Embedded newform 255.2.bg.a.11.6

• Label: 255.2.bg.a.11.6
• 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			11.6
Character	\(\chi\)	\(=\)	255.11
Dual form			255.2.bg.a.116.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.667761 + 1.61212i) q^{2} +(1.72180 + 0.188121i) q^{3} +(-0.738806 - 0.738806i) q^{4} +(0.555570 - 0.831470i) q^{5} +(-1.45303 + 2.65013i) q^{6} +(3.47691 - 2.32320i) q^{7} +(-1.53985 + 0.637826i) q^{8} +(2.92922 + 0.647817i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.667761	+	1.61212i	−0.472178	+	1.13994i	0.491020	+	0.871148i	\(0.336624\pi\)
							−0.963198	+	0.268791i	\(0.913376\pi\)
\(3\)	1.72180	+	0.188121i	0.994084	+	0.108612i
							\(5\)	0.555570	−	0.831470i	0.248459	−	0.371845i
\(7\)	3.47691	−	2.32320i	1.31415	−	0.878086i								0.316634	−	0.948548i	\(-0.397447\pi\)
							0.997514	+	0.0704624i	\(0.0224475\pi\)
\(11\)	0.185455	−	0.932345i	0.0559168	−	0.281113i	−0.942703	−	0.333633i	\(-0.891725\pi\)
							0.998620	+	0.0525202i	\(0.0167254\pi\)
\(13\)	−0.877210	+	0.877210i	−0.243294	+	0.243294i	−0.818212	−	0.574917i	\(-0.805034\pi\)
							0.574917	+	0.818212i	\(0.305034\pi\)
\(17\)	−2.01675	+	3.59621i	−0.489134	+	0.872209i
							\(19\)	−1.11121	−	0.460276i	−0.254928	−	0.105595i	0.251560	−	0.967842i	\(-0.419056\pi\)
−0.506488	+	0.862247i	\(0.669056\pi\)
\(23\)	−6.51211	−	1.29534i	−1.35787	−	0.270097i	−0.538143	−	0.842854i	\(-0.680874\pi\)
							−0.819725	+	0.572757i	\(0.805874\pi\)
\(29\)	0.0803055	+	0.0536585i	0.0149124	+	0.00996412i	0.563004	−	0.826454i	\(-0.309646\pi\)
							−0.548092	+	0.836418i	\(0.684646\pi\)
\(31\)	−10.1178	+	2.01256i	−1.81721	+	0.361466i	−0.982063	−	0.188553i	\(-0.939620\pi\)
							−0.835152	+	0.550020i	\(0.814620\pi\)
\(37\)	2.07990	+	10.4564i	0.341934	+	1.71902i	0.643392	+	0.765537i	\(0.277527\pi\)
							−0.301458	+	0.953479i	\(0.597473\pi\)
\(41\)	−4.86569	−	7.28201i	−0.759892	−	1.13726i	−0.986578	−	0.163291i	\(-0.947789\pi\)
							0.226685	−	0.973968i	\(-0.427211\pi\)
\(43\)	−1.84679	+	0.764964i	−0.281632	+	0.116656i	−0.519028	−	0.854757i	\(-0.673706\pi\)
							0.237396	+	0.971413i	\(0.423706\pi\)
\(47\)	5.54666	+	5.54666i	0.809064	+	0.809064i	0.984492	−	0.175428i	\(-0.0561310\pi\)
							−0.175428	+	0.984492i	\(0.556131\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	255.2.bg.a.11.6	✓	192
3.2	odd	2	inner	255.2.bg.a.11.19	yes	192
17.14	odd	16	inner	255.2.bg.a.116.19	yes	192
51.14	even	16	inner	255.2.bg.a.116.6	yes	192

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
255.2.bg.a.11.6	✓	192	1.1	even	1	trivial
255.2.bg.a.11.19	yes	192	3.2	odd	2	inner
255.2.bg.a.116.6	yes	192	51.14	even	16	inner
255.2.bg.a.116.19	yes	192	17.14	odd	16	inner