Embedded newform 273.2.bn.c.146.5

• Label: 273.2.bn.c.146.5
• Level: $273$
• Weight: $2$
• Character: 273.146
• 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.bn (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			146.5
Character	\(\chi\)	\(=\)	273.146
Dual form			273.2.bn.c.230.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.88922 + 1.09074i) q^{2} +(-1.60830 - 0.642938i) q^{3} +(1.37944 - 2.38926i) q^{4} -0.155426 q^{5} +(3.73972 - 0.539589i) q^{6} +(0.959965 + 2.46545i) q^{7} +1.65550i q^{8} +(2.17326 + 2.06808i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(92\)	\(106\)	\(157\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.88922	+	1.09074i	−1.33588	+	0.771272i	−0.986194	−	0.165594i	\(-0.947046\pi\)
							−0.349688	+	0.936866i	\(0.613713\pi\)
\(3\)	−1.60830	−	0.642938i	−0.928553	−	0.371201i
							\(5\)	−0.155426			−0.0695088			−0.0347544	−	0.999396i	\(-0.511065\pi\)
−0.0347544	+	0.999396i	\(0.511065\pi\)
\(7\)	0.959965	+	2.46545i	0.362833	+	0.931854i
							\(11\)	−4.82278	+	2.78444i	−1.45412	+	0.839539i	−0.998712	−	0.0507416i	\(-0.983842\pi\)
−0.455412	+	0.890281i	\(0.650508\pi\)
\(13\)	0.173851	−	3.60136i	0.0482175	−	0.998837i
							\(17\)	1.70733	−	2.95718i	0.414088	−	0.717221i	−0.581244	−	0.813729i	\(-0.697434\pi\)
0.995332	+	0.0965078i	\(0.0307673\pi\)
\(19\)	−6.24865	−	3.60766i	−1.43354	−	0.827654i	−0.436149	−	0.899874i	\(-0.643658\pi\)
							−0.997389	+	0.0722207i	\(0.976991\pi\)
\(23\)	3.78041	−	2.18262i	0.788269	−	0.455108i	−0.0510835	−	0.998694i	\(-0.516267\pi\)
							0.839353	+	0.543587i	\(0.182934\pi\)
\(29\)	−1.14529	+	0.661231i	−0.212674	+	0.122788i	−0.602554	−	0.798078i	\(-0.705850\pi\)
							0.389879	+	0.920866i	\(0.372517\pi\)
\(31\)		−	2.02590i		−	0.363863i	−0.983311	−	0.181932i	\(-0.941765\pi\)
							0.983311	−	0.181932i	\(-0.0582350\pi\)
\(37\)	−4.70398	−	8.14753i	−0.773329	−	1.33944i	−0.935729	−	0.352720i	\(-0.885257\pi\)
							0.162400	−	0.986725i	\(-0.448076\pi\)
\(41\)	−0.0869869	−	0.150666i	−0.0135851	−	0.0235300i	0.859153	−	0.511719i	\(-0.170991\pi\)
							−0.872738	+	0.488189i	\(0.837658\pi\)
\(43\)	0.147677	−	0.255784i	0.0225205	−	0.0390067i	−0.854546	−	0.519377i	\(-0.826164\pi\)
							0.877066	+	0.480370i	\(0.159498\pi\)
\(47\)	−10.8966			−1.58943			−0.794715	−	0.606983i	\(-0.792380\pi\)
							−0.794715	+	0.606983i	\(0.792380\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bn.c.146.5	✓	64
3.2	odd	2	inner	273.2.bn.c.146.27	yes	64
7.6	odd	2	inner	273.2.bn.c.146.6	yes	64
13.9	even	3	inner	273.2.bn.c.230.28	yes	64
21.20	even	2	inner	273.2.bn.c.146.28	yes	64
39.35	odd	6	inner	273.2.bn.c.230.6	yes	64
91.48	odd	6	inner	273.2.bn.c.230.27	yes	64
273.230	even	6	inner	273.2.bn.c.230.5	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bn.c.146.5	✓	64	1.1	even	1	trivial
273.2.bn.c.146.6	yes	64	7.6	odd	2	inner
273.2.bn.c.146.27	yes	64	3.2	odd	2	inner
273.2.bn.c.146.28	yes	64	21.20	even	2	inner
273.2.bn.c.230.5	yes	64	273.230	even	6	inner
273.2.bn.c.230.6	yes	64	39.35	odd	6	inner
273.2.bn.c.230.27	yes	64	91.48	odd	6	inner
273.2.bn.c.230.28	yes	64	13.9	even	3	inner