Embedded newform 43.10.c.a.6.7

• Label: 43.10.c.a.6.7
• Level: $43$
• Weight: $10$
• Character: 43.6
• Analytic conductor: $22.147$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.1465409550\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.7
Character	\(\chi\)	\(=\)	43.6
Dual form			43.10.c.a.36.7

$q$-expansion

\(f(q)\)	\(=\)	\(q-30.5461 q^{2} +(46.1090 - 79.8632i) q^{3} +421.064 q^{4} +(286.168 - 495.658i) q^{5} +(-1408.45 + 2439.51i) q^{6} +(319.069 + 552.644i) q^{7} +2777.74 q^{8} +(5589.41 + 9681.15i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−30.5461			−1.34996			−0.674980	−	0.737836i	\(-0.735848\pi\)
							−0.674980	+	0.737836i	\(0.735848\pi\)
\(3\)	46.1090	−	79.8632i	0.328655	−	0.569247i	−0.653590	−	0.756849i	\(-0.726738\pi\)
							0.982245	+	0.187601i	\(0.0600713\pi\)
\(5\)	286.168	−	495.658i	0.204765	−	0.354664i	−0.745293	−	0.666738i	\(-0.767690\pi\)
							0.950058	+	0.312073i	\(0.101024\pi\)
\(7\)	319.069	+	552.644i	0.0502277	+	0.0869970i	0.890046	−	0.455870i	\(-0.150672\pi\)
							−0.839818	+	0.542867i	\(0.817339\pi\)
\(11\)	−50651.5			−1.04310			−0.521549	−	0.853221i	\(-0.674646\pi\)
							−0.521549	+	0.853221i	\(0.674646\pi\)
\(13\)	20548.3	+	35590.7i	0.199540	+	0.345614i	0.948379	−	0.317138i	\(-0.102722\pi\)
							−0.748839	+	0.662752i	\(0.769388\pi\)
\(17\)	−250127.	−	433233.i	−0.726341	−	1.25806i	−0.958420	−	0.285363i	\(-0.907886\pi\)
							0.232078	−	0.972697i	\(-0.425447\pi\)
\(19\)	−5441.33	+	9424.65i	−0.00957886	+	0.0165911i	−0.870775	−	0.491682i	\(-0.836382\pi\)
							0.861196	+	0.508273i	\(0.169716\pi\)
\(23\)	−992007.	+	1.71821e6i	−0.739162	+	1.28027i	0.213711	+	0.976897i	\(0.431445\pi\)
							−0.952873	+	0.303369i	\(0.901888\pi\)
\(29\)	2.72855e6	+	4.72599e6i	0.716376	+	1.24080i	0.962426	+	0.271543i	\(0.0875340\pi\)
							−0.246050	+	0.969257i	\(0.579133\pi\)
\(31\)	2.35401e6	−	4.07727e6i	0.457805	−	0.792942i	−0.541039	−	0.840997i	\(-0.681969\pi\)
							0.998845	+	0.0480552i	\(0.0153023\pi\)
\(37\)	−6.16797e6	+	1.06832e7i	−0.541047	+	0.937120i	0.457798	+	0.889056i	\(0.348638\pi\)
							−0.998844	+	0.0480640i	\(0.984695\pi\)
\(41\)	2.38216e7			1.31657			0.658285	−	0.752769i	\(-0.271282\pi\)
							0.658285	+	0.752769i	\(0.271282\pi\)
\(43\)	−3.06703e6	+	2.22078e7i	−0.136808	+	0.990598i
							\(47\)	2.78757e6			0.0833271			0.0416635	−	0.999132i	\(-0.486734\pi\)
0.0416635	+	0.999132i	\(0.486734\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.6.7	✓	64
43.36	even	3	inner	43.10.c.a.36.7	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.7	✓	64	1.1	even	1	trivial
43.10.c.a.36.7	yes	64	43.36	even	3	inner