Embedded newform 273.2.bn.c.146.14

• Label: 273.2.bn.c.146.14
• 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			146.14
Character	\(\chi\)	\(=\)	273.146
Dual form			273.2.bn.c.230.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.755524 + 0.436202i) q^{2} +(0.0385029 - 1.73162i) q^{3} +(-0.619456 + 1.07293i) q^{4} -0.294723 q^{5} +(0.726247 + 1.32508i) q^{6} +(-1.73375 + 1.99853i) q^{7} -2.82564i q^{8} +(-2.99704 - 0.133345i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.755524	+	0.436202i	−0.534236	+	0.308441i	−0.742740	−	0.669580i	\(-0.766474\pi\)
							0.208504	+	0.978022i	\(0.433141\pi\)
\(3\)	0.0385029	−	1.73162i	0.0222297	−	0.999753i
							\(5\)	−0.294723			−0.131804			−0.0659022	−	0.997826i	\(-0.520993\pi\)
−0.0659022	+	0.997826i	\(0.520993\pi\)
\(7\)	−1.73375	+	1.99853i	−0.655296	+	0.755372i
							\(11\)	−1.54167	+	0.890085i	−0.464832	+	0.268371i	−0.714074	−	0.700071i	\(-0.753152\pi\)
0.249242	+	0.968441i	\(0.419819\pi\)
\(13\)	−2.29041	−	2.78460i	−0.635246	−	0.772310i
							\(17\)	−3.35504	+	5.81110i	−0.813716	+	1.40940i	0.0965301	+	0.995330i	\(0.469226\pi\)
−0.910246	+	0.414068i	\(0.864108\pi\)
\(19\)	2.08240	+	1.20227i	0.477735	+	0.275820i	0.719472	−	0.694521i	\(-0.244384\pi\)
							−0.241737	+	0.970342i	\(0.577717\pi\)
\(23\)	−6.31856	+	3.64802i	−1.31751	+	0.760665i	−0.983328	−	0.181843i	\(-0.941794\pi\)
							−0.334183	+	0.942508i	\(0.608461\pi\)
\(29\)	1.98808	−	1.14782i	0.369177	−	0.213144i	−0.303922	−	0.952697i	\(-0.598296\pi\)
							0.673099	+	0.739553i	\(0.264963\pi\)
\(31\)		−	6.64222i		−	1.19298i	−0.802622	−	0.596489i	\(-0.796562\pi\)
							0.802622	−	0.596489i	\(-0.203438\pi\)
\(37\)	3.69917	+	6.40715i	0.608140	+	1.05333i	0.991547	+	0.129750i	\(0.0414174\pi\)
							−0.383407	+	0.923580i	\(0.625249\pi\)
\(41\)	−3.49921	−	6.06080i	−0.546484	−	0.946538i	−0.998512	−	0.0545345i	\(-0.982633\pi\)
							0.452028	−	0.892004i	\(-0.350701\pi\)
\(43\)	2.03031	−	3.51660i	0.309619	−	0.536276i	−0.668660	−	0.743568i	\(-0.733132\pi\)
							0.978279	+	0.207292i	\(0.0664652\pi\)
\(47\)	3.42186			0.499130			0.249565	−	0.968358i	\(-0.419712\pi\)
							0.249565	+	0.968358i	\(0.419712\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bn.c.146.14	yes	64
3.2	odd	2	inner	273.2.bn.c.146.20	yes	64
7.6	odd	2	inner	273.2.bn.c.146.13	✓	64
13.9	even	3	inner	273.2.bn.c.230.19	yes	64
21.20	even	2	inner	273.2.bn.c.146.19	yes	64
39.35	odd	6	inner	273.2.bn.c.230.13	yes	64
91.48	odd	6	inner	273.2.bn.c.230.20	yes	64
273.230	even	6	inner	273.2.bn.c.230.14	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bn.c.146.13	✓	64	7.6	odd	2	inner
273.2.bn.c.146.14	yes	64	1.1	even	1	trivial
273.2.bn.c.146.19	yes	64	21.20	even	2	inner
273.2.bn.c.146.20	yes	64	3.2	odd	2	inner
273.2.bn.c.230.13	yes	64	39.35	odd	6	inner
273.2.bn.c.230.14	yes	64	273.230	even	6	inner
273.2.bn.c.230.19	yes	64	13.9	even	3	inner
273.2.bn.c.230.20	yes	64	91.48	odd	6	inner