Embedded newform 105.3.r.a.19.15

• Label: 105.3.r.a.19.15
• 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			19.15
Character	\(\chi\)	\(=\)	105.19
Dual form			105.3.r.a.94.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.95153 + 1.70407i) q^{2} +(0.866025 + 1.50000i) q^{3} +(3.80769 + 6.59511i) q^{4} +(-4.81594 - 1.34415i) q^{5} +5.90306i q^{6} +(5.14807 - 4.74314i) q^{7} +12.3217i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.95153	+	1.70407i	1.47577	+	0.852033i	0.999626	−	0.0273367i	\(-0.00870264\pi\)
							0.476139	+	0.879370i	\(0.342036\pi\)
\(3\)	0.866025	+	1.50000i	0.288675	+	0.500000i
							\(5\)	−4.81594	−	1.34415i	−0.963188	−	0.268830i
\(7\)	5.14807	−	4.74314i	0.735438	−	0.677592i
							\(11\)	0.694658	+	1.20318i	0.0631508	+	0.109380i	0.895872	−	0.444312i	\(-0.146552\pi\)
−0.832721	+	0.553692i	\(0.813218\pi\)
\(13\)	−3.78639			−0.291261			−0.145630	−	0.989339i	\(-0.546521\pi\)
							−0.145630	+	0.989339i	\(0.546521\pi\)
\(17\)	−15.8536	−	27.4592i	−0.932563	−	1.61525i	−0.778922	−	0.627121i	\(-0.784233\pi\)
							−0.153641	−	0.988127i	\(-0.549100\pi\)
\(19\)	12.8335	+	7.40942i	0.675447	+	0.389970i	0.798137	−	0.602475i	\(-0.205819\pi\)
							−0.122690	+	0.992445i	\(0.539152\pi\)
\(23\)	19.5874	+	11.3088i	0.851625	+	0.491686i	0.861199	−	0.508268i	\(-0.169714\pi\)
							−0.00957359	+	0.999954i	\(0.503047\pi\)
\(29\)	−42.9485			−1.48098			−0.740492	−	0.672065i	\(-0.765407\pi\)
							−0.740492	+	0.672065i	\(0.765407\pi\)
\(31\)	−28.0131	+	16.1734i	−0.903649	+	0.521722i	−0.878382	−	0.477959i	\(-0.841377\pi\)
							−0.0252666	+	0.999681i	\(0.508043\pi\)
\(37\)	7.29321	+	4.21074i	0.197114	+	0.113804i	0.595309	−	0.803497i	\(-0.297030\pi\)
							−0.398195	+	0.917301i	\(0.630363\pi\)
\(41\)			46.3613i			1.13076i	0.824829	+	0.565382i	\(0.191271\pi\)
							−0.824829	+	0.565382i	\(0.808729\pi\)
\(43\)		−	9.92743i		−	0.230871i	−0.993315	−	0.115435i	\(-0.963174\pi\)
							0.993315	−	0.115435i	\(-0.0368263\pi\)
\(47\)	27.2811	−	47.2522i	0.580448	−	1.00537i	−0.414978	−	0.909832i	\(-0.636211\pi\)
							0.995426	−	0.0955345i	\(-0.0304560\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.r.a.19.15	yes	32
3.2	odd	2		315.3.bi.e.19.2		32
5.2	odd	4		525.3.o.q.376.1		16
5.3	odd	4		525.3.o.p.376.8		16
5.4	even	2	inner	105.3.r.a.19.2	✓	32
7.2	even	3		735.3.e.a.244.13		32
7.3	odd	6	inner	105.3.r.a.94.2	yes	32
7.5	odd	6		735.3.e.a.244.5		32
15.14	odd	2		315.3.bi.e.19.15		32
21.17	even	6		315.3.bi.e.199.15		32
35.3	even	12		525.3.o.p.451.8		16
35.9	even	6		735.3.e.a.244.6		32
35.17	even	12		525.3.o.q.451.1		16
35.19	odd	6		735.3.e.a.244.14		32
35.24	odd	6	inner	105.3.r.a.94.15	yes	32
105.59	even	6		315.3.bi.e.199.2		32

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.2	✓	32	5.4	even	2	inner
105.3.r.a.19.15	yes	32	1.1	even	1	trivial
105.3.r.a.94.2	yes	32	7.3	odd	6	inner
105.3.r.a.94.15	yes	32	35.24	odd	6	inner
315.3.bi.e.19.2		32	3.2	odd	2
315.3.bi.e.19.15		32	15.14	odd	2
315.3.bi.e.199.2		32	105.59	even	6
315.3.bi.e.199.15		32	21.17	even	6
525.3.o.p.376.8		16	5.3	odd	4
525.3.o.p.451.8		16	35.3	even	12
525.3.o.q.376.1		16	5.2	odd	4
525.3.o.q.451.1		16	35.17	even	12
735.3.e.a.244.5		32	7.5	odd	6
735.3.e.a.244.6		32	35.9	even	6
735.3.e.a.244.13		32	7.2	even	3
735.3.e.a.244.14		32	35.19	odd	6