Embedded newform 460.2.q.a.11.19

• Label: 460.2.q.a.11.19
• 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			11.19
Character	\(\chi\)	\(=\)	460.11
Dual form			460.2.q.a.251.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.497467 - 1.32383i) q^{2} +(3.04838 + 0.438291i) q^{3} +(-1.50505 + 1.31712i) q^{4} +(0.281733 + 0.959493i) q^{5} +(-0.936246 - 4.25357i) q^{6} +(-1.74188 - 2.01024i) q^{7} +(2.49236 + 1.33721i) q^{8} +(6.22203 + 1.82695i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.497467	−	1.32383i	−0.351762	−	0.936089i
							\(3\)	3.04838	+	0.438291i	1.75998	+	0.253047i	0.945147	−	0.326646i	\(-0.105918\pi\)
0.814835	+	0.579693i	\(0.196827\pi\)
\(5\)	0.281733	+	0.959493i	0.125995	+	0.429098i
							\(7\)	−1.74188	−	2.01024i	−0.658371	−	0.759800i	0.324140	−	0.946009i	\(-0.394925\pi\)
−0.982510	+	0.186209i	\(0.940380\pi\)
\(11\)	4.23428	+	2.72120i	1.27668	+	0.820474i	0.990475	−	0.137694i	\(-0.0439690\pi\)
							0.286207	+	0.958168i	\(0.407605\pi\)
\(13\)	0.149193	−	0.172178i	0.0413787	−	0.0477535i	−0.734683	−	0.678411i	\(-0.762669\pi\)
							0.776062	+	0.630657i	\(0.217215\pi\)
\(17\)	−3.99260	+	1.82336i	−0.968347	+	0.442229i	−0.835852	−	0.548955i	\(-0.815026\pi\)
							−0.132494	+	0.991184i	\(0.542299\pi\)
\(19\)	1.80325	−	3.94856i	0.413694	−	0.905863i	−0.582003	−	0.813187i	\(-0.697731\pi\)
							0.995696	−	0.0926758i	\(-0.0295420\pi\)
\(23\)	4.45284	+	1.78108i	0.928481	+	0.371380i
							\(29\)	−3.60610	−	7.89625i	−0.669635	−	1.46630i	−0.873263	−	0.487249i	\(-0.838000\pi\)
0.203628	−	0.979048i	\(-0.434727\pi\)
\(31\)	−4.06768	+	0.584844i	−0.730576	+	0.105041i	−0.497557	−	0.867431i	\(-0.665770\pi\)
							−0.233019	+	0.972472i	\(0.574860\pi\)
\(37\)	−3.01217	+	10.2585i	−0.495198	+	1.68649i	0.210184	+	0.977662i	\(0.432594\pi\)
							−0.705382	+	0.708828i	\(0.749224\pi\)
\(41\)	5.96260	−	1.75078i	0.931201	−	0.273425i	0.219261	−	0.975666i	\(-0.429635\pi\)
							0.711939	+	0.702241i	\(0.247817\pi\)
\(43\)	0.273614	−	1.90303i	0.0417257	−	0.290209i	−0.958265	−	0.285882i	\(-0.907714\pi\)
							0.999991	−	0.00432705i	\(-0.00137735\pi\)
\(47\)		−	7.15392i		−	1.04351i	−0.853096	−	0.521754i	\(-0.825278\pi\)
							0.853096	−	0.521754i	\(-0.174722\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.q.a.11.19	✓	480
4.3	odd	2	inner	460.2.q.a.11.36	yes	480
23.21	odd	22	inner	460.2.q.a.251.36	yes	480
92.67	even	22	inner	460.2.q.a.251.19	yes	480

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.q.a.11.19	✓	480	1.1	even	1	trivial
460.2.q.a.11.36	yes	480	4.3	odd	2	inner
460.2.q.a.251.19	yes	480	92.67	even	22	inner
460.2.q.a.251.36	yes	480	23.21	odd	22	inner