Embedded newform 273.2.u.c.62.10

• Label: 273.2.u.c.62.10
• Level: $273$
• Weight: $2$
• Character: 273.62
• Analytic conductor: $2.180$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.u (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.17991597518\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			62.10
Character	\(\chi\)	\(=\)	273.62
Dual form			273.2.u.c.251.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.835434 - 1.44701i) q^{2} +(0.710596 - 1.57957i) q^{3} +(-0.395901 + 0.685720i) q^{4} -2.15210i q^{5} +(-2.87932 + 0.291388i) q^{6} +(-2.44178 + 1.01869i) q^{7} -2.01874 q^{8} +(-1.99011 - 2.24488i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 40 q^{4} - 6 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\)	\(92\)	\(106\)	\(157\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.835434	−	1.44701i	−0.590741	−	1.02319i	−0.994133	−	0.108166i	\(-0.965502\pi\)
							0.403392	−	0.915027i	\(-0.367831\pi\)
\(3\)	0.710596	−	1.57957i	0.410263	−	0.911967i
							\(5\)		−	2.15210i		−	0.962446i	−0.876598	−	0.481223i	\(-0.840193\pi\)
0.876598	−	0.481223i	\(-0.159807\pi\)
\(7\)	−2.44178	+	1.01869i	−0.922904	+	0.385030i
							\(11\)	2.84265	+	4.92362i	0.857092	+	1.48453i	0.874691	+	0.484682i	\(0.161065\pi\)
−0.0175988	+	0.999845i	\(0.505602\pi\)
\(13\)	−0.842729	−	3.50568i	−0.233731	−	0.972301i
							\(17\)	2.39056	−	4.14058i	0.579797	−	1.00424i	−0.415705	−	0.909499i	\(-0.636465\pi\)
0.995502	−	0.0947385i	\(-0.0302015\pi\)
\(19\)	1.84215	−	3.19070i	0.422618	−	0.731996i	−0.573577	−	0.819152i	\(-0.694444\pi\)
							0.996195	+	0.0871559i	\(0.0277778\pi\)
\(23\)	−2.16571	+	1.25037i	−0.451582	+	0.260721i	−0.708498	−	0.705713i	\(-0.750627\pi\)
							0.256916	+	0.966434i	\(0.417294\pi\)
\(29\)	1.76189	−	1.01723i	0.327174	−	0.188894i	−0.327412	−	0.944882i	\(-0.606176\pi\)
							0.654586	+	0.755988i	\(0.272843\pi\)
\(31\)	−1.53290			−0.275316			−0.137658	−	0.990480i	\(-0.543958\pi\)
							−0.137658	+	0.990480i	\(0.543958\pi\)
\(37\)	−5.72022	+	3.30257i	−0.940398	+	0.542939i	−0.890085	−	0.455794i	\(-0.849355\pi\)
							−0.0503132	+	0.998733i	\(0.516022\pi\)
\(41\)	1.25100	−	0.722267i	0.195374	−	0.112799i	−0.399122	−	0.916898i	\(-0.630685\pi\)
							0.594496	+	0.804099i	\(0.297352\pi\)
\(43\)	4.58026	−	7.93325i	0.698483	−	1.20981i	−0.270509	−	0.962718i	\(-0.587192\pi\)
							0.968992	−	0.247091i	\(-0.0794748\pi\)
\(47\)			0.512180i			0.0747092i	0.999302	+	0.0373546i	\(0.0118931\pi\)
							−0.999302	+	0.0373546i	\(0.988107\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.u.c.62.10	yes	64
3.2	odd	2	inner	273.2.u.c.62.24	yes	64
7.6	odd	2	inner	273.2.u.c.62.9	✓	64
13.4	even	6	inner	273.2.u.c.251.23	yes	64
21.20	even	2	inner	273.2.u.c.62.23	yes	64
39.17	odd	6	inner	273.2.u.c.251.9	yes	64
91.69	odd	6	inner	273.2.u.c.251.24	yes	64
273.251	even	6	inner	273.2.u.c.251.10	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.u.c.62.9	✓	64	7.6	odd	2	inner
273.2.u.c.62.10	yes	64	1.1	even	1	trivial
273.2.u.c.62.23	yes	64	21.20	even	2	inner
273.2.u.c.62.24	yes	64	3.2	odd	2	inner
273.2.u.c.251.9	yes	64	39.17	odd	6	inner
273.2.u.c.251.10	yes	64	273.251	even	6	inner
273.2.u.c.251.23	yes	64	13.4	even	6	inner
273.2.u.c.251.24	yes	64	91.69	odd	6	inner