Embedded newform 43.6.g.a.10.14

• Label: 43.6.g.a.10.14
• Level: $43$
• Weight: $6$
• Character: 43.10
• Analytic conductor: $6.897$
• Analytic rank: $0$
• Dimension: $204$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89650425196\)
Analytic rank:	\(0\)
Dimension:	\(204\)
Relative dimension:	\(17\) over \(\Q(\zeta_{21})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			10.14
Character	\(\chi\)	\(=\)	43.10
Dual form			43.6.g.a.13.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.56114 + 6.83979i) q^{2} +(17.9921 + 16.6943i) q^{3} +(-15.5146 + 7.47142i) q^{4} +(-101.474 + 15.2947i) q^{5} +(-86.0971 + 149.125i) q^{6} +(-71.7301 - 124.240i) q^{7} +(64.6514 + 81.0703i) q^{8} +(26.8592 + 358.411i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{21}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.56114	+	6.83979i	0.275973	+	1.20912i	0.902836	+	0.429986i	\(0.141481\pi\)
							−0.626863	+	0.779130i	\(0.715661\pi\)
\(3\)	17.9921	+	16.6943i	1.15420	+	1.07094i	0.996512	+	0.0834484i	\(0.0265934\pi\)
							0.157684	+	0.987490i	\(0.449597\pi\)
\(5\)	−101.474	+	15.2947i	−1.81522	+	0.273600i	−0.966764	−	0.255670i	\(-0.917704\pi\)
							−0.848453	+	0.529270i	\(0.822466\pi\)
\(7\)	−71.7301	−	124.240i	−0.553295	−	0.958334i	−0.998034	−	0.0626744i	\(-0.980037\pi\)
							0.444739	−	0.895660i	\(-0.353296\pi\)
\(11\)	656.677	+	316.239i	1.63633	+	0.788014i	0.999860	+	0.0167107i	\(0.00531942\pi\)
							0.636468	+	0.771303i	\(0.280395\pi\)
\(13\)	−77.2065	+	196.719i	−0.126705	+	0.322840i	−0.980124	−	0.198386i	\(-0.936430\pi\)
							0.853418	+	0.521226i	\(0.174525\pi\)
\(17\)	739.372	+	111.442i	0.620498	+	0.0935251i	0.451765	−	0.892137i	\(-0.350794\pi\)
							0.168733	+	0.985662i	\(0.446032\pi\)
\(19\)	−39.5886	+	528.273i	−0.0251586	+	0.335718i	0.970395	+	0.241523i	\(0.0776469\pi\)
							−0.995554	+	0.0941953i	\(0.969972\pi\)
\(23\)	−550.567	+	375.370i	−0.217016	+	0.147959i	−0.666949	−	0.745103i	\(-0.732400\pi\)
							0.449933	+	0.893062i	\(0.351448\pi\)
\(29\)	613.126	−	568.898i	0.135380	−	0.125614i	−0.609577	−	0.792727i	\(-0.708661\pi\)
							0.744957	+	0.667113i	\(0.232470\pi\)
\(31\)	−1568.86	−	483.928i	−0.293210	−	0.0904434i	0.144660	−	0.989481i	\(-0.453791\pi\)
							−0.437871	+	0.899038i	\(0.644267\pi\)
\(37\)	863.298	−	1495.28i	0.103671	−	0.179563i	−0.809524	−	0.587087i	\(-0.800275\pi\)
							0.913194	+	0.407524i	\(0.133608\pi\)
\(41\)	−4012.12	−	17578.2i	−0.372747	−	1.63311i	−0.719028	−	0.694981i	\(-0.755413\pi\)
							0.346281	−	0.938131i	\(-0.387444\pi\)
\(43\)	350.771	+	12119.6i	0.0289303	+	0.999581i
							\(47\)	22807.4	−	10983.5i	1.50602	−	0.725261i	0.514778	−	0.857323i	\(-0.327874\pi\)
0.991241	+	0.132063i	\(0.0421600\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.g.a.10.14	✓	204
43.13	even	21	inner	43.6.g.a.13.14	yes	204

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.g.a.10.14	✓	204	1.1	even	1	trivial
43.6.g.a.13.14	yes	204	43.13	even	21	inner