Embedded newform 105.3.o.b.74.15

• Label: 105.3.o.b.74.15
• Level: $105$
• Weight: $3$
• Character: 105.74
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			74.15
Character	\(\chi\)	\(=\)	105.74
Dual form			105.3.o.b.44.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.949639 + 1.64482i) q^{2} +(-0.107903 - 2.99806i) q^{3} +(0.196373 - 0.340128i) q^{4} +(-4.51617 - 2.14574i) q^{5} +(4.82880 - 3.02455i) q^{6} +(4.60961 - 5.26797i) q^{7} +8.34304 q^{8} +(-8.97671 + 0.647002i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 44 q^{4} + 80 q^{6} + 12 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.949639	+	1.64482i	0.474819	+	0.822411i	0.999584	−	0.0288361i	\(-0.00918008\pi\)
							−0.524765	+	0.851247i	\(0.675847\pi\)
\(3\)	−0.107903	−	2.99806i	−0.0359678	−	0.999353i
							\(5\)	−4.51617	−	2.14574i	−0.903234	−	0.429148i
\(7\)	4.60961	−	5.26797i	0.658515	−	0.752567i
							\(11\)	8.35863	+	4.82586i	0.759876	+	0.438714i	0.829251	−	0.558876i	\(-0.188767\pi\)
−0.0693754	+	0.997591i	\(0.522101\pi\)
\(13\)		−	16.9521i		−	1.30401i	−0.758216	−	0.652004i	\(-0.773929\pi\)
							0.758216	−	0.652004i	\(-0.226071\pi\)
\(17\)	−12.1835	+	21.1024i	−0.716674	+	1.24131i	0.245637	+	0.969362i	\(0.421003\pi\)
							−0.962311	+	0.271953i	\(0.912330\pi\)
\(19\)	6.95261	+	12.0423i	0.365927	+	0.633804i	0.988924	−	0.148420i	\(-0.0474187\pi\)
							−0.622997	+	0.782224i	\(0.714085\pi\)
\(23\)	−0.354602	−	0.614188i	−0.0154175	−	0.0267038i	0.858214	−	0.513292i	\(-0.171574\pi\)
							−0.873631	+	0.486589i	\(0.838241\pi\)
\(29\)			16.5872i			0.571971i	0.958234	+	0.285986i	\(0.0923209\pi\)
							−0.958234	+	0.285986i	\(0.907679\pi\)
\(31\)	7.12320	−	12.3377i	0.229781	−	0.397992i	−0.727962	−	0.685617i	\(-0.759532\pi\)
							0.957743	+	0.287625i	\(0.0928658\pi\)
\(37\)	1.08578	−	0.626873i	0.0293453	−	0.0169425i	−0.485256	−	0.874372i	\(-0.661273\pi\)
							0.514601	+	0.857430i	\(0.327940\pi\)
\(41\)		−	24.1024i		−	0.587862i	−0.955827	−	0.293931i	\(-0.905036\pi\)
							0.955827	−	0.293931i	\(-0.0949637\pi\)
\(43\)			57.6214i			1.34003i	0.742346	+	0.670017i	\(0.233713\pi\)
							−0.742346	+	0.670017i	\(0.766287\pi\)
\(47\)	−16.0840	−	27.8583i	−0.342213	−	0.592730i	0.642630	−	0.766176i	\(-0.277843\pi\)
							−0.984843	+	0.173446i	\(0.944510\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.o.b.74.15	yes	40
3.2	odd	2	inner	105.3.o.b.74.5	yes	40
5.4	even	2	inner	105.3.o.b.74.6	yes	40
7.2	even	3	inner	105.3.o.b.44.16	yes	40
15.14	odd	2	inner	105.3.o.b.74.16	yes	40
21.2	odd	6	inner	105.3.o.b.44.6	yes	40
35.9	even	6	inner	105.3.o.b.44.5	✓	40
105.44	odd	6	inner	105.3.o.b.44.15	yes	40

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.o.b.44.5	✓	40	35.9	even	6	inner
105.3.o.b.44.6	yes	40	21.2	odd	6	inner
105.3.o.b.44.15	yes	40	105.44	odd	6	inner
105.3.o.b.44.16	yes	40	7.2	even	3	inner
105.3.o.b.74.5	yes	40	3.2	odd	2	inner
105.3.o.b.74.6	yes	40	5.4	even	2	inner
105.3.o.b.74.15	yes	40	1.1	even	1	trivial
105.3.o.b.74.16	yes	40	15.14	odd	2	inner