Embedded newform 273.2.bn.c.146.8

• Label: 273.2.bn.c.146.8
• 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			146.8
Character	\(\chi\)	\(=\)	273.146
Dual form			273.2.bn.c.230.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.43804 + 0.830256i) q^{2} +(1.23680 - 1.21257i) q^{3} +(0.378649 - 0.655839i) q^{4} +1.88889 q^{5} +(-0.771823 + 2.77059i) q^{6} +(1.70787 - 2.02068i) q^{7} -2.06352i q^{8} +(0.0593312 - 2.99941i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.43804	+	0.830256i	−1.01685	+	0.587079i	−0.913190	−	0.407533i	\(-0.866389\pi\)
							−0.103661	+	0.994613i	\(0.533056\pi\)
\(3\)	1.23680	−	1.21257i	0.714065	−	0.700080i
							\(5\)	1.88889			0.844738			0.422369	−	0.906424i	\(-0.361199\pi\)
0.422369	+	0.906424i	\(0.361199\pi\)
\(7\)	1.70787	−	2.02068i	0.645516	−	0.763747i
							\(11\)	−1.52869	+	0.882590i	−0.460918	+	0.266111i	−0.712430	−	0.701743i	\(-0.752405\pi\)
0.251512	+	0.967854i	\(0.419072\pi\)
\(13\)	−3.51996	−	0.780953i	−0.976261	−	0.216597i
							\(17\)	1.02971	−	1.78351i	0.249741	−	0.432565i	−0.713713	−	0.700439i	\(-0.752988\pi\)
0.963454	+	0.267874i	\(0.0863211\pi\)
\(19\)	1.72776	+	0.997525i	0.396376	+	0.228848i	0.684919	−	0.728619i	\(-0.259837\pi\)
							−0.288543	+	0.957467i	\(0.593171\pi\)
\(23\)	4.43873	−	2.56270i	0.925538	−	0.534360i	0.0401406	−	0.999194i	\(-0.487219\pi\)
							0.885398	+	0.464834i	\(0.153886\pi\)
\(29\)	7.27489	−	4.20016i	1.35091	−	0.779950i	0.362536	−	0.931970i	\(-0.381911\pi\)
							0.988377	+	0.152020i	\(0.0485778\pi\)
\(31\)			8.13951i			1.46190i	0.682431	+	0.730950i	\(0.260923\pi\)
							−0.682431	+	0.730950i	\(0.739077\pi\)
\(37\)	2.24827	+	3.89412i	0.369614	+	0.640190i	0.989505	−	0.144498i	\(-0.0461567\pi\)
							−0.619891	+	0.784688i	\(0.712823\pi\)
\(41\)	4.68779	+	8.11949i	0.732109	+	1.26805i	0.955980	+	0.293432i	\(0.0947974\pi\)
							−0.223871	+	0.974619i	\(0.571869\pi\)
\(43\)	2.05277	−	3.55550i	0.313044	−	0.542209i	−0.665975	−	0.745974i	\(-0.731984\pi\)
							0.979020	+	0.203765i	\(0.0653178\pi\)
\(47\)	−8.61967			−1.25731			−0.628654	−	0.777685i	\(-0.716394\pi\)
							−0.628654	+	0.777685i	\(0.716394\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bn.c.146.8	yes	64
3.2	odd	2	inner	273.2.bn.c.146.26	yes	64
7.6	odd	2	inner	273.2.bn.c.146.7	✓	64
13.9	even	3	inner	273.2.bn.c.230.25	yes	64
21.20	even	2	inner	273.2.bn.c.146.25	yes	64
39.35	odd	6	inner	273.2.bn.c.230.7	yes	64
91.48	odd	6	inner	273.2.bn.c.230.26	yes	64
273.230	even	6	inner	273.2.bn.c.230.8	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bn.c.146.7	✓	64	7.6	odd	2	inner
273.2.bn.c.146.8	yes	64	1.1	even	1	trivial
273.2.bn.c.146.25	yes	64	21.20	even	2	inner
273.2.bn.c.146.26	yes	64	3.2	odd	2	inner
273.2.bn.c.230.7	yes	64	39.35	odd	6	inner
273.2.bn.c.230.8	yes	64	273.230	even	6	inner
273.2.bn.c.230.25	yes	64	13.9	even	3	inner
273.2.bn.c.230.26	yes	64	91.48	odd	6	inner