Embedded newform 105.3.r.a.19.14

• Label: 105.3.r.a.19.14
• 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			19.14
Character	\(\chi\)	\(=\)	105.19
Dual form			105.3.r.a.94.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.53945 + 1.46615i) q^{2} +(0.866025 + 1.50000i) q^{3} +(2.29920 + 3.98234i) q^{4} +(4.74629 - 1.57250i) q^{5} +5.07890i q^{6} +(-6.93149 - 0.976973i) q^{7} +1.75471i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.53945	+	1.46615i	1.26972	+	0.733076i	0.974936	−	0.222486i	\(-0.0714173\pi\)
							0.294789	+	0.955562i	\(0.404751\pi\)
\(3\)	0.866025	+	1.50000i	0.288675	+	0.500000i
							\(5\)	4.74629	−	1.57250i	0.949258	−	0.314499i
\(7\)	−6.93149	−	0.976973i	−0.990213	−	0.139568i
							\(11\)	−2.31170	−	4.00398i	−0.210154	−	0.363998i	0.741608	−	0.670833i	\(-0.234063\pi\)
−0.951763	+	0.306835i	\(0.900730\pi\)
\(13\)	−14.9844			−1.15265			−0.576324	−	0.817221i	\(-0.695513\pi\)
							−0.576324	+	0.817221i	\(0.695513\pi\)
\(17\)	8.38187	+	14.5178i	0.493051	+	0.853989i	0.999968	−	0.00800544i	\(-0.00254824\pi\)
							−0.506917	+	0.861995i	\(0.669215\pi\)
\(19\)	15.2091	+	8.78098i	0.800480	+	0.462157i	0.843639	−	0.536911i	\(-0.180409\pi\)
							−0.0431592	+	0.999068i	\(0.513742\pi\)
\(23\)	−36.9729	−	21.3463i	−1.60752	−	0.928101i	−0.989923	−	0.141605i	\(-0.954774\pi\)
							−0.617595	−	0.786496i	\(-0.711893\pi\)
\(29\)	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	−0.443033	−	0.896505i	\(-0.646098\pi\)
							0.554880	+	0.831931i	\(0.312764\pi\)
\(37\)	24.5533	+	14.1759i	0.663604	+	0.383132i	0.793649	−	0.608376i	\(-0.208179\pi\)
							−0.130045	+	0.991508i	\(0.541512\pi\)
\(41\)			44.5453i			1.08647i	0.839581	+	0.543235i	\(0.182801\pi\)
							−0.839581	+	0.543235i	\(0.817199\pi\)
\(43\)		−	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	0.337135	+	0.941456i	\(0.390542\pi\)
							−0.983893	+	0.178761i	\(0.942791\pi\)

(See \(a_n\) instead)

Twists

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

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.3	✓	32	5.4	even	2	inner
105.3.r.a.19.14	yes	32	1.1	even	1	trivial
105.3.r.a.94.3	yes	32	7.3	odd	6	inner
105.3.r.a.94.14	yes	32	35.24	odd	6	inner
315.3.bi.e.19.3		32	3.2	odd	2
315.3.bi.e.19.14		32	15.14	odd	2
315.3.bi.e.199.3		32	105.59	even	6
315.3.bi.e.199.14		32	21.17	even	6
525.3.o.p.376.7		16	5.3	odd	4
525.3.o.p.451.7		16	35.3	even	12
525.3.o.q.376.2		16	5.2	odd	4
525.3.o.q.451.2		16	35.17	even	12
735.3.e.a.244.15		32	7.5	odd	6
735.3.e.a.244.16		32	35.9	even	6
735.3.e.a.244.23		32	7.2	even	3
735.3.e.a.244.24		32	35.19	odd	6