Embedded newform 273.2.bn.c.146.17

• Label: 273.2.bn.c.146.17
• 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			146.17
Character	\(\chi\)	\(=\)	273.146
Dual form			273.2.bn.c.230.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.265128 - 0.153072i) q^{2} +(-0.0322229 + 1.73175i) q^{3} +(-0.953138 + 1.65088i) q^{4} +2.83438 q^{5} +(0.256539 + 0.464068i) q^{6} +(2.54431 - 0.725603i) q^{7} +1.19588i q^{8} +(-2.99792 - 0.111604i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.265128	−	0.153072i	0.187474	−	0.108238i	−0.403326	−	0.915057i	\(-0.632146\pi\)
							0.590799	+	0.806818i	\(0.298812\pi\)
\(3\)	−0.0322229	+	1.73175i	−0.0186039	+	0.999827i
							\(5\)	2.83438			1.26757			0.633787	−	0.773508i	\(-0.281500\pi\)
0.633787	+	0.773508i	\(0.281500\pi\)
\(7\)	2.54431	−	0.725603i	0.961658	−	0.274252i
							\(11\)	−3.56439	+	2.05790i	−1.07471	+	0.620481i	−0.929463	−	0.368915i	\(-0.879729\pi\)
−0.145242	+	0.989396i	\(0.546396\pi\)
\(13\)	0.617899	−	3.55221i	0.171374	−	0.985206i
							\(17\)	−2.00086	+	3.46559i	−0.485280	+	0.840530i	−0.999857	−	0.0169143i	\(-0.994616\pi\)
0.514577	+	0.857444i	\(0.327949\pi\)
\(19\)	4.59778	+	2.65453i	1.05480	+	0.608990i	0.923990	−	0.382417i	\(-0.124908\pi\)
							0.130812	+	0.991407i	\(0.458242\pi\)
\(23\)	5.48002	−	3.16389i	1.14266	−	0.659717i	0.195574	−	0.980689i	\(-0.437343\pi\)
							0.947089	+	0.320972i	\(0.104010\pi\)
\(29\)	−5.42350	+	3.13126i	−1.00712	+	0.581460i	−0.910347	−	0.413847i	\(-0.864185\pi\)
							−0.0967715	+	0.995307i	\(0.530852\pi\)
\(31\)			0.877974i			0.157689i	0.996887	+	0.0788444i	\(0.0251230\pi\)
							−0.996887	+	0.0788444i	\(0.974877\pi\)
\(37\)	−1.13283	−	1.96212i	−0.186236	−	0.322570i	0.757756	−	0.652537i	\(-0.226295\pi\)
							−0.943992	+	0.329968i	\(0.892962\pi\)
\(41\)	−3.10957	−	5.38594i	−0.485634	−	0.841143i	0.514230	−	0.857652i	\(-0.328078\pi\)
							−0.999864	+	0.0165098i	\(0.994745\pi\)
\(43\)	6.42522	−	11.1288i	0.979837	−	1.69713i	0.316888	−	0.948463i	\(-0.397362\pi\)
							0.662949	−	0.748664i	\(-0.269305\pi\)
\(47\)	2.14561			0.312970			0.156485	−	0.987680i	\(-0.449984\pi\)
							0.156485	+	0.987680i	\(0.449984\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bn.c.146.17	yes	64
3.2	odd	2	inner	273.2.bn.c.146.15	✓	64
7.6	odd	2	inner	273.2.bn.c.146.18	yes	64
13.9	even	3	inner	273.2.bn.c.230.16	yes	64
21.20	even	2	inner	273.2.bn.c.146.16	yes	64
39.35	odd	6	inner	273.2.bn.c.230.18	yes	64
91.48	odd	6	inner	273.2.bn.c.230.15	yes	64
273.230	even	6	inner	273.2.bn.c.230.17	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bn.c.146.15	✓	64	3.2	odd	2	inner
273.2.bn.c.146.16	yes	64	21.20	even	2	inner
273.2.bn.c.146.17	yes	64	1.1	even	1	trivial
273.2.bn.c.146.18	yes	64	7.6	odd	2	inner
273.2.bn.c.230.15	yes	64	91.48	odd	6	inner
273.2.bn.c.230.16	yes	64	13.9	even	3	inner
273.2.bn.c.230.17	yes	64	273.230	even	6	inner
273.2.bn.c.230.18	yes	64	39.35	odd	6	inner