Embedded newform 287.3.p.a.230.5

• Label: 287.3.p.a.230.5
• Level: $287$
• Weight: $3$
• Character: 287.230
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $216$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.p (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(216\)
Relative dimension:	\(54\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			230.5
Character	\(\chi\)	\(=\)	287.230
Dual form			287.3.p.a.146.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.07676 + 3.31392i) q^{2} -5.20007 q^{3} +(-6.58656 - 4.78542i) q^{4} +(-3.83595 + 5.27973i) q^{5} +(5.59921 - 17.2326i) q^{6} +(-2.02913 - 6.69945i) q^{7} +(11.6747 - 8.48214i) q^{8} +18.0408 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 6 q^{2} - 110 q^{4} - 5 q^{7} + 22 q^{8} + 552 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\)	\(206\)	\(211\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.07676	+	3.31392i	−0.538378	+	1.65696i	0.197856	+	0.980231i	\(0.436602\pi\)
							−0.736234	+	0.676727i	\(0.763398\pi\)
\(3\)	−5.20007			−1.73336			−0.866679	−	0.498867i	\(-0.833750\pi\)
							−0.866679	+	0.498867i	\(0.833750\pi\)
\(5\)	−3.83595	+	5.27973i	−0.767189	+	1.05595i	0.229392	+	0.973334i	\(0.426326\pi\)
							−0.996582	+	0.0826117i	\(0.973674\pi\)
\(7\)	−2.02913	−	6.69945i	−0.289876	−	0.957064i
							\(11\)	−5.80125	−	7.98474i	−0.527387	−	0.725885i	0.459343	−	0.888259i	\(-0.348085\pi\)
−0.986729	+	0.162374i	\(0.948085\pi\)
\(13\)	−2.67817	+	8.24257i	−0.206013	+	0.634044i	0.793657	+	0.608366i	\(0.208175\pi\)
							−0.999670	+	0.0256783i	\(0.991825\pi\)
\(17\)	−19.9239	+	14.4756i	−1.17199	+	0.851503i	−0.991246	−	0.132026i	\(-0.957852\pi\)
							−0.180748	+	0.983530i	\(0.557852\pi\)
\(19\)	−10.7325	−	33.0311i	−0.564866	−	1.73848i	−0.668349	−	0.743848i	\(-0.732999\pi\)
							0.103482	−	0.994631i	\(-0.467001\pi\)
\(23\)	−7.77370	+	23.9250i	−0.337987	+	1.04022i	0.627245	+	0.778822i	\(0.284183\pi\)
							−0.965232	+	0.261395i	\(0.915817\pi\)
\(29\)	−20.1821	+	27.7783i	−0.695934	+	0.957871i	0.304052	+	0.952655i	\(0.401660\pi\)
							−0.999986	+	0.00521568i	\(0.998340\pi\)
\(31\)	12.9292	+	17.7955i	0.417071	+	0.574049i	0.964925	−	0.262525i	\(-0.0845551\pi\)
							−0.547854	+	0.836574i	\(0.684555\pi\)
\(37\)	−29.4738	−	21.4140i	−0.796589	−	0.578756i	0.113322	−	0.993558i	\(-0.463851\pi\)
							−0.909912	+	0.414802i	\(0.863851\pi\)
\(41\)	40.6070	−	5.66318i	0.990415	−	0.138126i
							\(43\)	2.00850	−	6.18152i	0.0467092	−	0.143756i	−0.924982	−	0.380011i	\(-0.875920\pi\)
0.971691	+	0.236255i	\(0.0759201\pi\)
\(47\)	−4.62652	+	14.2390i	−0.0984366	+	0.302957i	−0.988134	−	0.153594i	\(-0.950915\pi\)
							0.889697	+	0.456551i	\(0.150915\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.p.a.230.5	yes	216
7.6	odd	2	inner	287.3.p.a.230.6	yes	216
41.23	even	10	inner	287.3.p.a.146.6	yes	216
287.146	odd	10	inner	287.3.p.a.146.5	✓	216

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.p.a.146.5	✓	216	287.146	odd	10	inner
287.3.p.a.146.6	yes	216	41.23	even	10	inner
287.3.p.a.230.5	yes	216	1.1	even	1	trivial
287.3.p.a.230.6	yes	216	7.6	odd	2	inner