Embedded newform 280.2.br.a.107.37

• Label: 280.2.br.a.107.37
• Level: $280$
• Weight: $2$
• Character: 280.107
• 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			107.37
Character	\(\chi\)	\(=\)	280.107
Dual form			280.2.br.a.123.37

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.20240 + 0.744462i) q^{2} +(2.12679 + 0.569871i) q^{3} +(0.891554 + 1.79029i) q^{4} +(-0.177544 - 2.22901i) q^{5} +(2.13301 + 2.26853i) q^{6} +(-2.48954 - 0.895661i) q^{7} +(-0.260793 + 2.81638i) q^{8} +(1.60039 + 0.923986i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.20240	+	0.744462i	0.850228	+	0.526414i
							\(3\)	2.12679	+	0.569871i	1.22790	+	0.329015i	0.813762	−	0.581199i	\(-0.197416\pi\)
0.414139	+	0.910214i	\(0.364083\pi\)
\(5\)	−0.177544	−	2.22901i	−0.0793999	−	0.996843i
							\(7\)	−2.48954	−	0.895661i	−0.940956	−	0.338528i
\(11\)	0.771347	+	1.33601i	0.232570	+	0.402823i								0.958564	−	0.284879i	\(-0.0919533\pi\)
							−0.725994	+	0.687701i	\(0.758620\pi\)
\(13\)	2.74298	+	2.74298i	0.760764	+	0.760764i	0.976461	−	0.215696i	\(-0.0692021\pi\)
							−0.215696	+	0.976461i	\(0.569202\pi\)
\(17\)	0.761410	−	2.84162i	0.184669	−	0.689195i	−0.810032	−	0.586386i	\(-0.800550\pi\)
							0.994701	−	0.102809i	\(-0.0327830\pi\)
\(19\)	−5.92101	−	3.41850i	−1.35837	−	0.784258i	−0.368969	−	0.929442i	\(-0.620289\pi\)
							−0.989405	+	0.145184i	\(0.953623\pi\)
\(23\)	−3.11339	+	0.834231i	−0.649187	+	0.173949i	−0.568361	−	0.822779i	\(-0.692422\pi\)
							−0.0808257	+	0.996728i	\(0.525756\pi\)
\(29\)	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	\(-0.543382\pi\)
							0.790062	+	0.613027i	\(0.210048\pi\)
\(37\)	−1.32324	−	4.93839i	−0.217539	−	0.811867i	−0.985257	−	0.171079i	\(-0.945275\pi\)
							0.767718	−	0.640788i	\(-0.221392\pi\)
\(41\)	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	\(0.255244\pi\)
\(47\)	2.69016	+	10.0398i	0.392400	+	1.46446i	0.826164	+	0.563429i	\(0.190518\pi\)
							−0.433765	+	0.901026i	\(0.642815\pi\)

(See \(a_n\) instead)

Twists

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

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.7	✓	176	7.4	even	3	inner
280.2.br.a.67.31	yes	176	56.11	odd	6	inner
280.2.br.a.107.29	yes	176	8.3	odd	2	inner
280.2.br.a.107.37	yes	176	1.1	even	1	trivial
280.2.br.a.123.29	yes	176	35.18	odd	12	inner
280.2.br.a.123.37	yes	176	280.123	even	12	inner
280.2.br.a.163.7	yes	176	40.3	even	4	inner
280.2.br.a.163.31	yes	176	5.3	odd	4	inner