Embedded newform 105.3.k.d.83.2

• Label: 105.3.k.d.83.2
• Level: $105$
• Weight: $3$
• Character: 105.83
• 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			83.2
Character	\(\chi\)	\(=\)	105.83
Dual form			105.3.k.d.62.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.63482 - 2.63482i) q^{2} +(2.54097 - 1.59482i) q^{3} +9.88460i q^{4} +(4.15332 - 2.78387i) q^{5} +(-10.8971 - 2.49295i) q^{6} +(6.57626 - 2.39850i) q^{7} +(15.5049 - 15.5049i) q^{8} +(3.91310 - 8.10479i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \)

Character values

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

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(e\left(\frac{3}{4}\right)\)	\(-1\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.63482	−	2.63482i	−1.31741	−	1.31741i	−0.915817	−	0.401595i	\(-0.868456\pi\)
							−0.401595	−	0.915817i	\(-0.631544\pi\)
\(3\)	2.54097	−	1.59482i	0.846991	−	0.531606i
							\(5\)	4.15332	−	2.78387i	0.830663	−	0.556775i
\(7\)	6.57626	−	2.39850i	0.939466	−	0.342643i
							\(11\)			5.66373i			0.514885i	0.966294	+	0.257442i	\(0.0828797\pi\)
−0.966294	+	0.257442i	\(0.917120\pi\)
\(13\)	1.68481	−	1.68481i	0.129601	−	0.129601i	−0.639331	−	0.768932i	\(-0.720789\pi\)
							0.768932	+	0.639331i	\(0.220789\pi\)
\(17\)	−14.0118	+	14.0118i	−0.824224	+	0.824224i	−0.986711	−	0.162486i	\(-0.948049\pi\)
							0.162486	+	0.986711i	\(0.448049\pi\)
\(19\)	−24.0066			−1.26351			−0.631753	−	0.775170i	\(-0.717664\pi\)
							−0.631753	+	0.775170i	\(0.717664\pi\)
\(23\)	3.17641	−	3.17641i	0.138105	−	0.138105i	−0.634675	−	0.772780i	\(-0.718866\pi\)
							0.772780	+	0.634675i	\(0.218866\pi\)
\(29\)	24.1064			0.831254			0.415627	−	0.909535i	\(-0.363562\pi\)
							0.415627	+	0.909535i	\(0.363562\pi\)
\(31\)			23.8436i			0.769148i	0.923094	+	0.384574i	\(0.125652\pi\)
							−0.923094	+	0.384574i	\(0.874348\pi\)
\(37\)	−13.8075	+	13.8075i	−0.373177	+	0.373177i	−0.868633	−	0.495456i	\(-0.835001\pi\)
							0.495456	+	0.868633i	\(0.335001\pi\)
\(41\)	−53.4368			−1.30334			−0.651668	−	0.758505i	\(-0.725930\pi\)
							−0.651668	+	0.758505i	\(0.725930\pi\)
\(43\)	25.9017	+	25.9017i	0.602366	+	0.602366i	0.940940	−	0.338574i	\(-0.109945\pi\)
							−0.338574	+	0.940940i	\(0.609945\pi\)
\(47\)	27.3968	−	27.3968i	0.582911	−	0.582911i	−0.352791	−	0.935702i	\(-0.614767\pi\)
							0.935702	+	0.352791i	\(0.114767\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.k.d.83.2	yes	32
3.2	odd	2	inner	105.3.k.d.83.16	yes	32
5.2	odd	4	inner	105.3.k.d.62.15	yes	32
7.6	odd	2	inner	105.3.k.d.83.1	yes	32
15.2	even	4	inner	105.3.k.d.62.1	✓	32
21.20	even	2	inner	105.3.k.d.83.15	yes	32
35.27	even	4	inner	105.3.k.d.62.16	yes	32
105.62	odd	4	inner	105.3.k.d.62.2	yes	32

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.k.d.62.1	✓	32	15.2	even	4	inner
105.3.k.d.62.2	yes	32	105.62	odd	4	inner
105.3.k.d.62.15	yes	32	5.2	odd	4	inner
105.3.k.d.62.16	yes	32	35.27	even	4	inner
105.3.k.d.83.1	yes	32	7.6	odd	2	inner
105.3.k.d.83.2	yes	32	1.1	even	1	trivial
105.3.k.d.83.15	yes	32	21.20	even	2	inner
105.3.k.d.83.16	yes	32	3.2	odd	2	inner