Embedded newform 43.6.c.a.6.6

• Label: 43.6.c.a.6.6
• 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			6.6
Character	\(\chi\)	\(=\)	43.6
Dual form			43.6.c.a.36.6

$q$-expansion

\(f(q)\)	\(=\)	\(q-4.45148 q^{2} +(9.81167 - 16.9943i) q^{3} -12.1844 q^{4} +(-39.8809 + 69.0757i) q^{5} +(-43.6764 + 75.6497i) q^{6} +(8.78791 + 15.2211i) q^{7} +196.686 q^{8} +(-71.0376 - 123.041i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−4.45148			−0.786917			−0.393459	−	0.919342i	\(-0.628722\pi\)
							−0.393459	+	0.919342i	\(0.628722\pi\)
\(3\)	9.81167	−	16.9943i	0.629419	−	1.09019i	−0.358250	−	0.933626i	\(-0.616626\pi\)
							0.987669	−	0.156559i	\(-0.0500403\pi\)
\(5\)	−39.8809	+	69.0757i	−0.713411	+	1.23566i	0.250159	+	0.968205i	\(0.419517\pi\)
							−0.963569	+	0.267458i	\(0.913816\pi\)
\(7\)	8.78791	+	15.2211i	0.0677861	+	0.117409i	0.897926	−	0.440145i	\(-0.145073\pi\)
							−0.830140	+	0.557554i	\(0.811740\pi\)
\(11\)	296.199			0.738077			0.369039	−	0.929414i	\(-0.379687\pi\)
							0.369039	+	0.929414i	\(0.379687\pi\)
\(13\)	198.091	+	343.104i	0.325093	+	0.563077i	0.981531	−	0.191303i	\(-0.0612712\pi\)
							−0.656438	+	0.754380i	\(0.727938\pi\)
\(17\)	676.236	+	1171.28i	0.567513	+	0.982962i	0.996811	+	0.0797988i	\(0.0254278\pi\)
							−0.429298	+	0.903163i	\(0.641239\pi\)
\(19\)	−680.888	+	1179.33i	−0.432704	+	0.749466i	−0.997105	−	0.0760348i	\(-0.975774\pi\)
							0.564401	+	0.825501i	\(0.309107\pi\)
\(23\)	−570.380	+	987.927i	−0.224825	+	0.389408i	−0.956267	−	0.292495i	\(-0.905514\pi\)
							0.731442	+	0.681904i	\(0.238848\pi\)
\(29\)	−1198.69	−	2076.18i	−0.264673	−	0.458428i	0.702805	−	0.711383i	\(-0.251931\pi\)
							−0.967478	+	0.252955i	\(0.918597\pi\)
\(31\)	−2838.29	+	4916.07i	−0.530460	+	0.918784i	0.468908	+	0.883247i	\(0.344648\pi\)
							−0.999368	+	0.0355371i	\(0.988686\pi\)
\(37\)	−3038.57	+	5262.96i	−0.364893	+	0.632013i	−0.988759	−	0.149518i	\(-0.952228\pi\)
							0.623866	+	0.781531i	\(0.285561\pi\)
\(41\)	10487.5			0.974345			0.487172	−	0.873306i	\(-0.338028\pi\)
							0.487172	+	0.873306i	\(0.338028\pi\)
\(43\)	865.356	+	12093.8i	0.0713713	+	0.997450i
							\(47\)	−26809.0			−1.77026			−0.885129	−	0.465346i	\(-0.845930\pi\)
−0.885129	+	0.465346i	\(0.845930\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.6.6	✓	34
43.36	even	3	inner	43.6.c.a.36.6	yes	34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.6	✓	34	1.1	even	1	trivial
43.6.c.a.36.6	yes	34	43.36	even	3	inner