Embedded newform 280.3.c.g.69.18

• Label: 280.3.c.g.69.18
• Level: $280$
• Weight: $3$
• Character: 280.69
• Analytic conductor: $7.629$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	280.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.62944740209\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.18
Character	\(\chi\)	\(=\)	280.69
Dual form			280.3.c.g.69.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.61056 - 1.18579i) q^{2} +3.23212i q^{3} +(1.18782 + 3.81957i) q^{4} +(-3.82711 - 3.21764i) q^{5} +(3.83261 - 5.20553i) q^{6} +(6.97525 - 0.588096i) q^{7} +(2.61615 - 7.56014i) q^{8} -1.44659 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 12 q^{4} - 224 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(57\)	\(71\)	\(141\)	\(241\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.61056	−	1.18579i	−0.805281	−	0.592894i
							\(3\)			3.23212i			1.07737i	0.842506	+	0.538686i	\(0.181079\pi\)
−0.842506	+	0.538686i	\(0.818921\pi\)
\(5\)	−3.82711	−	3.21764i	−0.765423	−	0.643528i
							\(7\)	6.97525	−	0.588096i	0.996465	−	0.0840137i
\(11\)			13.5631i			1.23301i								0.787352	+	0.616504i	\(0.211452\pi\)
							−0.787352	+	0.616504i	\(0.788548\pi\)
\(13\)		−	21.1906i		−	1.63004i	−0.579430	−	0.815022i	\(-0.696725\pi\)
							0.579430	−	0.815022i	\(-0.303275\pi\)
\(17\)	0.174717			0.0102775			0.00513874	−	0.999987i	\(-0.498364\pi\)
							0.00513874	+	0.999987i	\(0.498364\pi\)
\(19\)	20.7233			1.09070			0.545351	−	0.838208i	\(-0.316396\pi\)
							0.545351	+	0.838208i	\(0.316396\pi\)
\(23\)			27.0982i			1.17818i	0.808067	+	0.589091i	\(0.200514\pi\)
							−0.808067	+	0.589091i	\(0.799486\pi\)
\(29\)			18.8246i			0.649124i	0.945864	+	0.324562i	\(0.105217\pi\)
							−0.945864	+	0.324562i	\(0.894783\pi\)
\(31\)			7.48886i			0.241576i	0.992678	+	0.120788i	\(0.0385421\pi\)
							−0.992678	+	0.120788i	\(0.961458\pi\)
\(37\)	66.6203			1.80055			0.900274	−	0.435324i	\(-0.143366\pi\)
							0.900274	+	0.435324i	\(0.143366\pi\)
\(41\)			40.1326i			0.978844i	0.872047	+	0.489422i	\(0.162792\pi\)
							−0.872047	+	0.489422i	\(0.837208\pi\)
\(43\)	27.6721			0.643536			0.321768	−	0.946818i	\(-0.395723\pi\)
							0.321768	+	0.946818i	\(0.395723\pi\)
\(47\)	9.05114			0.192577			0.0962887	−	0.995353i	\(-0.469303\pi\)
							0.0962887	+	0.995353i	\(0.469303\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.3.c.g.69.18	yes	80
4.3	odd	2		1120.3.c.g.209.37		80
5.4	even	2	inner	280.3.c.g.69.63	yes	80
7.6	odd	2	inner	280.3.c.g.69.17	✓	80
8.3	odd	2		1120.3.c.g.209.36		80
8.5	even	2	inner	280.3.c.g.69.61	yes	80
20.19	odd	2		1120.3.c.g.209.8		80
28.27	even	2		1120.3.c.g.209.10		80
35.34	odd	2	inner	280.3.c.g.69.64	yes	80
40.19	odd	2		1120.3.c.g.209.9		80
40.29	even	2	inner	280.3.c.g.69.20	yes	80
56.13	odd	2	inner	280.3.c.g.69.62	yes	80
56.27	even	2		1120.3.c.g.209.7		80
140.139	even	2		1120.3.c.g.209.35		80
280.69	odd	2	inner	280.3.c.g.69.19	yes	80
280.139	even	2		1120.3.c.g.209.38		80

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.3.c.g.69.17	✓	80	7.6	odd	2	inner
280.3.c.g.69.18	yes	80	1.1	even	1	trivial
280.3.c.g.69.19	yes	80	280.69	odd	2	inner
280.3.c.g.69.20	yes	80	40.29	even	2	inner
280.3.c.g.69.61	yes	80	8.5	even	2	inner
280.3.c.g.69.62	yes	80	56.13	odd	2	inner
280.3.c.g.69.63	yes	80	5.4	even	2	inner
280.3.c.g.69.64	yes	80	35.34	odd	2	inner
1120.3.c.g.209.7		80	56.27	even	2
1120.3.c.g.209.8		80	20.19	odd	2
1120.3.c.g.209.9		80	40.19	odd	2
1120.3.c.g.209.10		80	28.27	even	2
1120.3.c.g.209.35		80	140.139	even	2
1120.3.c.g.209.36		80	8.3	odd	2
1120.3.c.g.209.37		80	4.3	odd	2
1120.3.c.g.209.38		80	280.139	even	2