Embedded newform 105.3.r.a.94.3

• Label: 105.3.r.a.94.3
• Level: $105$
• Weight: $3$
• Character: 105.94
• 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			94.3
Character	\(\chi\)	\(=\)	105.94
Dual form			105.3.r.a.19.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.53945 + 1.46615i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(2.29920 - 3.98234i) q^{4} +(1.01132 - 4.89665i) q^{5} -5.07890i q^{6} +(6.93149 - 0.976973i) q^{7} +1.75471i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.53945	+	1.46615i	−1.26972	+	0.733076i	−0.974936	−	0.222486i	\(-0.928583\pi\)
							−0.294789	+	0.955562i	\(0.595249\pi\)
\(3\)	−0.866025	+	1.50000i	−0.288675	+	0.500000i
							\(5\)	1.01132	−	4.89665i	0.202265	−	0.979331i
\(7\)	6.93149	−	0.976973i	0.990213	−	0.139568i
							\(11\)	−2.31170	+	4.00398i	−0.210154	+	0.363998i	−0.951763	−	0.306835i	\(-0.900730\pi\)
0.741608	+	0.670833i	\(0.234063\pi\)
\(13\)	14.9844			1.15265			0.576324	−	0.817221i	\(-0.304487\pi\)
							0.576324	+	0.817221i	\(0.304487\pi\)
\(17\)	−8.38187	+	14.5178i	−0.493051	+	0.853989i	−0.999968	−	0.00800544i	\(-0.997452\pi\)
							0.506917	+	0.861995i	\(0.330785\pi\)
\(19\)	15.2091	−	8.78098i	0.800480	−	0.462157i	−0.0431592	−	0.999068i	\(-0.513742\pi\)
							0.843639	+	0.536911i	\(0.180409\pi\)
\(23\)	36.9729	−	21.3463i	1.60752	−	0.928101i	0.617595	−	0.786496i	\(-0.288107\pi\)
							0.989923	−	0.141605i	\(-0.0452264\pi\)
\(29\)	18.1470			0.625760			0.312880	−	0.949793i	\(-0.398706\pi\)
							0.312880	+	0.949793i	\(0.398706\pi\)
\(31\)	3.46723	+	2.00181i	0.111846	+	0.0645745i	0.554880	−	0.831931i	\(-0.312764\pi\)
							−0.443033	+	0.896505i	\(0.646098\pi\)
\(37\)	−24.5533	+	14.1759i	−0.663604	+	0.383132i	−0.793649	−	0.608376i	\(-0.791821\pi\)
							0.130045	+	0.991508i	\(0.458488\pi\)
\(41\)		−	44.5453i		−	1.08647i	−0.839581	−	0.543235i	\(-0.817199\pi\)
							0.839581	−	0.543235i	\(-0.182801\pi\)
\(43\)		−	44.3306i		−	1.03094i	−0.856906	−	0.515472i	\(-0.827617\pi\)
							0.856906	−	0.515472i	\(-0.172383\pi\)
\(47\)	30.3976	+	52.6502i	0.646758	+	1.12022i	0.983893	+	0.178761i	\(0.0572088\pi\)
							−0.337135	+	0.941456i	\(0.609458\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.r.a.94.3	yes	32
3.2	odd	2		315.3.bi.e.199.14		32
5.2	odd	4		525.3.o.q.451.2		16
5.3	odd	4		525.3.o.p.451.7		16
5.4	even	2	inner	105.3.r.a.94.14	yes	32
7.3	odd	6		735.3.e.a.244.23		32
7.4	even	3		735.3.e.a.244.15		32
7.5	odd	6	inner	105.3.r.a.19.14	yes	32
15.14	odd	2		315.3.bi.e.199.3		32
21.5	even	6		315.3.bi.e.19.3		32
35.4	even	6		735.3.e.a.244.24		32
35.12	even	12		525.3.o.q.376.2		16
35.19	odd	6	inner	105.3.r.a.19.3	✓	32
35.24	odd	6		735.3.e.a.244.16		32
35.33	even	12		525.3.o.p.376.7		16
105.89	even	6		315.3.bi.e.19.14		32

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.3	✓	32	35.19	odd	6	inner
105.3.r.a.19.14	yes	32	7.5	odd	6	inner
105.3.r.a.94.3	yes	32	1.1	even	1	trivial
105.3.r.a.94.14	yes	32	5.4	even	2	inner
315.3.bi.e.19.3		32	21.5	even	6
315.3.bi.e.19.14		32	105.89	even	6
315.3.bi.e.199.3		32	15.14	odd	2
315.3.bi.e.199.14		32	3.2	odd	2
525.3.o.p.376.7		16	35.33	even	12
525.3.o.p.451.7		16	5.3	odd	4
525.3.o.q.376.2		16	35.12	even	12
525.3.o.q.451.2		16	5.2	odd	4
735.3.e.a.244.15		32	7.4	even	3
735.3.e.a.244.16		32	35.24	odd	6
735.3.e.a.244.23		32	7.3	odd	6
735.3.e.a.244.24		32	35.4	even	6