Embedded newform 105.3.k.d.62.14

• Label: 105.3.k.d.62.14
• 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			62.14
Character	\(\chi\)	\(=\)	105.62
Dual form			105.3.k.d.83.14

$q$-expansion

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

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	\(-0.451394\pi\)
							0.988364	−	0.152108i	\(-0.0486063\pi\)
\(3\)	2.80094	−	1.07458i	0.933647	−	0.358195i
							\(5\)	−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	\(0.169522\pi\)
−0.861506	+	0.507747i	\(0.830478\pi\)
\(13\)	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	0.476652	−	0.879092i	\(-0.341850\pi\)
							−0.879092	+	0.476652i	\(0.841850\pi\)
\(19\)	−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	\(0.00501183\pi\)
							0.0157445	+	0.999876i	\(0.494988\pi\)
\(29\)	−10.6354			−0.366738			−0.183369	−	0.983044i	\(-0.558700\pi\)
							−0.183369	+	0.983044i	\(0.558700\pi\)
\(31\)		−	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	\(-0.631687\pi\)
							−0.402005	+	0.915637i	\(0.631687\pi\)
\(43\)	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	\(0.0988431\pi\)
							0.305558	+	0.952173i	\(0.401157\pi\)

(See \(a_n\) instead)

Twists

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

    

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