Embedded newform 152.2.o.c.107.8

• Label: 152.2.o.c.107.8
• 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			107.8
Character	\(\chi\)	\(=\)	152.107
Dual form			152.2.o.c.27.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.151949 - 1.40603i) q^{2} +(-1.05104 + 0.606818i) q^{3} +(-1.95382 + 0.427288i) q^{4} +(-2.45005 + 1.41453i) q^{5} +(1.01291 + 1.38558i) q^{6} -0.450769i q^{7} +(0.897660 + 2.68220i) q^{8} +(-0.763544 + 1.32250i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.151949	−	1.40603i	−0.107444	−	0.994211i
							\(3\)	−1.05104	+	0.606818i	−0.606818	+	0.350346i	−0.771719	−	0.635964i	\(-0.780603\pi\)
0.164901	+	0.986310i	\(0.447269\pi\)
\(5\)	−2.45005	+	1.41453i	−1.09569	+	0.632599i	−0.935087	−	0.354419i	\(-0.884679\pi\)
							−0.160607	+	0.987018i	\(0.551345\pi\)
\(7\)		−	0.450769i		−	0.170375i	−0.996365	−	0.0851873i	\(-0.972851\pi\)
							0.996365	−	0.0851873i	\(-0.0271489\pi\)
\(11\)	−2.15933			−0.651064			−0.325532	−	0.945531i	\(-0.605543\pi\)
							−0.325532	+	0.945531i	\(0.605543\pi\)
\(13\)	−1.86406	+	3.22864i	−0.516996	+	0.895464i	0.482809	+	0.875726i	\(0.339617\pi\)
							−0.999805	+	0.0197382i	\(0.993717\pi\)
\(17\)	−0.716566	−	1.24113i	−0.173793	−	0.301018i	0.765950	−	0.642900i	\(-0.222269\pi\)
							−0.939743	+	0.341882i	\(0.888936\pi\)
\(19\)	−0.0305680	−	4.35879i	−0.00701278	−	0.999975i
							\(23\)	−1.12985	−	0.652319i	−0.235590	−	0.136018i	0.377558	−	0.925986i	\(-0.376764\pi\)
−0.613148	+	0.789968i	\(0.710097\pi\)
\(29\)	−4.22992	+	7.32644i	−0.785477	+	1.36049i	0.143237	+	0.989688i	\(0.454249\pi\)
							−0.928714	+	0.370797i	\(0.879085\pi\)
\(31\)	−0.497284			−0.0893149			−0.0446575	−	0.999002i	\(-0.514220\pi\)
							−0.0446575	+	0.999002i	\(0.514220\pi\)
\(37\)	6.72997			1.10640			0.553200	−	0.833049i	\(-0.313407\pi\)
							0.553200	+	0.833049i	\(0.313407\pi\)
\(41\)	−7.30919	+	4.21996i	−1.14150	+	0.659047i	−0.946802	−	0.321815i	\(-0.895707\pi\)
							−0.194701	+	0.980863i	\(0.562374\pi\)
\(43\)	2.90174	+	5.02595i	0.442511	+	0.766451i	0.997875	−	0.0651562i	\(-0.0207546\pi\)
							−0.555364	+	0.831607i	\(0.687421\pi\)
\(47\)	−0.567335	−	0.327551i	−0.0827543	−	0.0477782i	0.458052	−	0.888925i	\(-0.348547\pi\)
							−0.540806	+	0.841147i	\(0.681881\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.107.8	yes	28
4.3	odd	2		608.2.s.c.335.9		28
8.3	odd	2	inner	152.2.o.c.107.12	yes	28
8.5	even	2		608.2.s.c.335.10		28
19.8	odd	6	inner	152.2.o.c.27.12	yes	28
76.27	even	6		608.2.s.c.559.10		28
152.27	even	6	inner	152.2.o.c.27.8	✓	28
152.141	odd	6		608.2.s.c.559.9		28

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.8	✓	28	152.27	even	6	inner
152.2.o.c.27.12	yes	28	19.8	odd	6	inner
152.2.o.c.107.8	yes	28	1.1	even	1	trivial
152.2.o.c.107.12	yes	28	8.3	odd	2	inner
608.2.s.c.335.9		28	4.3	odd	2
608.2.s.c.335.10		28	8.5	even	2
608.2.s.c.559.9		28	152.141	odd	6
608.2.s.c.559.10		28	76.27	even	6