Embedded newform 105.3.k.d.62.3

• Label: 105.3.k.d.62.3
• Level: $105$
• Weight: $3$
• Character: 105.62
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			62.3
Character	\(\chi\)	\(=\)	105.62
Dual form			105.3.k.d.83.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.28094 + 2.28094i) q^{2} +(-1.07458 + 2.80094i) q^{3} -6.40541i q^{4} +(1.80941 - 4.66112i) q^{5} +(-3.93772 - 8.83986i) q^{6} +(-6.22100 - 3.20922i) q^{7} +(5.48661 + 5.48661i) q^{8} +(-6.69054 - 6.01969i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \)

Character values

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

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(e\left(\frac{1}{4}\right)\)	\(-1\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.28094	+	2.28094i	−1.14047	+	1.14047i	−0.152108	+	0.988364i	\(0.548606\pi\)
							−0.988364	+	0.152108i	\(0.951394\pi\)
\(3\)	−1.07458	+	2.80094i	−0.358195	+	0.933647i
							\(5\)	1.80941	−	4.66112i	0.361882	−	0.932224i
\(7\)	−6.22100	−	3.20922i	−0.888715	−	0.458460i
							\(11\)		−	11.1704i		−	1.01549i	−0.861506	−	0.507747i	\(-0.830478\pi\)
0.861506	−	0.507747i	\(-0.169522\pi\)
\(13\)	5.82807	+	5.82807i	0.448313	+	0.448313i	0.894794	−	0.446480i	\(-0.147323\pi\)
							−0.446480	+	0.894794i	\(0.647323\pi\)
\(17\)	6.84147	+	6.84147i	0.402440	+	0.402440i	0.879092	−	0.476652i	\(-0.158150\pi\)
							−0.476652	+	0.879092i	\(0.658150\pi\)
\(19\)	−25.0261			−1.31716			−0.658581	−	0.752510i	\(-0.728843\pi\)
							−0.658581	+	0.752510i	\(0.728843\pi\)
\(23\)	−23.3593	−	23.3593i	−1.01562	−	1.01562i	−0.999876	−	0.0157445i	\(-0.994988\pi\)
							−0.0157445	−	0.999876i	\(-0.505012\pi\)
\(29\)	10.6354			0.366738			0.183369	−	0.983044i	\(-0.441300\pi\)
							0.183369	+	0.983044i	\(0.441300\pi\)
\(31\)		−	26.9470i		−	0.869257i	−0.900610	−	0.434629i	\(-0.856880\pi\)
							0.900610	−	0.434629i	\(-0.143120\pi\)
\(37\)	−20.8846	−	20.8846i	−0.564448	−	0.564448i	0.366120	−	0.930568i	\(-0.380686\pi\)
							−0.930568	+	0.366120i	\(0.880686\pi\)
\(41\)	32.9644			0.804010			0.402005	−	0.915637i	\(-0.368313\pi\)
							0.402005	+	0.915637i	\(0.368313\pi\)
\(43\)	1.25060	−	1.25060i	0.0290836	−	0.0290836i	−0.692415	−	0.721499i	\(-0.743453\pi\)
							0.721499	+	0.692415i	\(0.243453\pi\)
\(47\)	−59.1134	−	59.1134i	−1.25773	−	1.25773i	−0.952173	−	0.305558i	\(-0.901157\pi\)
							−0.305558	−	0.952173i	\(-0.598843\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.k.d.62.3	✓	32
3.2	odd	2	inner	105.3.k.d.62.14	yes	32
5.3	odd	4	inner	105.3.k.d.83.13	yes	32
7.6	odd	2	inner	105.3.k.d.62.4	yes	32
15.8	even	4	inner	105.3.k.d.83.4	yes	32
21.20	even	2	inner	105.3.k.d.62.13	yes	32
35.13	even	4	inner	105.3.k.d.83.14	yes	32
105.83	odd	4	inner	105.3.k.d.83.3	yes	32

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.k.d.62.3	✓	32	1.1	even	1	trivial
105.3.k.d.62.4	yes	32	7.6	odd	2	inner
105.3.k.d.62.13	yes	32	21.20	even	2	inner
105.3.k.d.62.14	yes	32	3.2	odd	2	inner
105.3.k.d.83.3	yes	32	105.83	odd	4	inner
105.3.k.d.83.4	yes	32	15.8	even	4	inner
105.3.k.d.83.13	yes	32	5.3	odd	4	inner
105.3.k.d.83.14	yes	32	35.13	even	4	inner