Embedded newform 43.11.d.a.7.16

• Label: 43.11.d.a.7.16
• Level: $43$
• Weight: $11$
• Character: 43.7
• Analytic conductor: $27.320$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.3203618650\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.16
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.21

$q$-expansion

\(f(q)\)	\(=\)	\(q-13.0858i q^{2} +(106.382 - 61.4196i) q^{3} +852.763 q^{4} +(-2217.26 + 1280.13i) q^{5} +(-803.723 - 1392.09i) q^{6} +(8609.98 + 4970.97i) q^{7} -24558.9i q^{8} +(-21979.8 + 38070.1i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	13.0858i		−	0.408930i	−0.978874	−	0.204465i	\(-0.934454\pi\)
							0.978874	−	0.204465i	\(-0.0655455\pi\)
\(3\)	106.382	−	61.4196i	0.437785	−	0.252756i	−0.264872	−	0.964283i	\(-0.585330\pi\)
							0.702658	+	0.711528i	\(0.251996\pi\)
\(5\)	−2217.26	+	1280.13i	−0.709523	+	0.409643i	−0.810884	−	0.585207i	\(-0.801013\pi\)
							0.101362	+	0.994850i	\(0.467680\pi\)
\(7\)	8609.98	+	4970.97i	0.512285	+	0.295768i	0.733773	−	0.679395i	\(-0.237758\pi\)
							−0.221487	+	0.975163i	\(0.571091\pi\)
\(11\)	158615.			0.984873			0.492437	−	0.870348i	\(-0.336106\pi\)
							0.492437	+	0.870348i	\(0.336106\pi\)
\(13\)	−296217.	+	513064.i	−0.797800	+	1.38183i	0.123247	+	0.992376i	\(0.460669\pi\)
							−0.921046	+	0.389453i	\(0.872664\pi\)
\(17\)	−461009.	+	798492.i	−0.324687	+	0.562375i	−0.981449	−	0.191723i	\(-0.938592\pi\)
							0.656762	+	0.754098i	\(0.271926\pi\)
\(19\)	−250215.	+	144462.i	−0.101052	+	0.0583424i	−0.549674	−	0.835379i	\(-0.685248\pi\)
							0.448622	+	0.893721i	\(0.351915\pi\)
\(23\)	−3.67844e6	−	6.37124e6i	−0.571511	−	0.989885i	−0.996411	−	0.0846453i	\(-0.973024\pi\)
							0.424901	−	0.905240i	\(-0.360309\pi\)
\(29\)	1.56502e7	+	9.03563e6i	0.763008	+	0.440523i	0.830375	−	0.557205i	\(-0.188126\pi\)
							−0.0673665	+	0.997728i	\(0.521460\pi\)
\(31\)	2.67550e7	+	4.63411e7i	0.934538	+	1.61867i	0.775456	+	0.631402i	\(0.217520\pi\)
							0.159082	+	0.987265i	\(0.449147\pi\)
\(37\)	8.85787e7	−	5.11409e7i	1.27738	−	0.737497i	0.301015	−	0.953619i	\(-0.402674\pi\)
							0.976366	+	0.216123i	\(0.0693411\pi\)
\(41\)	−6.58197e7			−0.568115			−0.284058	−	0.958807i	\(-0.591681\pi\)
							−0.284058	+	0.958807i	\(0.591681\pi\)
\(43\)	8.50972e7	+	1.19875e8i	0.578859	+	0.815428i
							\(47\)	4.04928e8			1.76558			0.882792	−	0.469764i	\(-0.155661\pi\)
0.882792	+	0.469764i	\(0.155661\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.16	✓	72
43.37	odd	6	inner	43.11.d.a.37.21	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.16	✓	72	1.1	even	1	trivial
43.11.d.a.37.21	yes	72	43.37	odd	6	inner