Embedded newform 273.2.u.c.62.20

• Label: 273.2.u.c.62.20
• 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			62.20
Character	\(\chi\)	\(=\)	273.62
Dual form			273.2.u.c.251.20

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.376715 + 0.652489i) q^{2} +(0.798779 - 1.53686i) q^{3} +(0.716172 - 1.24045i) q^{4} +2.14750i q^{5} +(1.30370 - 0.0577652i) q^{6} +(1.87127 + 1.87038i) q^{7} +2.58603 q^{8} +(-1.72391 - 2.45523i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 40 q^{4} - 6 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.376715	+	0.652489i	0.266378	+	0.461380i	0.967924	−	0.251244i	\(-0.0808398\pi\)
							−0.701546	+	0.712624i	\(0.747506\pi\)
\(3\)	0.798779	−	1.53686i	0.461175	−	0.887309i
							\(5\)			2.14750i			0.960391i	0.877161	+	0.480196i	\(0.159434\pi\)
−0.877161	+	0.480196i	\(0.840566\pi\)
\(7\)	1.87127	+	1.87038i	0.707275	+	0.706939i
							\(11\)	0.0743945	+	0.128855i	0.0224308	+	0.0388513i	0.877023	−	0.480449i	\(-0.159526\pi\)
−0.854592	+	0.519300i	\(0.826193\pi\)
\(13\)	−3.58004	+	0.428160i	−0.992924	+	0.118750i
							\(17\)	2.50706	−	4.34235i	0.608051	−	1.05317i	−0.383511	−	0.923537i	\(-0.625285\pi\)
0.991561	−	0.129638i	\(-0.0413816\pi\)
\(19\)	−0.254791	+	0.441311i	−0.0584531	+	0.101244i	−0.893771	−	0.448523i	\(-0.851950\pi\)
							0.835318	+	0.549767i	\(0.185283\pi\)
\(23\)	0.305719	−	0.176507i	0.0637468	−	0.0368042i	−0.467788	−	0.883841i	\(-0.654949\pi\)
							0.531535	+	0.847037i	\(0.321616\pi\)
\(29\)	−7.97057	+	4.60181i	−1.48010	+	0.854535i	−0.999746	−	0.0225416i	\(-0.992824\pi\)
							−0.480351	+	0.877076i	\(0.659491\pi\)
\(31\)	−2.08035			−0.373642			−0.186821	−	0.982394i	\(-0.559818\pi\)
							−0.186821	+	0.982394i	\(0.559818\pi\)
\(37\)	−7.26104	+	4.19217i	−1.19371	+	0.689188i	−0.959146	−	0.282913i	\(-0.908699\pi\)
							−0.234563	+	0.972101i	\(0.575366\pi\)
\(41\)	2.21829	−	1.28073i	0.346438	−	0.200016i	−0.316677	−	0.948533i	\(-0.602567\pi\)
							0.663115	+	0.748517i	\(0.269234\pi\)
\(43\)	0.758169	−	1.31319i	0.115620	−	0.200259i	−0.802408	−	0.596776i	\(-0.796448\pi\)
							0.918027	+	0.396517i	\(0.129781\pi\)
\(47\)			11.0663i			1.61418i	0.590428	+	0.807091i	\(0.298959\pi\)
							−0.590428	+	0.807091i	\(0.701041\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.u.c.62.20	yes	64
3.2	odd	2	inner	273.2.u.c.62.14	yes	64
7.6	odd	2	inner	273.2.u.c.62.19	yes	64
13.4	even	6	inner	273.2.u.c.251.13	yes	64
21.20	even	2	inner	273.2.u.c.62.13	✓	64
39.17	odd	6	inner	273.2.u.c.251.19	yes	64
91.69	odd	6	inner	273.2.u.c.251.14	yes	64
273.251	even	6	inner	273.2.u.c.251.20	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.u.c.62.13	✓	64	21.20	even	2	inner
273.2.u.c.62.14	yes	64	3.2	odd	2	inner
273.2.u.c.62.19	yes	64	7.6	odd	2	inner
273.2.u.c.62.20	yes	64	1.1	even	1	trivial
273.2.u.c.251.13	yes	64	13.4	even	6	inner
273.2.u.c.251.14	yes	64	91.69	odd	6	inner
273.2.u.c.251.19	yes	64	39.17	odd	6	inner
273.2.u.c.251.20	yes	64	273.251	even	6	inner