Embedded newform 273.4.i.e.235.9

• Label: 273.4.i.e.235.9
• Level: $273$
• Weight: $4$
• Character: 273.235
• Analytic conductor: $16.108$
• Analytic rank: $0$
• Dimension: $26$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	273.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(16.1075214316\)
Analytic rank:	\(0\)
Dimension:	\(26\)
Relative dimension:	\(13\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.9
Character	\(\chi\)	\(=\)	273.235
Dual form			273.4.i.e.79.9

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.896185 + 1.55224i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(2.39370 - 4.14602i) q^{4} +(-0.238290 - 0.412731i) q^{5} -5.37711 q^{6} +(-17.3425 - 6.49897i) q^{7} +22.9198 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 3 q^{2} - 39 q^{3} - 55 q^{4} - 15 q^{5} + 18 q^{6} - 13 q^{7} - 12 q^{8} - 117 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(92\)	\(106\)	\(157\)
\(\chi(n)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.896185	+	1.55224i	0.316849	+	0.548799i	0.979829	−	0.199838i	\(-0.0640417\pi\)
							−0.662980	+	0.748637i	\(0.730708\pi\)
\(3\)	−1.50000	+	2.59808i	−0.288675	+	0.500000i
							\(5\)	−0.238290	−	0.412731i	−0.0213133	−	0.0369158i	0.855172	−	0.518344i	\(-0.173451\pi\)
−0.876485	+	0.481429i	\(0.840118\pi\)
\(7\)	−17.3425	−	6.49897i	−0.936409	−	0.350911i
							\(11\)	−7.96112	+	13.7891i	−0.218215	+	0.377960i	−0.954262	−	0.298970i	\(-0.903357\pi\)
0.736047	+	0.676930i	\(0.236690\pi\)
\(13\)	13.0000			0.277350
							\(17\)	27.9555	−	48.4203i	0.398835	−	0.690803i	−0.594747	−	0.803913i	\(-0.702748\pi\)
0.993582	+	0.113110i	\(0.0360812\pi\)
\(19\)	−82.1698	−	142.322i	−0.992161	−	1.71847i	−0.604307	−	0.796752i	\(-0.706550\pi\)
							−0.387854	−	0.921721i	\(-0.626783\pi\)
\(23\)	−47.4988	−	82.2704i	−0.430617	−	0.745851i	0.566309	−	0.824193i	\(-0.308371\pi\)
							−0.996927	+	0.0783420i	\(0.975037\pi\)
\(29\)	183.799			1.17692			0.588460	−	0.808526i	\(-0.299734\pi\)
							0.588460	+	0.808526i	\(0.299734\pi\)
\(31\)	−24.3895	+	42.2439i	−0.141306	+	0.244749i	−0.927989	−	0.372608i	\(-0.878463\pi\)
							0.786683	+	0.617358i	\(0.211797\pi\)
\(37\)	46.4892	+	80.5216i	0.206561	+	0.357775i	0.950629	−	0.310329i	\(-0.100439\pi\)
							−0.744068	+	0.668104i	\(0.767106\pi\)
\(41\)	−105.115			−0.400397			−0.200198	−	0.979755i	\(-0.564159\pi\)
							−0.200198	+	0.979755i	\(0.564159\pi\)
\(43\)	−50.2025			−0.178042			−0.0890211	−	0.996030i	\(-0.528374\pi\)
							−0.0890211	+	0.996030i	\(0.528374\pi\)
\(47\)	−170.466	−	295.255i	−0.529042	−	0.916328i	−0.999426	−	0.0338665i	\(-0.989218\pi\)
							0.470384	−	0.882462i	\(-0.344115\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.4.i.e.235.9	yes	26
7.2	even	3	inner	273.4.i.e.79.9	✓	26
7.3	odd	6		1911.4.a.bb.1.5		13
7.4	even	3		1911.4.a.bc.1.5		13

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.4.i.e.79.9	✓	26	7.2	even	3	inner
273.4.i.e.235.9	yes	26	1.1	even	1	trivial
1911.4.a.bb.1.5		13	7.3	odd	6
1911.4.a.bc.1.5		13	7.4	even	3