Embedded newform 280.2.br.a.67.39

• Label: 280.2.br.a.67.39
• 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			67.39
Character	\(\chi\)	\(=\)	280.67
Dual form			280.2.br.a.163.39

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.26895 - 0.624317i) q^{2} +(0.552175 + 2.06075i) q^{3} +(1.22046 - 1.58445i) q^{4} +(-1.28687 + 1.82865i) q^{5} +(1.98724 + 2.27025i) q^{6} +(0.126396 + 2.64273i) q^{7} +(0.559495 - 2.77254i) q^{8} +(-1.34370 + 0.775786i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.26895	−	0.624317i	0.897282	−	0.441459i
							\(3\)	0.552175	+	2.06075i	0.318799	+	1.18977i	0.920401	+	0.390976i	\(0.127863\pi\)
−0.601602	+	0.798796i	\(0.705471\pi\)
\(5\)	−1.28687	+	1.82865i	−0.575507	+	0.817797i
							\(7\)	0.126396	+	2.64273i	0.0477733	+	0.998858i
\(11\)	−0.610032	+	1.05661i	−0.183932	+	0.318579i								−0.943216	−	0.332180i	\(-0.892216\pi\)
							0.759284	+	0.650759i	\(0.225549\pi\)
\(13\)	−2.68783	−	2.68783i	−0.745469	−	0.745469i	0.228155	−	0.973625i	\(-0.426731\pi\)
							−0.973625	+	0.228155i	\(0.926731\pi\)
\(17\)	6.90315	−	1.84969i	1.67426	−	0.448616i	0.708005	−	0.706207i	\(-0.249595\pi\)
							0.966254	+	0.257591i	\(0.0829287\pi\)
\(19\)	0.485494	−	0.280300i	0.111380	−	0.0643052i	−0.443275	−	0.896386i	\(-0.646184\pi\)
							0.554655	+	0.832080i	\(0.312850\pi\)
\(23\)	1.57579	−	5.88093i	0.328575	−	1.22626i	−0.582094	−	0.813121i	\(-0.697766\pi\)
							0.910669	−	0.413137i	\(-0.135567\pi\)
\(29\)	−6.36373			−1.18172			−0.590858	−	0.806776i	\(-0.701211\pi\)
							−0.590858	+	0.806776i	\(0.701211\pi\)
\(31\)	5.87051	+	3.38934i	1.05437	+	0.608743i	0.923871	−	0.382705i	\(-0.125007\pi\)
							0.130504	+	0.991448i	\(0.458341\pi\)
\(37\)	4.32578	+	1.15909i	0.711153	+	0.190553i	0.596221	−	0.802820i	\(-0.296668\pi\)
							0.114932	+	0.993373i	\(0.463335\pi\)
\(41\)	−11.6461			−1.81882			−0.909410	−	0.415901i	\(-0.863466\pi\)
							−0.909410	+	0.415901i	\(0.863466\pi\)
\(43\)	3.61709	−	3.61709i	0.551600	−	0.551600i	−0.375302	−	0.926903i	\(-0.622461\pi\)
							0.926903	+	0.375302i	\(0.122461\pi\)
\(47\)	−2.05817	−	0.551484i	−0.300214	−	0.0804422i	0.105567	−	0.994412i	\(-0.466334\pi\)
							−0.405782	+	0.913970i	\(0.633001\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.67.39	yes	176
5.3	odd	4	inner	280.2.br.a.123.17	yes	176
7.2	even	3	inner	280.2.br.a.107.10	yes	176
8.3	odd	2	inner	280.2.br.a.67.14	✓	176
35.23	odd	12	inner	280.2.br.a.163.14	yes	176
40.3	even	4	inner	280.2.br.a.123.10	yes	176
56.51	odd	6	inner	280.2.br.a.107.17	yes	176
280.163	even	12	inner	280.2.br.a.163.39	yes	176

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.14	✓	176	8.3	odd	2	inner
280.2.br.a.67.39	yes	176	1.1	even	1	trivial
280.2.br.a.107.10	yes	176	7.2	even	3	inner
280.2.br.a.107.17	yes	176	56.51	odd	6	inner
280.2.br.a.123.10	yes	176	40.3	even	4	inner
280.2.br.a.123.17	yes	176	5.3	odd	4	inner
280.2.br.a.163.14	yes	176	35.23	odd	12	inner
280.2.br.a.163.39	yes	176	280.163	even	12	inner