Embedded newform 273.2.bn.c.146.3

• Label: 273.2.bn.c.146.3
• 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			146.3
Character	\(\chi\)	\(=\)	273.146
Dual form			273.2.bn.c.230.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.01386 + 1.16270i) q^{2} +(-1.06546 - 1.36557i) q^{3} +(1.70376 - 2.95099i) q^{4} -0.993521 q^{5} +(3.73345 + 1.51126i) q^{6} +(-0.593544 - 2.57831i) q^{7} +3.27304i q^{8} +(-0.729580 + 2.90993i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.01386	+	1.16270i	−1.42401	+	0.822155i	−0.996639	−	0.0819189i	\(-0.973895\pi\)
							−0.427376	+	0.904074i	\(0.640562\pi\)
\(3\)	−1.06546	−	1.36557i	−0.615145	−	0.788414i
							\(5\)	−0.993521			−0.444316			−0.222158	−	0.975011i	\(-0.571310\pi\)
−0.222158	+	0.975011i	\(0.571310\pi\)
\(7\)	−0.593544	−	2.57831i	−0.224339	−	0.974511i
							\(11\)	2.81046	−	1.62262i	0.847386	−	0.489238i	−0.0123823	−	0.999923i	\(-0.503941\pi\)
0.859768	+	0.510685i	\(0.170608\pi\)
\(13\)	−2.75926	+	2.32088i	−0.765281	+	0.643696i
							\(17\)	−1.72639	+	2.99020i	−0.418712	+	0.725230i	−0.995810	−	0.0914447i	\(-0.970852\pi\)
0.577099	+	0.816675i	\(0.304185\pi\)
\(19\)	−1.33408	−	0.770230i	−0.306058	−	0.176703i	0.339103	−	0.940749i	\(-0.389877\pi\)
							−0.645161	+	0.764046i	\(0.723210\pi\)
\(23\)	−4.81226	+	2.77836i	−1.00343	+	0.579328i	−0.909260	−	0.416228i	\(-0.863352\pi\)
							−0.0941659	+	0.995557i	\(0.530018\pi\)
\(29\)	−2.42166	+	1.39814i	−0.449690	+	0.259629i	−0.707699	−	0.706514i	\(-0.750267\pi\)
							0.258009	+	0.966143i	\(0.416934\pi\)
\(31\)		−	0.253865i		−	0.0455955i	−0.999740	−	0.0227977i	\(-0.992743\pi\)
							0.999740	−	0.0227977i	\(-0.00725737\pi\)
\(37\)	0.572688	+	0.991924i	0.0941493	+	0.163071i	0.909253	−	0.416243i	\(-0.136654\pi\)
							−0.815104	+	0.579315i	\(0.803320\pi\)
\(41\)	−1.42995	−	2.47675i	−0.223321	−	0.386803i	0.732494	−	0.680774i	\(-0.238356\pi\)
							−0.955814	+	0.293971i	\(0.905023\pi\)
\(43\)	−5.92223	+	10.2576i	−0.903131	+	1.56427i	−0.0797249	+	0.996817i	\(0.525404\pi\)
							−0.823406	+	0.567452i	\(0.807929\pi\)
\(47\)	6.13878			0.895433			0.447716	−	0.894176i	\(-0.352237\pi\)
							0.447716	+	0.894176i	\(0.352237\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bn.c.146.3	✓	64
3.2	odd	2	inner	273.2.bn.c.146.30	yes	64
7.6	odd	2	inner	273.2.bn.c.146.4	yes	64
13.9	even	3	inner	273.2.bn.c.230.29	yes	64
21.20	even	2	inner	273.2.bn.c.146.29	yes	64
39.35	odd	6	inner	273.2.bn.c.230.4	yes	64
91.48	odd	6	inner	273.2.bn.c.230.30	yes	64
273.230	even	6	inner	273.2.bn.c.230.3	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bn.c.146.3	✓	64	1.1	even	1	trivial
273.2.bn.c.146.4	yes	64	7.6	odd	2	inner
273.2.bn.c.146.29	yes	64	21.20	even	2	inner
273.2.bn.c.146.30	yes	64	3.2	odd	2	inner
273.2.bn.c.230.3	yes	64	273.230	even	6	inner
273.2.bn.c.230.4	yes	64	39.35	odd	6	inner
273.2.bn.c.230.29	yes	64	13.9	even	3	inner
273.2.bn.c.230.30	yes	64	91.48	odd	6	inner