Embedded newform 460.2.q.a.11.14

• Label: 460.2.q.a.11.14
• Level: $460$
• Weight: $2$
• Character: 460.11
• Analytic conductor: $3.673$
• Analytic rank: $0$
• Dimension: $480$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.q (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.67311849298\)
Analytic rank:	\(0\)
Dimension:	\(480\)
Relative dimension:	\(48\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.14
Character	\(\chi\)	\(=\)	460.11
Dual form			460.2.q.a.251.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.745947 - 1.20148i) q^{2} +(0.934803 + 0.134404i) q^{3} +(-0.887125 + 1.79249i) q^{4} +(0.281733 + 0.959493i) q^{5} +(-0.535829 - 1.22341i) q^{6} +(2.39561 + 2.76468i) q^{7} +(2.81539 - 0.271235i) q^{8} +(-2.02269 - 0.593915i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(231\)	\(277\)	\(281\)
\(\chi(n)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.745947	−	1.20148i	−0.527464	−	0.849577i
							\(3\)	0.934803	+	0.134404i	0.539709	+	0.0775984i	0.406778	−	0.913527i	\(-0.366652\pi\)
0.132930	+	0.991125i	\(0.457561\pi\)
\(5\)	0.281733	+	0.959493i	0.125995	+	0.429098i
							\(7\)	2.39561	+	2.76468i	0.905457	+	1.04495i	0.998783	+	0.0493171i	\(0.0157045\pi\)
−0.0933266	+	0.995636i	\(0.529750\pi\)
\(11\)	0.0319668	+	0.0205438i	0.00963835	+	0.00619419i	0.545451	−	0.838143i	\(-0.316358\pi\)
							−0.535813	+	0.844337i	\(0.679995\pi\)
\(13\)	−4.24090	+	4.89426i	−1.17621	+	1.35742i	−0.255680	+	0.966762i	\(0.582299\pi\)
							−0.920534	+	0.390662i	\(0.872246\pi\)
\(17\)	−0.722073	+	0.329760i	−0.175128	+	0.0799785i	−0.501050	−	0.865418i	\(-0.667053\pi\)
							0.325922	+	0.945397i	\(0.394325\pi\)
\(19\)	−2.61816	+	5.73296i	−0.600646	+	1.31523i	0.328145	+	0.944627i	\(0.393577\pi\)
							−0.928791	+	0.370604i	\(0.879151\pi\)
\(23\)	4.15610	−	2.39309i	0.866606	−	0.498993i
							\(29\)	2.89662	+	6.34272i	0.537890	+	1.17781i	0.962212	+	0.272303i	\(0.0877852\pi\)
−0.424322	+	0.905511i	\(0.639488\pi\)
\(31\)	7.43165	−	1.06851i	1.33476	−	0.191910i	0.562281	−	0.826946i	\(-0.309924\pi\)
							0.772483	+	0.635036i	\(0.219015\pi\)
\(37\)	2.08605	−	7.10444i	0.342945	−	1.16796i	−0.589838	−	0.807522i	\(-0.700808\pi\)
							0.932782	−	0.360440i	\(-0.117374\pi\)
\(41\)	1.99786	−	0.586624i	0.312013	−	0.0916153i	−0.121977	−	0.992533i	\(-0.538923\pi\)
							0.433990	+	0.900918i	\(0.357105\pi\)
\(43\)	0.588300	−	4.09171i	0.0897149	−	0.623981i	−0.894509	−	0.447051i	\(-0.852474\pi\)
							0.984223	−	0.176930i	\(-0.0566166\pi\)
\(47\)		−	5.49487i		−	0.801509i	−0.916186	−	0.400754i	\(-0.868748\pi\)
							0.916186	−	0.400754i	\(-0.131252\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.q.a.11.14	✓	480
4.3	odd	2	inner	460.2.q.a.11.32	yes	480
23.21	odd	22	inner	460.2.q.a.251.32	yes	480
92.67	even	22	inner	460.2.q.a.251.14	yes	480

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.q.a.11.14	✓	480	1.1	even	1	trivial
460.2.q.a.11.32	yes	480	4.3	odd	2	inner
460.2.q.a.251.14	yes	480	92.67	even	22	inner
460.2.q.a.251.32	yes	480	23.21	odd	22	inner