0.591316i	0.643296	−	0.765618i	\(-0.277567\pi\)
							−0.984692	+	0.174302i	\(0.944233\pi\)
\(19\)	−548.500	+	950.029i	−0.348572	+	0.603744i	−0.985996	−	0.166769i	\(-0.946667\pi\)
							0.637424	+	0.770513i	\(0.280000\pi\)
\(23\)	−1429.37	+	2475.75i	−0.563412	+	0.975859i	0.433783	+	0.901017i	\(0.357178\pi\)
							−0.997195	+	0.0748415i	\(0.976155\pi\)
\(29\)	3905.30	+	6764.18i	0.862303	+	1.49355i	0.869701	+	0.493579i	\(0.164312\pi\)
							−0.00739834	+	0.999973i	\(0.502355\pi\)
\(31\)	1206.95	−	2090.49i	0.225571	−	0.390701i	−0.730920	−	0.682464i	\(-0.760909\pi\)
							0.956491	+	0.291763i	\(0.0942419\pi\)
\(37\)	−3725.79	+	6453.25i	−0.447418	+	0.774951i	−0.998217	−	0.0596871i	\(-0.980990\pi\)
							0.550799	+	0.834638i	\(0.314323\pi\)
\(41\)	15259.8			1.41771			0.708856	−	0.705353i	\(-0.249212\pi\)
							0.708856	+	0.705353i	\(0.249212\pi\)
\(43\)	−12106.0	−	673.174i	−0.998458	−	0.0555209i
							\(47\)	−15397.4			−1.01672			−0.508361	−	0.861144i	\(-0.669749\pi\)
−0.508361	+	0.861144i	\(0.669749\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.6.15	✓	34
43.36	even	3	inner	43.6.c.a.36.15	yes	34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.15	✓	34	1.1	even	1	trivial
43.6.c.a.36.15	yes	34	43.36	even	3	inner