Embedded newform 43.5.h.a.26.1

• Label: 43.5.h.a.26.1
• Level: $43$
• Weight: $5$
• Character: 43.26
• Analytic conductor: $4.445$
• Analytic rank: $0$
• Dimension: $168$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.h (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.44490841261\)
Analytic rank:	\(0\)
Dimension:	\(168\)
Relative dimension:	\(14\) over \(\Q(\zeta_{42})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			26.1
Character	\(\chi\)	\(=\)	43.26
Dual form			43.5.h.a.5.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-6.99583 + 1.59675i) q^{2} +(1.41459 + 4.58598i) q^{3} +(31.9766 - 15.3991i) q^{4} +(-39.9449 - 15.6772i) q^{5} +(-17.2189 - 29.8240i) q^{6} +(11.2347 + 6.48633i) q^{7} +(-109.351 + 87.2042i) q^{8} +(47.8952 - 32.6544i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{2} - 20 q^{3} + 220 q^{4} - 11 q^{5} - 22 q^{6} - 150 q^{7} + 322 q^{8} - 660 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{17}{42}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−6.99583	+	1.59675i	−1.74896	+	0.399188i	−0.972855	−	0.231417i	\(-0.925664\pi\)
							−0.776104	+	0.630605i	\(0.782807\pi\)
\(3\)	1.41459	+	4.58598i	0.157176	+	0.509553i	0.999570	−	0.0293087i	\(-0.00933060\pi\)
							−0.842394	+	0.538862i	\(0.818854\pi\)
\(5\)	−39.9449	−	15.6772i	−1.59780	−	0.627089i	−0.611378	−	0.791338i	\(-0.709385\pi\)
							−0.986419	+	0.164249i	\(0.947480\pi\)
\(7\)	11.2347	+	6.48633i	0.229279	+	0.132374i	0.610239	−	0.792217i	\(-0.291073\pi\)
							−0.380961	+	0.924591i	\(0.624407\pi\)
\(11\)	95.9073	+	46.1865i	0.792622	+	0.381707i	0.785965	−	0.618271i	\(-0.212167\pi\)
							0.00665713	+	0.999978i	\(0.497881\pi\)
\(13\)	105.668	−	15.9269i	0.625254	−	0.0942419i	0.171230	−	0.985231i	\(-0.445226\pi\)
							0.454024	+	0.890989i	\(0.349988\pi\)
\(17\)	143.781	+	366.348i	0.497512	+	1.26764i	0.930517	+	0.366248i	\(0.119358\pi\)
							−0.433005	+	0.901391i	\(0.642547\pi\)
\(19\)	212.984	−	312.390i	0.589983	−	0.865346i	−0.408901	−	0.912579i	\(-0.634088\pi\)
							0.998884	+	0.0472327i	\(0.0150402\pi\)
\(23\)	−61.9154	−	826.204i	−0.117042	−	1.56182i	−0.678678	−	0.734436i	\(-0.737447\pi\)
							0.561635	−	0.827385i	\(-0.310172\pi\)
\(29\)	353.746	−	1146.82i	0.420625	−	1.36363i	−0.459198	−	0.888334i	\(-0.651863\pi\)
							0.879824	−	0.475300i	\(-0.157661\pi\)
\(31\)	363.712	−	337.476i	0.378473	−	0.351171i	−0.467882	−	0.883791i	\(-0.654983\pi\)
							0.846355	+	0.532619i	\(0.178792\pi\)
\(37\)	−1395.27	+	805.559i	−1.01919	+	0.588429i	−0.913869	−	0.406009i	\(-0.866920\pi\)
							−0.105320	+	0.994438i	\(0.533587\pi\)
\(41\)	108.422	+	475.026i	0.0644983	+	0.282585i	0.996884	−	0.0788790i	\(-0.0251341\pi\)
							−0.932386	+	0.361464i	\(0.882277\pi\)
\(43\)	1839.89	+	183.341i	0.995072	+	0.0991568i
							\(47\)	−692.962	+	333.713i	−0.313699	+	0.151070i	−0.584108	−	0.811676i	\(-0.698556\pi\)
0.270409	+	0.962746i	\(0.412841\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.h.a.26.1	yes	168
43.5	odd	42	inner	43.5.h.a.5.1	✓	168

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.h.a.5.1	✓	168	43.5	odd	42	inner
43.5.h.a.26.1	yes	168	1.1	even	1	trivial