Embedded newform 280.2.br.a.67.7

• Label: 280.2.br.a.67.7
• 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			67.7
Character	\(\chi\)	\(=\)	280.67
Dual form			280.2.br.a.163.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.24593 + 0.669082i) q^{2} +(-0.569871 - 2.12679i) q^{3} +(1.10466 - 1.66725i) q^{4} +(2.01915 + 0.960747i) q^{5} +(2.13301 + 2.26853i) q^{6} +(0.895661 + 2.48954i) q^{7} +(-0.260793 + 2.81638i) q^{8} +(-1.60039 + 0.923986i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.24593	+	0.669082i	−0.881002	+	0.473112i
							\(3\)	−0.569871	−	2.12679i	−0.329015	−	1.22790i	−0.910214	−	0.414139i	\(-0.864083\pi\)
0.581199	−	0.813762i	\(-0.302584\pi\)
\(5\)	2.01915	+	0.960747i	0.902991	+	0.429659i
							\(7\)	0.895661	+	2.48954i	0.338528	+	0.940956i
\(11\)	0.771347	−	1.33601i	0.232570	−	0.402823i								−0.725994	−	0.687701i	\(-0.758620\pi\)
							0.958564	+	0.284879i	\(0.0919533\pi\)
\(13\)	2.74298	+	2.74298i	0.760764	+	0.760764i	0.976461	−	0.215696i	\(-0.0692021\pi\)
							−0.215696	+	0.976461i	\(0.569202\pi\)
\(17\)	−2.84162	+	0.761410i	−0.689195	+	0.184669i	−0.586386	−	0.810032i	\(-0.699450\pi\)
							−0.102809	+	0.994701i	\(0.532783\pi\)
\(19\)	5.92101	−	3.41850i	1.35837	−	0.784258i	0.368969	−	0.929442i	\(-0.379711\pi\)
							0.989405	+	0.145184i	\(0.0463774\pi\)
\(23\)	0.834231	−	3.11339i	0.173949	−	0.649187i	−0.822779	−	0.568361i	\(-0.807578\pi\)
							0.996728	−	0.0808257i	\(-0.0257557\pi\)
\(29\)	0.336699			0.0625234			0.0312617	−	0.999511i	\(-0.490047\pi\)
							0.0312617	+	0.999511i	\(0.490047\pi\)
\(31\)	−3.64240	−	2.10294i	−0.654195	−	0.377700i	0.135866	−	0.990727i	\(-0.456618\pi\)
							−0.790062	+	0.613027i	\(0.789952\pi\)
\(37\)	4.93839	+	1.32324i	0.811867	+	0.217539i	0.640788	−	0.767718i	\(-0.278608\pi\)
							0.171079	+	0.985257i	\(0.445275\pi\)
\(41\)	4.49493			0.701990			0.350995	−	0.936377i	\(-0.385843\pi\)
							0.350995	+	0.936377i	\(0.385843\pi\)
\(43\)	−0.152775	+	0.152775i	−0.0232980	+	0.0232980i	−0.718660	−	0.695362i	\(-0.755244\pi\)
							0.695362	+	0.718660i	\(0.255244\pi\)
\(47\)	−10.0398	−	2.69016i	−1.46446	−	0.392400i	−0.563429	−	0.826164i	\(-0.690518\pi\)
							−0.901026	+	0.433765i	\(0.857185\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.67.7	✓	176
5.3	odd	4	inner	280.2.br.a.123.29	yes	176
7.2	even	3	inner	280.2.br.a.107.37	yes	176
8.3	odd	2	inner	280.2.br.a.67.31	yes	176
35.23	odd	12	inner	280.2.br.a.163.31	yes	176
40.3	even	4	inner	280.2.br.a.123.37	yes	176
56.51	odd	6	inner	280.2.br.a.107.29	yes	176
280.163	even	12	inner	280.2.br.a.163.7	yes	176

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.7	✓	176	1.1	even	1	trivial
280.2.br.a.67.31	yes	176	8.3	odd	2	inner
280.2.br.a.107.29	yes	176	56.51	odd	6	inner
280.2.br.a.107.37	yes	176	7.2	even	3	inner
280.2.br.a.123.29	yes	176	5.3	odd	4	inner
280.2.br.a.123.37	yes	176	40.3	even	4	inner
280.2.br.a.163.7	yes	176	280.163	even	12	inner
280.2.br.a.163.31	yes	176	35.23	odd	12	inner