Embedded newform 280.2.br.a.67.23

• Label: 280.2.br.a.67.23
• Level: $280$
• Weight: $2$
• Character: 280.67
• Analytic conductor: $2.236$
• Analytic rank: $0$
• Dimension: $176$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.br (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.23581125660\)
Analytic rank:	\(0\)
Dimension:	\(176\)
Relative dimension:	\(44\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.23
Character	\(\chi\)	\(=\)	280.67
Dual form			280.2.br.a.163.23

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.0614353 - 1.41288i) q^{2} +(0.231015 + 0.862160i) q^{3} +(-1.99245 - 0.173601i) q^{4} +(2.23447 + 0.0844371i) q^{5} +(1.23232 - 0.273429i) q^{6} +(-1.19273 + 2.36165i) q^{7} +(-0.367684 + 2.80443i) q^{8} +(1.90812 - 1.10166i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\)	\(57\)	\(71\)	\(141\)	\(241\)
\(\chi(n)\)	\(e\left(\frac{1}{4}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.0614353	−	1.41288i	0.0434413	−	0.999056i
							\(3\)	0.231015	+	0.862160i	0.133377	+	0.497768i	0.999999	−	0.00119575i	\(-0.000380621\pi\)
−0.866623	+	0.498964i	\(0.833714\pi\)
\(5\)	2.23447	+	0.0844371i	0.999287	+	0.0377614i
							\(7\)	−1.19273	+	2.36165i	−0.450811	+	0.892620i
\(11\)	2.58625	−	4.47952i	0.779784	−	1.35063i								−0.152281	−	0.988337i	\(-0.548662\pi\)
							0.932066	−	0.362289i	\(-0.118005\pi\)
\(13\)	2.64215	+	2.64215i	0.732800	+	0.732800i	0.971174	−	0.238374i	\(-0.0766142\pi\)
							−0.238374	+	0.971174i	\(0.576614\pi\)
\(17\)	2.70689	−	0.725310i	0.656518	−	0.175913i	0.0848439	−	0.996394i	\(-0.472961\pi\)
							0.571674	+	0.820481i	\(0.306294\pi\)
\(19\)	−5.82319	+	3.36202i	−1.33593	+	0.771301i	−0.986201	−	0.165550i	\(-0.947060\pi\)
							−0.349730	+	0.936850i	\(0.613727\pi\)
\(23\)	1.38495	−	5.16870i	0.288782	−	1.07775i	−0.657249	−	0.753673i	\(-0.728280\pi\)
							0.946031	−	0.324076i	\(-0.105053\pi\)
\(29\)	−8.59297			−1.59567			−0.797837	−	0.602873i	\(-0.794022\pi\)
							−0.797837	+	0.602873i	\(0.794022\pi\)
\(31\)	−1.82817	−	1.05549i	−0.328349	−	0.189572i	0.326759	−	0.945108i	\(-0.394043\pi\)
							−0.655108	+	0.755535i	\(0.727377\pi\)
\(37\)	1.67990	+	0.450128i	0.276174	+	0.0740005i	0.394247	−	0.919004i	\(-0.371005\pi\)
							−0.118074	+	0.993005i	\(0.537672\pi\)
\(41\)	−2.04040			−0.318658			−0.159329	−	0.987226i	\(-0.550933\pi\)
							−0.159329	+	0.987226i	\(0.550933\pi\)
\(43\)	−3.38710	+	3.38710i	−0.516528	+	0.516528i	−0.916519	−	0.399991i	\(-0.869013\pi\)
							0.399991	+	0.916519i	\(0.369013\pi\)
\(47\)	−1.82399	−	0.488737i	−0.266056	−	0.0712895i	0.123325	−	0.992366i	\(-0.460644\pi\)
							−0.389381	+	0.921077i	\(0.627311\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.67.23	✓	176
5.3	odd	4	inner	280.2.br.a.123.2	yes	176
7.2	even	3	inner	280.2.br.a.107.7	yes	176
8.3	odd	2	inner	280.2.br.a.67.29	yes	176
35.23	odd	12	inner	280.2.br.a.163.29	yes	176
40.3	even	4	inner	280.2.br.a.123.7	yes	176
56.51	odd	6	inner	280.2.br.a.107.2	yes	176
280.163	even	12	inner	280.2.br.a.163.23	yes	176

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.23	✓	176	1.1	even	1	trivial
280.2.br.a.67.29	yes	176	8.3	odd	2	inner
280.2.br.a.107.2	yes	176	56.51	odd	6	inner
280.2.br.a.107.7	yes	176	7.2	even	3	inner
280.2.br.a.123.2	yes	176	5.3	odd	4	inner
280.2.br.a.123.7	yes	176	40.3	even	4	inner
280.2.br.a.163.23	yes	176	280.163	even	12	inner
280.2.br.a.163.29	yes	176	35.23	odd	12	inner