Embedded newform 105.3.r.a.19.11

• Label: 105.3.r.a.19.11
• Level: $105$
• Weight: $3$
• Character: 105.19
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.11
Character	\(\chi\)	\(=\)	105.19
Dual form			105.3.r.a.94.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.32532 + 0.765175i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-0.829016 - 1.43590i) q^{4} +(1.02421 - 4.89398i) q^{5} -2.65064i q^{6} +(-6.34933 - 2.94719i) q^{7} -8.65876i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.32532	+	0.765175i	0.662661	+	0.382587i	0.793290	−	0.608844i	\(-0.208366\pi\)
							−0.130629	+	0.991431i	\(0.541700\pi\)
\(3\)	−0.866025	−	1.50000i	−0.288675	−	0.500000i
							\(5\)	1.02421	−	4.89398i	0.204841	−	0.978795i
\(7\)	−6.34933	−	2.94719i	−0.907048	−	0.421028i
							\(11\)	6.68282	+	11.5750i	0.607529	+	1.05227i	0.991646	+	0.128987i	\(0.0411726\pi\)
−0.384117	+	0.923284i	\(0.625494\pi\)
\(13\)	15.5994			1.19996			0.599979	−	0.800016i	\(-0.295176\pi\)
							0.599979	+	0.800016i	\(0.295176\pi\)
\(17\)	−10.4267	−	18.0595i	−0.613333	−	1.06232i	−0.990674	−	0.136250i	\(-0.956495\pi\)
							0.377341	−	0.926074i	\(-0.376838\pi\)
\(19\)	23.3408	+	13.4758i	1.22846	+	0.709253i	0.966708	−	0.255881i	\(-0.0823655\pi\)
							0.261755	+	0.965134i	\(0.415699\pi\)
\(23\)	20.1960	+	11.6602i	0.878086	+	0.506963i	0.870027	−	0.493004i	\(-0.164101\pi\)
							0.00805929	+	0.999968i	\(0.497435\pi\)
\(29\)	−43.9323			−1.51491			−0.757453	−	0.652890i	\(-0.773557\pi\)
							−0.757453	+	0.652890i	\(0.773557\pi\)
\(31\)	27.3477	−	15.7892i	0.882183	−	0.509328i	0.0108052	−	0.999942i	\(-0.496561\pi\)
							0.871377	+	0.490613i	\(0.163227\pi\)
\(37\)	30.6172	+	17.6768i	0.827491	+	0.477752i	0.852993	−	0.521923i	\(-0.174785\pi\)
							−0.0255017	+	0.999675i	\(0.508118\pi\)
\(41\)		−	19.4847i		−	0.475237i	−0.971359	−	0.237618i	\(-0.923633\pi\)
							0.971359	−	0.237618i	\(-0.0763667\pi\)
\(43\)		−	18.7524i		−	0.436102i	−0.975937	−	0.218051i	\(-0.930030\pi\)
							0.975937	−	0.218051i	\(-0.0699699\pi\)
\(47\)	−1.46083	+	2.53023i	−0.0310815	+	0.0538348i	−0.881148	−	0.472841i	\(-0.843228\pi\)
							0.850066	+	0.526676i	\(0.176562\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.r.a.19.11	yes	32
3.2	odd	2		315.3.bi.e.19.6		32
5.2	odd	4		525.3.o.p.376.3		16
5.3	odd	4		525.3.o.q.376.6		16
5.4	even	2	inner	105.3.r.a.19.6	✓	32
7.2	even	3		735.3.e.a.244.29		32
7.3	odd	6	inner	105.3.r.a.94.6	yes	32
7.5	odd	6		735.3.e.a.244.9		32
15.14	odd	2		315.3.bi.e.19.11		32
21.17	even	6		315.3.bi.e.199.11		32
35.3	even	12		525.3.o.q.451.6		16
35.9	even	6		735.3.e.a.244.10		32
35.17	even	12		525.3.o.p.451.3		16
35.19	odd	6		735.3.e.a.244.30		32
35.24	odd	6	inner	105.3.r.a.94.11	yes	32
105.59	even	6		315.3.bi.e.199.6		32

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.6	✓	32	5.4	even	2	inner
105.3.r.a.19.11	yes	32	1.1	even	1	trivial
105.3.r.a.94.6	yes	32	7.3	odd	6	inner
105.3.r.a.94.11	yes	32	35.24	odd	6	inner
315.3.bi.e.19.6		32	3.2	odd	2
315.3.bi.e.19.11		32	15.14	odd	2
315.3.bi.e.199.6		32	105.59	even	6
315.3.bi.e.199.11		32	21.17	even	6
525.3.o.p.376.3		16	5.2	odd	4
525.3.o.p.451.3		16	35.17	even	12
525.3.o.q.376.6		16	5.3	odd	4
525.3.o.q.451.6		16	35.3	even	12
735.3.e.a.244.9		32	7.5	odd	6
735.3.e.a.244.10		32	35.9	even	6
735.3.e.a.244.29		32	7.2	even	3
735.3.e.a.244.30		32	35.19	odd	6