Embedded newform 152.2.o.c.107.1

• Label: 152.2.o.c.107.1
• 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			107.1
Character	\(\chi\)	\(=\)	152.107
Dual form			152.2.o.c.27.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.40620 + 0.150327i) q^{2} +(-2.03079 + 1.17247i) q^{3} +(1.95480 - 0.422781i) q^{4} +(1.50560 - 0.869259i) q^{5} +(2.67944 - 1.95402i) q^{6} +2.63359i q^{7} +(-2.68529 + 0.888375i) q^{8} +(1.24939 - 2.16401i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.40620	+	0.150327i	−0.994334	+	0.106297i
							\(3\)	−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	−0.124010	−	0.992281i	\(-0.539576\pi\)
							0.797335	+	0.603537i	\(0.206242\pi\)
\(7\)			2.63359i			0.995402i	0.867349	+	0.497701i	\(0.165822\pi\)
							−0.867349	+	0.497701i	\(0.834178\pi\)
\(11\)	−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	\(0.501869\pi\)
							−0.863075	+	0.505075i	\(0.831465\pi\)
\(17\)	−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	0.962187	−	0.272390i	\(-0.0878142\pi\)
0.245196	+	0.969473i	\(0.421148\pi\)
\(29\)	0.579314	−	1.00340i	0.107576	−	0.186327i	−0.807212	−	0.590262i	\(-0.799024\pi\)
							0.914788	+	0.403935i	\(0.132358\pi\)
\(31\)	3.82638			0.687238			0.343619	−	0.939109i	\(-0.388347\pi\)
							0.343619	+	0.939109i	\(0.388347\pi\)
\(37\)	3.55090			0.583764			0.291882	−	0.956454i	\(-0.405719\pi\)
							0.291882	+	0.956454i	\(0.405719\pi\)
\(41\)	−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	−0.0740221	−	0.997257i	\(-0.523584\pi\)
							−0.900661	+	0.434523i	\(0.856917\pi\)

(See \(a_n\) instead)

Twists

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

    

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