Embedded newform 151.2.h.a.44.7

• Label: 151.2.h.a.44.7
• Level: $151$
• Weight: $2$
• Character: 151.44
• Analytic conductor: $1.206$
• Analytic rank: $0$
• Dimension: $220$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.h (of order \(25\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.20574107052\)
Analytic rank:	\(0\)
Dimension:	\(220\)
Relative dimension:	\(11\) over \(\Q(\zeta_{25})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			44.7
Character	\(\chi\)	\(=\)	151.44
Dual form			151.2.h.a.127.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.383748 + 0.278810i) q^{2} +(1.11035 + 2.35961i) q^{3} +(-0.548506 - 1.68813i) q^{4} +(-1.78697 + 2.16008i) q^{5} +(-0.231787 + 1.21507i) q^{6} +(-0.184632 + 2.93465i) q^{7} +(0.553336 - 1.70299i) q^{8} +(-2.42260 + 2.92842i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/151\mathbb{Z}\right)^\times\).

\(n\)	\(6\)
\(\chi(n)\)	\(e\left(\frac{14}{25}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.383748	+	0.278810i	0.271351	+	0.197148i	0.715136	−	0.698985i	\(-0.246365\pi\)
							−0.443785	+	0.896133i	\(0.646365\pi\)
\(3\)	1.11035	+	2.35961i	0.641059	+	1.36232i	0.916125	+	0.400894i	\(0.131300\pi\)
							−0.275066	+	0.961425i	\(0.588700\pi\)
\(5\)	−1.78697	+	2.16008i	−0.799159	+	0.966018i	−0.999907	−	0.0136252i	\(-0.995663\pi\)
							0.200748	+	0.979643i	\(0.435663\pi\)
\(7\)	−0.184632	+	2.93465i	−0.0697844	+	1.10919i	0.794855	+	0.606799i	\(0.207547\pi\)
							−0.864640	+	0.502393i	\(0.832453\pi\)
\(11\)	1.92399	−	4.08869i	0.580106	−	1.23279i	−0.372345	−	0.928095i	\(-0.621446\pi\)
							0.952451	−	0.304693i	\(-0.0985539\pi\)
\(13\)	4.85668	−	0.613542i	1.34700	−	0.170166i	0.581472	−	0.813567i	\(-0.302477\pi\)
							0.765530	+	0.643401i	\(0.222477\pi\)
\(17\)	−0.126608	−	2.01238i	−0.0307070	−	0.488073i	−0.983085	−	0.183152i	\(-0.941370\pi\)
							0.952378	−	0.304921i	\(-0.0986301\pi\)
\(19\)	0.727599	+	2.23932i	0.166923	+	0.513735i	0.999173	−	0.0406650i	\(-0.0129476\pi\)
							−0.832250	+	0.554400i	\(0.812948\pi\)
\(23\)	−2.02324	−	6.22688i	−0.421874	−	1.29839i	−0.905956	−	0.423372i	\(-0.860846\pi\)
							0.484082	−	0.875023i	\(-0.339154\pi\)
\(29\)	6.49299	−	3.56955i	1.20572	−	0.662849i	0.253225	−	0.967407i	\(-0.418509\pi\)
							0.952494	+	0.304558i	\(0.0985088\pi\)
\(31\)	−4.51894	+	7.12071i	−0.811625	+	1.27892i	0.145534	+	0.989353i	\(0.453510\pi\)
							−0.957159	+	0.289563i	\(0.906490\pi\)
\(37\)	−6.70422	+	0.846939i	−1.10217	+	0.139236i	−0.655303	−	0.755366i	\(-0.727459\pi\)
							−0.446863	+	0.894602i	\(0.647459\pi\)
\(41\)	1.07590	−	5.64005i	0.168027	−	0.880828i	−0.794009	−	0.607906i	\(-0.792010\pi\)
							0.962036	−	0.272922i	\(-0.0879901\pi\)
\(43\)	−0.584073	−	9.28357i	−0.0890702	−	1.41573i	−0.748086	−	0.663602i	\(-0.769027\pi\)
							0.659016	−	0.752129i	\(-0.270973\pi\)
\(47\)	−0.412196	+	2.16081i	−0.0601249	+	0.315186i	−0.999626	−	0.0273611i	\(-0.991290\pi\)
							0.939501	+	0.342547i	\(0.111290\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.h.a.44.7	✓	220
151.127	even	25	inner	151.2.h.a.127.7	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.h.a.44.7	✓	220	1.1	even	1	trivial
151.2.h.a.127.7	yes	220	151.127	even	25	inner