Embedded newform 273.2.y.b.101.10

• Label: 273.2.y.b.101.10
• Level: $273$
• Weight: $2$
• Character: 273.101
• Analytic conductor: $2.180$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.y (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			101.10
Character	\(\chi\)	\(=\)	273.101
Dual form			273.2.y.b.173.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.638569 + 1.10603i) q^{2} +(1.72991 - 0.0860586i) q^{3} +(0.184460 + 0.319495i) q^{4} +(-2.29307 + 1.32390i) q^{5} +(-1.00948 + 1.96829i) q^{6} +(-0.551092 + 2.58772i) q^{7} -3.02544 q^{8} +(2.98519 - 0.297747i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 28 q^{4} - 12 q^{7}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.638569	+	1.10603i	−0.451536	+	0.782084i	−0.998482	−	0.0550846i	\(-0.982457\pi\)
							0.546946	+	0.837168i	\(0.315790\pi\)
\(3\)	1.72991	−	0.0860586i	0.998765	−	0.0496859i
							\(5\)	−2.29307	+	1.32390i	−1.02549	+	0.592068i	−0.915690	−	0.401885i	\(-0.868355\pi\)
−0.109802	+	0.993953i	\(0.535022\pi\)
\(7\)	−0.551092	+	2.58772i	−0.208293	+	0.978066i
							\(11\)	−1.85563			−0.559495			−0.279747	−	0.960074i	\(-0.590251\pi\)
−0.279747	+	0.960074i	\(0.590251\pi\)
\(13\)	−2.83799	−	2.22391i	−0.787118	−	0.616803i
							\(17\)	1.91592	+	3.31847i	0.464679	+	0.804848i	0.999187	−	0.0403155i	\(-0.0128363\pi\)
−0.534508	+	0.845164i	\(0.679503\pi\)
\(19\)	7.64086			1.75293			0.876466	−	0.481463i	\(-0.159894\pi\)
							0.876466	+	0.481463i	\(0.159894\pi\)
\(23\)	2.37351	+	1.37035i	0.494911	+	0.285737i	0.726610	−	0.687051i	\(-0.241095\pi\)
							−0.231698	+	0.972788i	\(0.574428\pi\)
\(29\)	0.988255	−	0.570569i	0.183514	−	0.105952i	−0.405428	−	0.914127i	\(-0.632878\pi\)
							0.588943	+	0.808175i	\(0.299544\pi\)
\(31\)	−0.675990	+	1.17085i	−0.121411	+	0.210291i	−0.920324	−	0.391156i	\(-0.872075\pi\)
							0.798913	+	0.601446i	\(0.205409\pi\)
\(37\)	2.91537	+	1.68319i	0.479285	+	0.276715i	0.720118	−	0.693851i	\(-0.244087\pi\)
							−0.240834	+	0.970566i	\(0.577421\pi\)
\(41\)	2.70294	−	1.56054i	0.422129	−	0.243716i	−0.273859	−	0.961770i	\(-0.588300\pi\)
							0.695988	+	0.718054i	\(0.254967\pi\)
\(43\)	−5.33446	+	9.23956i	−0.813498	+	1.40902i	0.0969032	+	0.995294i	\(0.469106\pi\)
							−0.910401	+	0.413726i	\(0.864227\pi\)
\(47\)	3.14987	−	1.81858i	0.459456	−	0.265267i	−0.252359	−	0.967634i	\(-0.581207\pi\)
							0.711816	+	0.702366i	\(0.247873\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.y.b.101.10	✓	64
3.2	odd	2	inner	273.2.y.b.101.23	yes	64
7.5	odd	6		273.2.br.b.257.23	yes	64
13.4	even	6		273.2.br.b.17.10	yes	64
21.5	even	6		273.2.br.b.257.10	yes	64
39.17	odd	6		273.2.br.b.17.23	yes	64
91.82	odd	6	inner	273.2.y.b.173.23	yes	64
273.173	even	6	inner	273.2.y.b.173.10	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.y.b.101.10	✓	64	1.1	even	1	trivial
273.2.y.b.101.23	yes	64	3.2	odd	2	inner
273.2.y.b.173.10	yes	64	273.173	even	6	inner
273.2.y.b.173.23	yes	64	91.82	odd	6	inner
273.2.br.b.17.10	yes	64	13.4	even	6
273.2.br.b.17.23	yes	64	39.17	odd	6
273.2.br.b.257.10	yes	64	21.5	even	6
273.2.br.b.257.23	yes	64	7.5	odd	6