Embedded newform 43.10.c.a.6.14

• Label: 43.10.c.a.6.14
• 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			6.14
Character	\(\chi\)	\(=\)	43.6
Dual form			43.10.c.a.36.14

$q$-expansion

\(f(q)\)	\(=\)	\(q-10.8555 q^{2} +(83.9447 - 145.396i) q^{3} -394.158 q^{4} +(1237.61 - 2143.60i) q^{5} +(-911.262 + 1578.35i) q^{6} +(6087.74 + 10544.3i) q^{7} +9836.80 q^{8} +(-4251.92 - 7364.54i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−10.8555			−0.479750			−0.239875	−	0.970804i	\(-0.577106\pi\)
							−0.239875	+	0.970804i	\(0.577106\pi\)
\(3\)	83.9447	−	145.396i	0.598339	−	1.03635i	−0.394727	−	0.918798i	\(-0.629161\pi\)
							0.993066	−	0.117556i	\(-0.0375058\pi\)
\(5\)	1237.61	−	2143.60i	0.885561	−	1.53384i	0.0404912	−	0.999180i	\(-0.487108\pi\)
							0.845070	−	0.534656i	\(-0.179559\pi\)
\(7\)	6087.74	+	10544.3i	0.958330	+	1.65988i	0.726557	+	0.687106i	\(0.241119\pi\)
							0.231773	+	0.972770i	\(0.425547\pi\)
\(11\)	82455.1			1.69805			0.849025	−	0.528352i	\(-0.177190\pi\)
							0.849025	+	0.528352i	\(0.177190\pi\)
\(13\)	36873.5	+	63866.7i	0.358071	+	0.620197i	0.987639	−	0.156749i	\(-0.0501013\pi\)
							−0.629568	+	0.776946i	\(0.716768\pi\)
\(17\)	63396.2	+	109805.i	0.184096	+	0.318863i	0.943271	−	0.332023i	\(-0.107731\pi\)
							−0.759176	+	0.650886i	\(0.774398\pi\)
\(19\)	71379.7	−	123633.i	0.125656	−	0.217643i	−0.796333	−	0.604858i	\(-0.793230\pi\)
							0.921989	+	0.387216i	\(0.126563\pi\)
\(23\)	−651521.	+	1.12847e6i	−0.485460	+	0.840841i	−0.999860	−	0.0167091i	\(-0.994681\pi\)
							0.514401	+	0.857550i	\(0.328014\pi\)
\(29\)	1.36934e6	+	2.37177e6i	0.359518	+	0.622703i	0.987880	−	0.155218i	\(-0.0496079\pi\)
							−0.628363	+	0.777921i	\(0.716275\pi\)
\(31\)	466941.	−	808765.i	0.0908101	−	0.157288i	−0.817042	−	0.576578i	\(-0.804388\pi\)
							0.907852	+	0.419290i	\(0.137721\pi\)
\(37\)	6.26589e6	−	1.08528e7i	0.549635	−	0.951997i	−0.448664	−	0.893701i	\(-0.648100\pi\)
							0.998299	−	0.0582960i	\(-0.0185667\pi\)
\(41\)	1.63158e7			0.901738			0.450869	−	0.892590i	\(-0.351114\pi\)
							0.450869	+	0.892590i	\(0.351114\pi\)
\(43\)	−2.19968e7	−	4.32811e6i	−0.981187	−	0.193059i
							\(47\)	−3.10948e7			−0.929496			−0.464748	−	0.885443i	\(-0.653855\pi\)
−0.464748	+	0.885443i	\(0.653855\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.6.14	✓	64
43.36	even	3	inner	43.10.c.a.36.14	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.14	✓	64	1.1	even	1	trivial
43.10.c.a.36.14	yes	64	43.36	even	3	inner