Embedded newform 43.6.c.a.6.13

• Label: 43.6.c.a.6.13
• 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			6.13
Character	\(\chi\)	\(=\)	43.6
Dual form			43.6.c.a.36.13

$q$-expansion

\(f(q)\)	\(=\)	\(q+4.50187 q^{2} +(14.9934 - 25.9693i) q^{3} -11.7331 q^{4} +(16.1936 - 28.0482i) q^{5} +(67.4982 - 116.910i) q^{6} +(70.7811 + 122.596i) q^{7} -196.881 q^{8} +(-328.101 - 568.288i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	4.50187			0.795826			0.397913	−	0.917423i	\(-0.369735\pi\)
							0.397913	+	0.917423i	\(0.369735\pi\)
\(3\)	14.9934	−	25.9693i	0.961824	−	1.66593i	0.243908	−	0.969798i	\(-0.421570\pi\)
							0.717916	−	0.696130i	\(-0.245096\pi\)
\(5\)	16.1936	−	28.0482i	0.289681	−	0.501741i	−0.684053	−	0.729432i	\(-0.739784\pi\)
							0.973733	+	0.227691i	\(0.0731176\pi\)
\(7\)	70.7811	+	122.596i	0.545974	+	0.945655i	0.998545	+	0.0539263i	\(0.0171736\pi\)
							−0.452571	+	0.891728i	\(0.649493\pi\)
\(11\)	210.154			0.523668			0.261834	−	0.965113i	\(-0.415673\pi\)
							0.261834	+	0.965113i	\(0.415673\pi\)
\(13\)	55.4098	+	95.9727i	0.0909345	+	0.157503i	0.907905	−	0.419177i	\(-0.137681\pi\)
							−0.816970	+	0.576680i	\(0.804348\pi\)
\(17\)	856.791	+	1484.01i	0.719039	+	1.24541i	0.961381	+	0.275221i	\(0.0887511\pi\)
							−0.242342	+	0.970191i	\(0.577916\pi\)
\(19\)	1234.85	−	2138.82i	0.784747	−	1.35922i	−0.144402	−	0.989519i	\(-0.546126\pi\)
							0.929150	−	0.369703i	\(-0.120541\pi\)
\(23\)	1245.82	−	2157.82i	0.491061	−	0.850542i	−0.508886	−	0.860834i	\(-0.669943\pi\)
							0.999947	+	0.0102917i	\(0.00327600\pi\)
\(29\)	2343.61	+	4059.25i	0.517476	+	0.896295i	0.999794	+	0.0202989i	\(0.00646178\pi\)
							−0.482318	+	0.875996i	\(0.660205\pi\)
\(31\)	−3511.19	+	6081.57i	−0.656222	+	1.13661i	0.325364	+	0.945589i	\(0.394513\pi\)
							−0.981586	+	0.191020i	\(0.938820\pi\)
\(37\)	−3163.28	+	5478.96i	−0.379868	+	0.657951i	−0.991043	−	0.133545i	\(-0.957364\pi\)
							0.611174	+	0.791496i	\(0.290697\pi\)
\(41\)	−6712.78			−0.623652			−0.311826	−	0.950139i	\(-0.600941\pi\)
							−0.311826	+	0.950139i	\(0.600941\pi\)
\(43\)	−7752.06	−	9322.77i	−0.639361	−	0.768907i
							\(47\)	−387.683			−0.0255995			−0.0127998	−	0.999918i	\(-0.504074\pi\)
−0.0127998	+	0.999918i	\(0.504074\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.6.13	✓	34
43.36	even	3	inner	43.6.c.a.36.13	yes	34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.13	✓	34	1.1	even	1	trivial
43.6.c.a.36.13	yes	34	43.36	even	3	inner