Embedded newform 460.2.j.a.47.14

• Label: 460.2.j.a.47.14
• Level: $460$
• Weight: $2$
• Character: 460.47
• Analytic conductor: $3.673$
• Analytic rank: $0$
• Dimension: $132$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.67311849298\)
Analytic rank:	\(0\)
Dimension:	\(132\)
Relative dimension:	\(66\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.14
Character	\(\chi\)	\(=\)	460.47
Dual form			460.2.j.a.323.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.19284 - 0.759687i) q^{2} +(0.971542 + 0.971542i) q^{3} +(0.845751 + 1.81238i) q^{4} +(0.361417 - 2.20667i) q^{5} +(-0.420830 - 1.89697i) q^{6} +(2.60162 - 2.60162i) q^{7} +(0.367989 - 2.80439i) q^{8} -1.11221i q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{8}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\)	\(231\)	\(277\)	\(281\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{1}{4}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.19284	−	0.759687i	−0.843468	−	0.537180i
							\(3\)	0.971542	+	0.971542i	0.560920	+	0.560920i	0.929569	−	0.368649i	\(-0.120180\pi\)
−0.368649	+	0.929569i	\(0.620180\pi\)
\(5\)	0.361417	−	2.20667i	0.161630	−	0.986851i
							\(7\)	2.60162	−	2.60162i	0.983320	−	0.983320i	−0.0165428	−	0.999863i	\(-0.505266\pi\)
0.999863	+	0.0165428i	\(0.00526598\pi\)
\(11\)		−	3.26630i		−	0.984825i	−0.870362	−	0.492413i	\(-0.836115\pi\)
							0.870362	−	0.492413i	\(-0.163885\pi\)
\(13\)	−3.95028	+	3.95028i	−1.09561	+	1.09561i	−0.100692	+	0.994918i	\(0.532106\pi\)
							−0.994918	+	0.100692i	\(0.967894\pi\)
\(17\)	−0.351920	−	0.351920i	−0.0853533	−	0.0853533i	0.663141	−	0.748494i	\(-0.269223\pi\)
							−0.748494	+	0.663141i	\(0.769223\pi\)
\(19\)	−3.67345			−0.842746			−0.421373	−	0.906887i	\(-0.638452\pi\)
							−0.421373	+	0.906887i	\(0.638452\pi\)
\(23\)	−0.707107	−	0.707107i	−0.147442	−	0.147442i
							\(29\)			0.336636i			0.0625117i	0.999511	+	0.0312558i	\(0.00995067\pi\)
−0.999511	+	0.0312558i	\(0.990049\pi\)
\(31\)		−	7.34437i		−	1.31909i	−0.751666	−	0.659544i	\(-0.770750\pi\)
							0.751666	−	0.659544i	\(-0.229250\pi\)
\(37\)	4.98189	+	4.98189i	0.819018	+	0.819018i	0.985966	−	0.166948i	\(-0.0533911\pi\)
							−0.166948	+	0.985966i	\(0.553391\pi\)
\(41\)	11.8273			1.84711			0.923554	−	0.383469i	\(-0.125271\pi\)
							0.923554	+	0.383469i	\(0.125271\pi\)
\(43\)	5.70897	+	5.70897i	0.870609	+	0.870609i	0.992539	−	0.121929i	\(-0.0389082\pi\)
							−0.121929	+	0.992539i	\(0.538908\pi\)
\(47\)	−2.11068	+	2.11068i	−0.307874	+	0.307874i	−0.844085	−	0.536210i	\(-0.819855\pi\)
							0.536210	+	0.844085i	\(0.319855\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.j.a.47.14	✓	132
4.3	odd	2	inner	460.2.j.a.47.20	yes	132
5.3	odd	4	inner	460.2.j.a.323.20	yes	132
20.3	even	4	inner	460.2.j.a.323.14	yes	132

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.j.a.47.14	✓	132	1.1	even	1	trivial
460.2.j.a.47.20	yes	132	4.3	odd	2	inner
460.2.j.a.323.14	yes	132	20.3	even	4	inner
460.2.j.a.323.20	yes	132	5.3	odd	4	inner