Embedded newform 105.3.v.a.88.6

• Label: 105.3.v.a.88.6
• Level: $105$
• Weight: $3$
• Character: 105.88
• 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			88.6
Character	\(\chi\)	\(=\)	105.88
Dual form			105.3.v.a.37.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.84280 - 0.493776i) q^{2} +(1.67303 - 0.448288i) q^{3} +(-0.312015 - 0.180142i) q^{4} +(-1.82066 + 4.65674i) q^{5} -3.30441 q^{6} +(-6.63712 + 2.22456i) q^{7} +(5.88211 + 5.88211i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.84280	−	0.493776i	−0.921399	−	0.246888i	−0.233216	−	0.972425i	\(-0.574925\pi\)
							−0.688183	+	0.725537i	\(0.741591\pi\)
\(3\)	1.67303	−	0.448288i	0.557678	−	0.149429i
							\(5\)	−1.82066	+	4.65674i	−0.364131	+	0.931348i
\(7\)	−6.63712	+	2.22456i	−0.948160	+	0.317795i
							\(11\)	−5.24180	+	9.07906i	−0.476527	+	0.825369i	−0.999638	−	0.0268951i	\(-0.991438\pi\)
0.523111	+	0.852265i	\(0.324771\pi\)
\(13\)	1.40565	+	1.40565i	0.108127	+	0.108127i	0.759101	−	0.650973i	\(-0.225639\pi\)
							−0.650973	+	0.759101i	\(0.725639\pi\)
\(17\)	6.55621	+	24.4681i	0.385659	+	1.43930i	0.837125	+	0.547012i	\(0.184235\pi\)
							−0.451465	+	0.892289i	\(0.649099\pi\)
\(19\)	−9.07193	+	5.23768i	−0.477470	+	0.275667i	−0.719362	−	0.694636i	\(-0.755566\pi\)
							0.241892	+	0.970303i	\(0.422232\pi\)
\(23\)	−7.89111	+	29.4500i	−0.343092	+	1.28044i	0.551734	+	0.834020i	\(0.313966\pi\)
							−0.894826	+	0.446416i	\(0.852700\pi\)
\(29\)		−	55.6217i		−	1.91799i	−0.283425	−	0.958994i	\(-0.591471\pi\)
							0.283425	−	0.958994i	\(-0.408529\pi\)
\(31\)	8.12663	−	14.0757i	0.262149	−	0.454056i	−0.704664	−	0.709542i	\(-0.748902\pi\)
							0.966813	+	0.255486i	\(0.0822354\pi\)
\(37\)	14.8150	+	3.96966i	0.400404	+	0.107288i	0.453401	−	0.891307i	\(-0.350211\pi\)
							−0.0529966	+	0.998595i	\(0.516877\pi\)
\(41\)	−28.7305			−0.700743			−0.350371	−	0.936611i	\(-0.613945\pi\)
							−0.350371	+	0.936611i	\(0.613945\pi\)
\(43\)	3.17014	+	3.17014i	0.0737243	+	0.0737243i	0.743007	−	0.669283i	\(-0.233399\pi\)
							−0.669283	+	0.743007i	\(0.733399\pi\)
\(47\)	−1.71038	−	0.458294i	−0.0363910	−	0.00975094i	0.240578	−	0.970630i	\(-0.422663\pi\)
							−0.276969	+	0.960879i	\(0.589330\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.v.a.88.6	yes	64
3.2	odd	2		315.3.ca.b.298.11		64
5.2	odd	4	inner	105.3.v.a.67.11	yes	64
7.2	even	3	inner	105.3.v.a.58.11	yes	64
15.2	even	4		315.3.ca.b.172.6		64
21.2	odd	6		315.3.ca.b.163.6		64
35.2	odd	12	inner	105.3.v.a.37.6	✓	64
105.2	even	12		315.3.ca.b.37.11		64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.6	✓	64	35.2	odd	12	inner
105.3.v.a.58.11	yes	64	7.2	even	3	inner
105.3.v.a.67.11	yes	64	5.2	odd	4	inner
105.3.v.a.88.6	yes	64	1.1	even	1	trivial
315.3.ca.b.37.11		64	105.2	even	12
315.3.ca.b.163.6		64	21.2	odd	6
315.3.ca.b.172.6		64	15.2	even	4
315.3.ca.b.298.11		64	3.2	odd	2