Embedded newform 152.2.o.c.107.11

• Label: 152.2.o.c.107.11
• Level: $152$
• Weight: $2$
• Character: 152.107
• Analytic conductor: $1.214$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.21372611072\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.11
Character	\(\chi\)	\(=\)	152.107
Dual form			152.2.o.c.27.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.771641 - 1.18515i) q^{2} +(-2.65547 + 1.53314i) q^{3} +(-0.809140 - 1.82901i) q^{4} +(2.25688 - 1.30301i) q^{5} +(-0.232080 + 4.33015i) q^{6} -4.30088i q^{7} +(-2.79201 - 0.452395i) q^{8} +(3.20101 - 5.54431i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).

\(n\)	\(39\)	\(77\)	\(97\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.771641	−	1.18515i	0.545633	−	0.838024i
							\(3\)	−2.65547	+	1.53314i	−1.53314	+	0.885156i	−0.533921	+	0.845534i	\(0.679282\pi\)
−0.999215	+	0.0396221i	\(0.987385\pi\)
\(5\)	2.25688	−	1.30301i	1.00931	−	0.582723i	0.0983176	−	0.995155i	\(-0.468654\pi\)
							0.910988	+	0.412432i	\(0.135321\pi\)
\(7\)		−	4.30088i		−	1.62558i	−0.582556	−	0.812791i	\(-0.697947\pi\)
							0.582556	−	0.812791i	\(-0.302053\pi\)
\(11\)	−0.349633			−0.105418			−0.0527092	−	0.998610i	\(-0.516786\pi\)
							−0.0527092	+	0.998610i	\(0.516786\pi\)
\(13\)	−0.839767	+	1.45452i	−0.232910	+	0.403411i	−0.958663	−	0.284544i	\(-0.908158\pi\)
							0.725754	+	0.687955i	\(0.241491\pi\)
\(17\)	0.357047	+	0.618424i	0.0865967	+	0.149990i	0.906070	−	0.423127i	\(-0.139068\pi\)
							−0.819474	+	0.573117i	\(0.805734\pi\)
\(19\)	4.35063	−	0.268300i	0.998104	−	0.0615522i
							\(23\)	1.38083	+	0.797223i	0.287923	+	0.166233i	0.637005	−	0.770860i	\(-0.280173\pi\)
−0.349082	+	0.937092i	\(0.613506\pi\)
\(29\)	−0.463655	+	0.803074i	−0.0860985	+	0.149127i	−0.905859	−	0.423580i	\(-0.860773\pi\)
							0.819760	+	0.572707i	\(0.194107\pi\)
\(31\)	2.80517			0.503824			0.251912	−	0.967750i	\(-0.418941\pi\)
							0.251912	+	0.967750i	\(0.418941\pi\)
\(37\)	−10.2099			−1.67849			−0.839245	−	0.543753i	\(-0.817003\pi\)
							−0.839245	+	0.543753i	\(0.817003\pi\)
\(41\)	4.87850	−	2.81660i	0.761893	−	0.439879i	−0.0680819	−	0.997680i	\(-0.521688\pi\)
							0.829975	+	0.557801i	\(0.188355\pi\)
\(43\)	4.32286	+	7.48741i	0.659230	+	1.14182i	0.980815	+	0.194939i	\(0.0624508\pi\)
							−0.321586	+	0.946880i	\(0.604216\pi\)
\(47\)	6.26395	+	3.61649i	0.913691	+	0.527520i	0.881617	−	0.471966i	\(-0.156455\pi\)
							0.0320740	+	0.999485i	\(0.489789\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.107.11	yes	28
4.3	odd	2		608.2.s.c.335.14		28
8.3	odd	2	inner	152.2.o.c.107.14	yes	28
8.5	even	2		608.2.s.c.335.13		28
19.8	odd	6	inner	152.2.o.c.27.14	yes	28
76.27	even	6		608.2.s.c.559.13		28
152.27	even	6	inner	152.2.o.c.27.11	✓	28
152.141	odd	6		608.2.s.c.559.14		28

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.11	✓	28	152.27	even	6	inner
152.2.o.c.27.14	yes	28	19.8	odd	6	inner
152.2.o.c.107.11	yes	28	1.1	even	1	trivial
152.2.o.c.107.14	yes	28	8.3	odd	2	inner
608.2.s.c.335.13		28	8.5	even	2
608.2.s.c.335.14		28	4.3	odd	2
608.2.s.c.559.13		28	76.27	even	6
608.2.s.c.559.14		28	152.141	odd	6