Embedded newform 152.2.o.c.107.6

• Label: 152.2.o.c.107.6
• 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			107.6
Character	\(\chi\)	\(=\)	152.107
Dual form			152.2.o.c.27.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.833288 + 1.14264i) q^{2} +(-2.03079 + 1.17247i) q^{3} +(-0.611263 - 1.90430i) q^{4} +(-1.50560 + 0.869259i) q^{5} +(0.352510 - 3.29747i) q^{6} -2.63359i q^{7} +(2.68529 + 0.888375i) q^{8} +(1.24939 - 2.16401i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.833288	+	1.14264i	−0.589223	+	0.807970i
							\(3\)	−2.03079	+	1.17247i	−1.17247	+	0.676929i	−0.954262	−	0.298972i	\(-0.903356\pi\)
−0.218213	+	0.975901i	\(0.570023\pi\)
\(5\)	−1.50560	+	0.869259i	−0.673325	+	0.388744i	−0.797335	−	0.603537i	\(-0.793758\pi\)
							0.124010	+	0.992281i	\(0.460424\pi\)
\(7\)		−	2.63359i		−	0.995402i	−0.867349	−	0.497701i	\(-0.834178\pi\)
							0.867349	−	0.497701i	\(-0.165822\pi\)
\(11\)	−3.51485			−1.05977			−0.529883	−	0.848071i	\(-0.677764\pi\)
							−0.529883	+	0.848071i	\(0.677764\pi\)
\(13\)	3.13303	−	5.42656i	0.868946	−	1.50506i	0.00587005	−	0.999983i	\(-0.498131\pi\)
							0.863075	−	0.505075i	\(-0.168535\pi\)
\(17\)	−0.535037	−	0.926710i	−0.129765	−	0.224760i	0.793820	−	0.608153i	\(-0.208089\pi\)
							−0.923586	+	0.383392i	\(0.874756\pi\)
\(19\)	−3.79871	+	2.13770i	−0.871485	+	0.490422i
							\(23\)	−5.79041	−	3.34309i	−1.20738	−	0.697083i	−0.245196	−	0.969473i	\(-0.578852\pi\)
−0.962187	+	0.272390i	\(0.912186\pi\)
\(29\)	−0.579314	+	1.00340i	−0.107576	+	0.186327i	−0.914788	−	0.403935i	\(-0.867642\pi\)
							0.807212	+	0.590262i	\(0.200976\pi\)
\(31\)	−3.82638			−0.687238			−0.343619	−	0.939109i	\(-0.611653\pi\)
							−0.343619	+	0.939109i	\(0.611653\pi\)
\(37\)	−3.55090			−0.583764			−0.291882	−	0.956454i	\(-0.594281\pi\)
							−0.291882	+	0.956454i	\(0.594281\pi\)
\(41\)	−4.54864	+	2.62616i	−0.710378	+	0.410137i	−0.811201	−	0.584767i	\(-0.801186\pi\)
							0.100823	+	0.994904i	\(0.467852\pi\)
\(43\)	−0.164324	−	0.284617i	−0.0250591	−	0.0434036i	0.853224	−	0.521545i	\(-0.174644\pi\)
							−0.878283	+	0.478141i	\(0.841311\pi\)
\(47\)	6.68209	+	3.85791i	0.974683	+	0.562733i	0.900661	−	0.434523i	\(-0.143083\pi\)
							0.0740221	+	0.997257i	\(0.476416\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.107.6	yes	28
4.3	odd	2		608.2.s.c.335.11		28
8.3	odd	2	inner	152.2.o.c.107.1	yes	28
8.5	even	2		608.2.s.c.335.12		28
19.8	odd	6	inner	152.2.o.c.27.1	✓	28
76.27	even	6		608.2.s.c.559.12		28
152.27	even	6	inner	152.2.o.c.27.6	yes	28
152.141	odd	6		608.2.s.c.559.11		28

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.1	✓	28	19.8	odd	6	inner
152.2.o.c.27.6	yes	28	152.27	even	6	inner
152.2.o.c.107.1	yes	28	8.3	odd	2	inner
152.2.o.c.107.6	yes	28	1.1	even	1	trivial
608.2.s.c.335.11		28	4.3	odd	2
608.2.s.c.335.12		28	8.5	even	2
608.2.s.c.559.11		28	152.141	odd	6
608.2.s.c.559.12		28	76.27	even	6