Embedded newform 43.6.e.a.11.17

• Label: 43.6.e.a.11.17
• 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			11.17
Character	\(\chi\)	\(=\)	43.11
Dual form			43.6.e.a.4.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(6.33304 + 7.94138i) q^{2} +(4.01851 - 5.03906i) q^{3} +(-15.8374 + 69.3884i) q^{4} +(-53.4066 + 25.7193i) q^{5} +65.4665 q^{6} -5.04361 q^{7} +(-358.491 + 172.640i) q^{8} +(44.8289 + 196.408i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	6.33304	+	7.94138i	1.11953	+	1.40385i	0.904094	+	0.427333i	\(0.140547\pi\)
							0.215439	+	0.976517i	\(0.430882\pi\)
\(3\)	4.01851	−	5.03906i	0.257788	−	0.323256i	−0.636049	−	0.771649i	\(-0.719432\pi\)
							0.893836	+	0.448393i	\(0.148004\pi\)
\(5\)	−53.4066	+	25.7193i	−0.955366	+	0.460080i	−0.845564	−	0.533874i	\(-0.820736\pi\)
							−0.109802	+	0.993954i	\(0.535022\pi\)
\(7\)	−5.04361			−0.0389042			−0.0194521	−	0.999811i	\(-0.506192\pi\)
							−0.0194521	+	0.999811i	\(0.506192\pi\)
\(11\)	62.1446	+	272.273i	0.154854	+	0.678459i	0.991433	+	0.130614i	\(0.0416947\pi\)
							−0.836580	+	0.547846i	\(0.815448\pi\)
\(13\)	1004.45	−	483.716i	1.64842	−	0.793838i	0.648968	−	0.760816i	\(-0.275201\pi\)
							0.999455	−	0.0330227i	\(-0.0105134\pi\)
\(17\)	148.218	+	71.3780i	0.124388	+	0.0599021i	0.495043	−	0.868869i	\(-0.335152\pi\)
							−0.370655	+	0.928771i	\(0.620867\pi\)
\(19\)	355.367	−	1556.97i	0.225836	−	0.989453i	−0.727159	−	0.686469i	\(-0.759160\pi\)
							0.952995	−	0.302984i	\(-0.0979830\pi\)
\(23\)	−408.722	−	1790.73i	−0.161105	−	0.705846i	−0.989359	−	0.145494i	\(-0.953523\pi\)
							0.828254	−	0.560352i	\(-0.189334\pi\)
\(29\)	−929.436	−	1165.48i	−0.205222	−	0.257341i	0.668560	−	0.743658i	\(-0.266911\pi\)
							−0.873782	+	0.486318i	\(0.838340\pi\)
\(31\)	5257.60	+	6592.82i	0.982615	+	1.23216i	0.972666	+	0.232209i	\(0.0745955\pi\)
							0.00994891	+	0.999951i	\(0.496833\pi\)
\(37\)	−543.788			−0.0653018			−0.0326509	−	0.999467i	\(-0.510395\pi\)
							−0.0326509	+	0.999467i	\(0.510395\pi\)
\(41\)	−9978.85	−	12513.1i	−0.927087	−	1.16253i	−0.986412	−	0.164292i	\(-0.947466\pi\)
							0.0593243	−	0.998239i	\(-0.481105\pi\)
\(43\)	11158.6	+	4742.70i	0.920323	+	0.391160i
							\(47\)	−3292.01	+	14423.2i	−0.217378	+	0.952397i	0.742028	+	0.670369i	\(0.233864\pi\)
−0.959406	+	0.282028i	\(0.908993\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.11.17	yes	108
43.4	even	7	inner	43.6.e.a.4.17	✓	108

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.17	✓	108	43.4	even	7	inner
43.6.e.a.11.17	yes	108	1.1	even	1	trivial