Embedded newform 280.2.br.a.123.43

• Label: 280.2.br.a.123.43
• Level: $280$
• Weight: $2$
• Character: 280.123
• 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			123.43
Character	\(\chi\)	\(=\)	280.123
Dual form			280.2.br.a.107.43

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.38436 - 0.289031i) q^{2} +(-1.63560 + 0.438259i) q^{3} +(1.83292 - 0.800248i) q^{4} +(-1.55370 - 1.60811i) q^{5} +(-2.13760 + 1.07945i) q^{6} +(2.49314 - 0.885584i) q^{7} +(2.30613 - 1.63760i) q^{8} +(-0.114945 + 0.0663635i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.38436	−	0.289031i	0.978893	−	0.204376i
							\(3\)	−1.63560	+	0.438259i	−0.944317	+	0.253029i	−0.697949	−	0.716148i	\(-0.745904\pi\)
−0.246368	+	0.969176i	\(0.579237\pi\)
\(5\)	−1.55370	−	1.60811i	−0.694836	−	0.719168i
							\(7\)	2.49314	−	0.885584i	0.942318	−	0.334719i
\(11\)	2.94194	−	5.09559i	0.887029	−	1.53638i								0.0436583	−	0.999047i	\(-0.486099\pi\)
							0.843371	−	0.537332i	\(-0.180568\pi\)
\(13\)	1.49331	−	1.49331i	0.414169	−	0.414169i	−0.469019	−	0.883188i	\(-0.655392\pi\)
							0.883188	+	0.469019i	\(0.155392\pi\)
\(17\)	1.45569	+	5.43270i	0.353056	+	1.31762i	0.882913	+	0.469536i	\(0.155579\pi\)
							−0.529857	+	0.848087i	\(0.677754\pi\)
\(19\)	−3.10041	+	1.79002i	−0.711282	+	0.410659i	−0.811536	−	0.584303i	\(-0.801368\pi\)
							0.100253	+	0.994962i	\(0.468035\pi\)
\(23\)	−2.49897	−	0.669597i	−0.521071	−	0.139621i	−0.0113092	−	0.999936i	\(-0.503600\pi\)
							−0.509762	+	0.860315i	\(0.670267\pi\)
\(29\)	−6.02158			−1.11818			−0.559090	−	0.829107i	\(-0.688849\pi\)
							−0.559090	+	0.829107i	\(0.688849\pi\)
\(31\)	−1.05541	−	0.609340i	−0.189557	−	0.109441i	0.402218	−	0.915544i	\(-0.368239\pi\)
							−0.591775	+	0.806103i	\(0.701573\pi\)
\(37\)	−2.68783	+	10.0311i	−0.441876	+	1.64910i	0.282180	+	0.959362i	\(0.408943\pi\)
							−0.724055	+	0.689742i	\(0.757724\pi\)
\(41\)	2.44353			0.381615			0.190807	−	0.981627i	\(-0.438889\pi\)
							0.190807	+	0.981627i	\(0.438889\pi\)
\(43\)	7.70492	+	7.70492i	1.17499	+	1.17499i	0.981005	+	0.193985i	\(0.0621412\pi\)
							0.193985	+	0.981005i	\(0.437859\pi\)
\(47\)	1.11455	−	4.15954i	0.162573	−	0.606732i	−0.835764	−	0.549089i	\(-0.814975\pi\)
							0.998337	−	0.0576429i	\(-0.0183585\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.123.43	yes	176
5.2	odd	4	inner	280.2.br.a.67.25	yes	176
7.2	even	3	inner	280.2.br.a.163.13	yes	176
8.3	odd	2	inner	280.2.br.a.123.35	yes	176
35.2	odd	12	inner	280.2.br.a.107.35	yes	176
40.27	even	4	inner	280.2.br.a.67.13	✓	176
56.51	odd	6	inner	280.2.br.a.163.25	yes	176
280.107	even	12	inner	280.2.br.a.107.43	yes	176

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.13	✓	176	40.27	even	4	inner
280.2.br.a.67.25	yes	176	5.2	odd	4	inner
280.2.br.a.107.35	yes	176	35.2	odd	12	inner
280.2.br.a.107.43	yes	176	280.107	even	12	inner
280.2.br.a.123.35	yes	176	8.3	odd	2	inner
280.2.br.a.123.43	yes	176	1.1	even	1	trivial
280.2.br.a.163.13	yes	176	7.2	even	3	inner
280.2.br.a.163.25	yes	176	56.51	odd	6	inner