Embedded newform 105.3.o.b.44.15

• Label: 105.3.o.b.44.15
• Level: $105$
• Weight: $3$
• Character: 105.44
• 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			44.15
Character	\(\chi\)	\(=\)	105.44
Dual form			105.3.o.b.74.15

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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	−0.524765	−	0.851247i	\(-0.675847\pi\)
							0.999584	+	0.0288361i	\(0.00918008\pi\)
\(3\)	−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	−0.0693754	−	0.997591i	\(-0.522101\pi\)
0.829251	+	0.558876i	\(0.188767\pi\)
\(13\)			16.9521i			1.30401i	0.758216	+	0.652004i	\(0.226071\pi\)
							−0.758216	+	0.652004i	\(0.773929\pi\)
\(17\)	−12.1835	−	21.1024i	−0.716674	−	1.24131i	−0.962311	−	0.271953i	\(-0.912330\pi\)
							0.245637	−	0.969362i	\(-0.421003\pi\)
\(19\)	6.95261	−	12.0423i	0.365927	−	0.633804i	−0.622997	−	0.782224i	\(-0.714085\pi\)
							0.988924	+	0.148420i	\(0.0474187\pi\)
\(23\)	−0.354602	+	0.614188i	−0.0154175	+	0.0267038i	−0.873631	−	0.486589i	\(-0.838241\pi\)
							0.858214	+	0.513292i	\(0.171574\pi\)
\(29\)		−	16.5872i		−	0.571971i	−0.958234	−	0.285986i	\(-0.907679\pi\)
							0.958234	−	0.285986i	\(-0.0923209\pi\)
\(31\)	7.12320	+	12.3377i	0.229781	+	0.397992i	0.957743	−	0.287625i	\(-0.0928658\pi\)
							−0.727962	+	0.685617i	\(0.759532\pi\)
\(37\)	1.08578	+	0.626873i	0.0293453	+	0.0169425i	0.514601	−	0.857430i	\(-0.327940\pi\)
							−0.485256	+	0.874372i	\(0.661273\pi\)
\(41\)			24.1024i			0.587862i	0.955827	+	0.293931i	\(0.0949637\pi\)
							−0.955827	+	0.293931i	\(0.905036\pi\)
\(43\)		−	57.6214i		−	1.34003i	−0.742346	−	0.670017i	\(-0.766287\pi\)
							0.742346	−	0.670017i	\(-0.233713\pi\)
\(47\)	−16.0840	+	27.8583i	−0.342213	+	0.592730i	−0.984843	−	0.173446i	\(-0.944510\pi\)
							0.642630	+	0.766176i	\(0.277843\pi\)

(See \(a_n\) instead)

Twists

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

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.o.b.44.5	✓	40	3.2	odd	2	inner
105.3.o.b.44.6	yes	40	5.4	even	2	inner
105.3.o.b.44.15	yes	40	1.1	even	1	trivial
105.3.o.b.44.16	yes	40	15.14	odd	2	inner
105.3.o.b.74.5	yes	40	35.4	even	6	inner
105.3.o.b.74.6	yes	40	21.11	odd	6	inner
105.3.o.b.74.15	yes	40	105.74	odd	6	inner
105.3.o.b.74.16	yes	40	7.4	even	3	inner