Embedded newform 43.6.g.a.24.7

• Label: 43.6.g.a.24.7
• 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			24.7
Character	\(\chi\)	\(=\)	43.24
Dual form			43.6.g.a.9.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.80763 + 2.26670i) q^{2} +(21.5746 - 3.25185i) q^{3} +(5.25028 + 23.0030i) q^{4} +(62.1654 - 42.3837i) q^{5} +(-31.6280 + 54.7813i) q^{6} +(1.33082 + 2.30504i) q^{7} +(-145.219 - 69.9337i) q^{8} +(222.685 - 68.6892i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.80763	+	2.26670i	−0.319548	+	0.400700i	−0.915499	−	0.402321i	\(-0.868204\pi\)
							0.595951	+	0.803021i	\(0.296775\pi\)
\(3\)	21.5746	−	3.25185i	1.38401	−	0.208606i	0.585542	−	0.810642i	\(-0.300882\pi\)
							0.798469	+	0.602036i	\(0.205644\pi\)
\(5\)	62.1654	−	42.3837i	1.11205	−	0.758182i	0.139348	−	0.990243i	\(-0.455499\pi\)
							0.972701	+	0.232061i	\(0.0745470\pi\)
\(7\)	1.33082	+	2.30504i	0.0102653	+	0.0177801i	0.871112	−	0.491084i	\(-0.163399\pi\)
							−0.860847	+	0.508864i	\(0.830066\pi\)
\(11\)	124.242	−	544.341i	0.309590	−	1.35640i	−0.545580	−	0.838058i	\(-0.683691\pi\)
							0.855171	−	0.518346i	\(-0.173452\pi\)
\(13\)	82.1364	+	1096.03i	0.134796	+	1.79873i	0.498165	+	0.867082i	\(0.334007\pi\)
							−0.363369	+	0.931645i	\(0.618373\pi\)
\(17\)	522.203	+	356.032i	0.438245	+	0.298790i	0.762271	−	0.647258i	\(-0.224084\pi\)
							−0.324026	+	0.946048i	\(0.605037\pi\)
\(19\)	22.1918	+	6.84526i	0.0141029	+	0.00435017i	0.301799	−	0.953372i	\(-0.402413\pi\)
							−0.287696	+	0.957722i	\(0.592889\pi\)
\(23\)	495.405	+	459.669i	0.195272	+	0.181186i	0.771749	−	0.635927i	\(-0.219382\pi\)
							−0.576476	+	0.817114i	\(0.695573\pi\)
\(29\)	−8135.05	−	1226.16i	−1.79624	−	0.270740i	−0.835764	−	0.549088i	\(-0.814975\pi\)
							−0.960480	+	0.278348i	\(0.910213\pi\)
\(31\)	−2825.48	−	7199.20i	−0.528066	−	1.34549i	−0.907415	−	0.420236i	\(-0.861947\pi\)
							0.379349	−	0.925254i	\(-0.376148\pi\)
\(37\)	−2449.75	+	4243.10i	−0.294183	+	0.509540i	−0.974795	−	0.223104i	\(-0.928381\pi\)
							0.680611	+	0.732645i	\(0.261714\pi\)
\(41\)	−634.352	+	795.453i	−0.0589347	+	0.0739017i	−0.810425	−	0.585842i	\(-0.800764\pi\)
							0.751490	+	0.659744i	\(0.229335\pi\)
\(43\)	4687.88	+	11181.8i	0.386639	+	0.922231i
							\(47\)	−2523.30	−	11055.3i	−0.166619	−	0.730004i	−0.987333	−	0.158665i	\(-0.949281\pi\)
0.820714	−	0.571340i	\(-0.193576\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.g.a.24.7	yes	204
43.9	even	21	inner	43.6.g.a.9.7	✓	204

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.g.a.9.7	✓	204	43.9	even	21	inner
43.6.g.a.24.7	yes	204	1.1	even	1	trivial