Embedded newform 43.5.d.a.7.9

• Label: 43.5.d.a.7.9
• Level: $43$
• Weight: $5$
• Character: 43.7
• Analytic conductor: $4.445$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.44490841261\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.9
Character	\(\chi\)	\(=\)	43.7
Dual form			43.5.d.a.37.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+1.02950i q^{2} +(-6.61850 + 3.82119i) q^{3} +14.9401 q^{4} +(-23.6208 + 13.6375i) q^{5} +(-3.93391 - 6.81373i) q^{6} +(-37.2107 - 21.4836i) q^{7} +31.8528i q^{8} +(-11.2970 + 19.5669i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)			1.02950i			0.257374i	0.991685	+	0.128687i	\(0.0410763\pi\)
							−0.991685	+	0.128687i	\(0.958924\pi\)
\(3\)	−6.61850	+	3.82119i	−0.735389	+	0.424577i	−0.820390	−	0.571804i	\(-0.806244\pi\)
							0.0850014	+	0.996381i	\(0.472911\pi\)
\(5\)	−23.6208	+	13.6375i	−0.944833	+	0.545500i	−0.891472	−	0.453076i	\(-0.850327\pi\)
							−0.0533609	+	0.998575i	\(0.516993\pi\)
\(7\)	−37.2107	−	21.4836i	−0.759402	−	0.438441i	0.0696791	−	0.997569i	\(-0.477802\pi\)
							−0.829081	+	0.559129i	\(0.811136\pi\)
\(11\)	−144.067			−1.19063			−0.595317	−	0.803491i	\(-0.702973\pi\)
							−0.595317	+	0.803491i	\(0.702973\pi\)
\(13\)	−62.0578	+	107.487i	−0.367206	+	0.636019i	−0.989128	−	0.147060i	\(-0.953019\pi\)
							0.621922	+	0.783079i	\(0.286352\pi\)
\(17\)	−32.5880	+	56.4441i	−0.112761	+	0.195308i	−0.916883	−	0.399157i	\(-0.869303\pi\)
							0.804121	+	0.594465i	\(0.202636\pi\)
\(19\)	410.952	−	237.263i	1.13837	−	0.657239i	0.192344	−	0.981328i	\(-0.438391\pi\)
							0.946027	+	0.324089i	\(0.105058\pi\)
\(23\)	411.181	+	712.186i	0.777279	+	1.34629i	0.933505	+	0.358565i	\(0.116734\pi\)
							−0.156226	+	0.987721i	\(0.549933\pi\)
\(29\)	128.081	+	73.9475i	0.152296	+	0.0879280i	0.574211	−	0.818707i	\(-0.305309\pi\)
							−0.421916	+	0.906635i	\(0.638642\pi\)
\(31\)	194.426	+	336.756i	0.202316	+	0.350422i	0.949274	−	0.314449i	\(-0.101820\pi\)
							−0.746958	+	0.664871i	\(0.768486\pi\)
\(37\)	191.434	−	110.524i	0.139835	−	0.0807337i	−0.428450	−	0.903565i	\(-0.640940\pi\)
							0.568285	+	0.822832i	\(0.307607\pi\)
\(41\)	−1102.62			−0.655929			−0.327965	−	0.944690i	\(-0.606363\pi\)
							−0.327965	+	0.944690i	\(0.606363\pi\)
\(43\)	−721.525	+	1702.41i	−0.390225	+	0.920720i
							\(47\)	−3551.16			−1.60759			−0.803794	−	0.594908i	\(-0.797188\pi\)
−0.803794	+	0.594908i	\(0.797188\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.d.a.7.9	✓	28
43.37	odd	6	inner	43.5.d.a.37.6	yes	28

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.d.a.7.9	✓	28	1.1	even	1	trivial
43.5.d.a.37.6	yes	28	43.37	odd	6	inner