Embedded newform 255.2.bg.a.11.4

• Label: 255.2.bg.a.11.4
• Level: $255$
• Weight: $2$
• Character: 255.11
• Analytic conductor: $2.036$
• Analytic rank: $0$
• Dimension: $192$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 255 = 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	255.bg (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.03618525154\)
Analytic rank:	\(0\)
Dimension:	\(192\)
Relative dimension:	\(24\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			11.4
Character	\(\chi\)	\(=\)	255.11
Dual form			255.2.bg.a.116.4

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.831217 + 2.00674i) q^{2} +(-1.50735 - 0.853176i) q^{3} +(-1.92185 - 1.92185i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(2.96503 - 2.31567i) q^{6} +(-3.12757 + 2.08978i) q^{7} +(1.44065 - 0.596737i) q^{8} +(1.54418 + 2.57206i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/255\mathbb{Z}\right)^\times\).

\(n\)	\(52\)	\(86\)	\(241\)
\(\chi(n)\)	\(1\)	\(-1\)	\(e\left(\frac{7}{16}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.831217	+	2.00674i	−0.587759	+	1.41898i	0.297881	+	0.954603i	\(0.403720\pi\)
							−0.885640	+	0.464373i	\(0.846280\pi\)
\(3\)	−1.50735	−	0.853176i	−0.870266	−	0.492581i
							\(5\)	−0.555570	+	0.831470i	−0.248459	+	0.371845i
\(7\)	−3.12757	+	2.08978i	−1.18211	+	0.789861i								−0.981809	−	0.189873i	\(-0.939192\pi\)
							−0.200302	+	0.979734i	\(0.564192\pi\)
\(11\)	0.954434	−	4.79826i	0.287773	−	1.44673i	−0.518445	−	0.855111i	\(-0.673489\pi\)
							0.806217	−	0.591619i	\(-0.201511\pi\)
\(13\)	4.20602	−	4.20602i	1.16654	−	1.16654i	0.183526	−	0.983015i	\(-0.441249\pi\)
							0.983015	−	0.183526i	\(-0.0587510\pi\)
\(17\)	−3.11598	−	2.70013i	−0.755735	−	0.654877i
							\(19\)	0.111150	+	0.0460397i	0.0254995	+	0.0105622i	0.395397	−	0.918510i	\(-0.370607\pi\)
−0.369897	+	0.929073i	\(0.620607\pi\)
\(23\)	−3.10985	−	0.618588i	−0.648449	−	0.128985i	−0.140102	−	0.990137i	\(-0.544743\pi\)
							−0.508347	+	0.861152i	\(0.669743\pi\)
\(29\)	−3.49690	−	2.33655i	−0.649357	−	0.433887i	0.186784	−	0.982401i	\(-0.440194\pi\)
							−0.836141	+	0.548514i	\(0.815194\pi\)
\(31\)	−5.60013	+	1.11393i	−1.00581	+	0.200069i	−0.670398	−	0.742002i	\(-0.733877\pi\)
							−0.335415	+	0.942070i	\(0.608877\pi\)
\(37\)	1.19020	+	5.98356i	0.195668	+	0.983691i	0.946379	+	0.323060i	\(0.104711\pi\)
							−0.750710	+	0.660632i	\(0.770289\pi\)
\(41\)	2.95562	+	4.42340i	0.461591	+	0.690819i	0.987125	−	0.159953i	\(-0.0511344\pi\)
							−0.525534	+	0.850773i	\(0.676134\pi\)
\(43\)	−5.05756	+	2.09491i	−0.771270	+	0.319471i	−0.733387	−	0.679812i	\(-0.762062\pi\)
							−0.0378834	+	0.999282i	\(0.512062\pi\)
\(47\)	−6.29991	−	6.29991i	−0.918937	−	0.918937i	0.0780154	−	0.996952i	\(-0.475142\pi\)
							−0.996952	+	0.0780154i	\(0.975142\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	255.2.bg.a.11.4	✓	192
3.2	odd	2	inner	255.2.bg.a.11.21	yes	192
17.14	odd	16	inner	255.2.bg.a.116.21	yes	192
51.14	even	16	inner	255.2.bg.a.116.4	yes	192

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
255.2.bg.a.11.4	✓	192	1.1	even	1	trivial
255.2.bg.a.11.21	yes	192	3.2	odd	2	inner
255.2.bg.a.116.4	yes	192	51.14	even	16	inner
255.2.bg.a.116.21	yes	192	17.14	odd	16	inner