Embedded newform 43.6.g.a.24.2

• Label: 43.6.g.a.24.2
• Level: $43$
• Weight: $6$
• Character: 43.24
• 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			24.2
Character	\(\chi\)	\(=\)	43.24
Dual form			43.6.g.a.9.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-5.80705 + 7.28181i) q^{2} +(-18.0713 + 2.72380i) q^{3} +(-12.1822 - 53.3739i) q^{4} +(-87.0006 + 59.3160i) q^{5} +(85.1064 - 147.409i) q^{6} +(-25.6945 - 44.5042i) q^{7} +(190.876 + 91.9209i) q^{8} +(86.9470 - 26.8196i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{20}{21}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−5.80705	+	7.28181i	−1.02655	+	1.28725i	−0.0694229	+	0.997587i	\(0.522116\pi\)
							−0.957128	+	0.289666i	\(0.906456\pi\)
\(3\)	−18.0713	+	2.72380i	−1.15927	+	0.174732i	−0.700387	−	0.713764i	\(-0.746989\pi\)
							−0.458885	+	0.888496i	\(0.651751\pi\)
\(5\)	−87.0006	+	59.3160i	−1.55631	+	1.06108i	−0.588794	+	0.808283i	\(0.700397\pi\)
							−0.967520	+	0.252794i	\(0.918651\pi\)
\(7\)	−25.6945	−	44.5042i	−0.198196	−	0.343286i	0.749747	−	0.661724i	\(-0.230175\pi\)
							−0.947944	+	0.318438i	\(0.896842\pi\)
\(11\)	−89.3088	+	391.288i	−0.222542	+	0.975022i	0.733014	+	0.680214i	\(0.238113\pi\)
							−0.955556	+	0.294808i	\(0.904744\pi\)
\(13\)	66.5463	+	887.998i	0.109211	+	1.45732i	0.735394	+	0.677640i	\(0.236997\pi\)
							−0.626183	+	0.779676i	\(0.715384\pi\)
\(17\)	938.053	+	639.553i	0.787236	+	0.536728i	0.888906	−	0.458090i	\(-0.151466\pi\)
							−0.101670	+	0.994818i	\(0.532419\pi\)
\(19\)	−2471.40	−	762.326i	−1.57058	−	0.484459i	−0.617344	−	0.786694i	\(-0.711791\pi\)
							−0.953234	+	0.302235i	\(0.902267\pi\)
\(23\)	−785.281	−	728.634i	−0.309532	−	0.287204i	0.510075	−	0.860130i	\(-0.329618\pi\)
							−0.819607	+	0.572926i	\(0.805808\pi\)
\(29\)	−1435.42	−	216.355i	−0.316945	−	0.0477718i	−0.0113569	−	0.999936i	\(-0.503615\pi\)
							−0.305589	+	0.952164i	\(0.598853\pi\)
\(31\)	−16.1137	−	41.0572i	−0.00301157	−	0.00767334i	0.929360	−	0.369175i	\(-0.120360\pi\)
							−0.932372	+	0.361501i	\(0.882264\pi\)
\(37\)	125.215	−	216.878i	0.0150366	−	0.0260442i	−0.858409	−	0.512966i	\(-0.828547\pi\)
							0.873446	+	0.486921i	\(0.161880\pi\)
\(41\)	−8967.44	+	11244.8i	−0.833123	+	1.04470i	0.165168	+	0.986265i	\(0.447183\pi\)
							−0.998291	+	0.0584376i	\(0.981388\pi\)
\(43\)	−1197.46	+	12065.4i	−0.0987616	+	0.995111i
							\(47\)	−939.225	−	4115.01i	−0.0620190	−	0.271723i	0.934405	−	0.356211i	\(-0.115932\pi\)
−0.996424	+	0.0844881i	\(0.973075\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.g.a.24.2	yes	204
43.9	even	21	inner	43.6.g.a.9.2	✓	204

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.g.a.9.2	✓	204	43.9	even	21	inner
43.6.g.a.24.2	yes	204	1.1	even	1	trivial