Embedded newform 105.3.v.a.67.2

• Label: 105.3.v.a.67.2
• Level: $105$
• Weight: $3$
• Character: 105.67
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(16\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.2
Character	\(\chi\)	\(=\)	105.67
Dual form			105.3.v.a.58.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.914152 + 3.41166i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(-7.33966 - 4.23756i) q^{4} +(2.17799 - 4.50071i) q^{5} +6.11763 q^{6} +(-2.92953 - 6.35750i) q^{7} +(11.1766 - 11.1766i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8}+O(q^{10}) \)

Character values

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

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(e\left(\frac{1}{4}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.914152	+	3.41166i	−0.457076	+	1.70583i	0.224836	+	0.974397i	\(0.427815\pi\)
							−0.681912	+	0.731435i	\(0.738851\pi\)
\(3\)	−0.448288	−	1.67303i	−0.149429	−	0.557678i
							\(5\)	2.17799	−	4.50071i	0.435597	−	0.900142i
\(7\)	−2.92953	−	6.35750i	−0.418505	−	0.908215i
							\(11\)	8.72135	−	15.1058i	0.792850	−	1.37326i	−0.131345	−	0.991337i	\(-0.541930\pi\)
0.924195	−	0.381920i	\(-0.124737\pi\)
\(13\)	−8.72144	+	8.72144i	−0.670880	+	0.670880i	−0.957919	−	0.287039i	\(-0.907329\pi\)
							0.287039	+	0.957919i	\(0.407329\pi\)
\(17\)	−11.2788	+	3.02215i	−0.663461	+	0.177774i	−0.574807	−	0.818289i	\(-0.694923\pi\)
							−0.0886535	+	0.996063i	\(0.528256\pi\)
\(19\)	3.12903	−	1.80655i	0.164686	−	0.0950814i	−0.415392	−	0.909643i	\(-0.636356\pi\)
							0.580078	+	0.814561i	\(0.303022\pi\)
\(23\)	23.1890	+	6.21349i	1.00822	+	0.270152i	0.724885	−	0.688870i	\(-0.241893\pi\)
							0.283334	+	0.959021i	\(0.408559\pi\)
\(29\)		−	46.5831i		−	1.60631i	−0.595767	−	0.803157i	\(-0.703152\pi\)
							0.595767	−	0.803157i	\(-0.296848\pi\)
\(31\)	−1.10507	+	1.91403i	−0.0356474	+	0.0617430i	−0.883299	−	0.468811i	\(-0.844683\pi\)
							0.847651	+	0.530554i	\(0.178016\pi\)
\(37\)	7.87211	−	29.3791i	0.212760	−	0.794030i	−0.774183	−	0.632961i	\(-0.781839\pi\)
							0.986943	−	0.161069i	\(-0.0514942\pi\)
\(41\)	29.9435			0.730329			0.365165	−	0.930943i	\(-0.381013\pi\)
							0.365165	+	0.930943i	\(0.381013\pi\)
\(43\)	−19.6771	+	19.6771i	−0.457608	+	0.457608i	−0.897869	−	0.440262i	\(-0.854886\pi\)
							0.440262	+	0.897869i	\(0.354886\pi\)
\(47\)	−21.2083	+	79.1503i	−0.451240	+	1.68405i	0.247674	+	0.968844i	\(0.420334\pi\)
							−0.698913	+	0.715206i	\(0.746333\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.v.a.67.2	yes	64
3.2	odd	2		315.3.ca.b.172.15		64
5.3	odd	4	inner	105.3.v.a.88.15	yes	64
7.2	even	3	inner	105.3.v.a.37.15	✓	64
15.8	even	4		315.3.ca.b.298.2		64
21.2	odd	6		315.3.ca.b.37.2		64
35.23	odd	12	inner	105.3.v.a.58.2	yes	64
105.23	even	12		315.3.ca.b.163.15		64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.15	✓	64	7.2	even	3	inner
105.3.v.a.58.2	yes	64	35.23	odd	12	inner
105.3.v.a.67.2	yes	64	1.1	even	1	trivial
105.3.v.a.88.15	yes	64	5.3	odd	4	inner
315.3.ca.b.37.2		64	21.2	odd	6
315.3.ca.b.163.15		64	105.23	even	12
315.3.ca.b.172.15		64	3.2	odd	2
315.3.ca.b.298.2		64	15.8	even	4