Embedded newform 152.2.o.c.107.10

• Label: 152.2.o.c.107.10
• 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			107.10
Character	\(\chi\)	\(=\)	152.107
Dual form			152.2.o.c.27.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.540330 + 1.30692i) q^{2} +(2.07624 - 1.19872i) q^{3} +(-1.41609 + 1.41234i) q^{4} +(-0.418341 + 0.241529i) q^{5} +(2.68848 + 2.06578i) q^{6} +1.56686i q^{7} +(-2.61097 - 1.08759i) q^{8} +(1.37385 - 2.37958i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.540330	+	1.30692i	0.382071	+	0.924133i
							\(3\)	2.07624	−	1.19872i	1.19872	−	0.692080i	0.238449	−	0.971155i	\(-0.423361\pi\)
0.960269	+	0.279075i	\(0.0900278\pi\)
\(5\)	−0.418341	+	0.241529i	−0.187088	+	0.108015i	−0.590618	−	0.806951i	\(-0.701116\pi\)
							0.403531	+	0.914966i	\(0.367783\pi\)
\(7\)			1.56686i			0.592217i	0.955154	+	0.296109i	\(0.0956891\pi\)
							−0.955154	+	0.296109i	\(0.904311\pi\)
\(11\)	1.24363			0.374967			0.187484	−	0.982268i	\(-0.439967\pi\)
							0.187484	+	0.982268i	\(0.439967\pi\)
\(13\)	1.80015	−	3.11796i	0.499273	−	0.864766i	−0.500727	−	0.865605i	\(-0.666934\pi\)
							1.00000		0.000839577i	\(0.000267246\pi\)
\(17\)	−1.35570	−	2.34815i	−0.328807	−	0.569510i	0.653469	−	0.756954i	\(-0.273313\pi\)
							−0.982275	+	0.187444i	\(0.939980\pi\)
\(19\)	−4.25703	−	0.936862i	−0.976629	−	0.214931i
							\(23\)	−5.52533	−	3.19005i	−1.15211	−	0.665171i	−0.202710	−	0.979239i	\(-0.564975\pi\)
−0.949401	+	0.314068i	\(0.898308\pi\)
\(29\)	−0.695157	+	1.20405i	−0.129087	+	0.223586i	−0.923323	−	0.384024i	\(-0.874538\pi\)
							0.794236	+	0.607610i	\(0.207871\pi\)
\(31\)	−4.86016			−0.872910			−0.436455	−	0.899726i	\(-0.643766\pi\)
							−0.436455	+	0.899726i	\(0.643766\pi\)
\(37\)	10.9720			1.80379			0.901894	−	0.431957i	\(-0.142177\pi\)
							0.901894	+	0.431957i	\(0.142177\pi\)
\(41\)	1.10008	−	0.635132i	0.171804	−	0.0991909i	−0.411632	−	0.911350i	\(-0.635041\pi\)
							0.583436	+	0.812159i	\(0.301708\pi\)
\(43\)	4.78175	+	8.28223i	0.729210	+	1.26303i	0.957218	+	0.289369i	\(0.0934455\pi\)
							−0.228008	+	0.973659i	\(0.573221\pi\)
\(47\)	−7.26763	−	4.19597i	−1.06009	−	0.612045i	−0.134635	−	0.990895i	\(-0.542986\pi\)
							−0.925458	+	0.378850i	\(0.876320\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.107.10	yes	28
4.3	odd	2		608.2.s.c.335.1		28
8.3	odd	2	inner	152.2.o.c.107.4	yes	28
8.5	even	2		608.2.s.c.335.2		28
19.8	odd	6	inner	152.2.o.c.27.4	✓	28
76.27	even	6		608.2.s.c.559.2		28
152.27	even	6	inner	152.2.o.c.27.10	yes	28
152.141	odd	6		608.2.s.c.559.1		28

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.4	✓	28	19.8	odd	6	inner
152.2.o.c.27.10	yes	28	152.27	even	6	inner
152.2.o.c.107.4	yes	28	8.3	odd	2	inner
152.2.o.c.107.10	yes	28	1.1	even	1	trivial
608.2.s.c.335.1		28	4.3	odd	2
608.2.s.c.335.2		28	8.5	even	2
608.2.s.c.559.1		28	152.141	odd	6
608.2.s.c.559.2		28	76.27	even	6