Embedded newform 151.2.g.a.105.12

• Label: 151.2.g.a.105.12
• Level: $151$
• Weight: $2$
• Character: 151.105
• Analytic conductor: $1.206$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.g (of order \(15\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.20574107052\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(12\) over \(\Q(\zeta_{15})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			105.12
Character	\(\chi\)	\(=\)	151.105
Dual form			151.2.g.a.128.12

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.27637 + 2.21074i) q^{2} +(0.130320 + 0.401084i) q^{3} +(-2.25824 + 3.91138i) q^{4} +(-0.658964 - 0.293390i) q^{5} +(-0.720354 + 0.800034i) q^{6} +(-1.31592 - 0.585885i) q^{7} -6.42389 q^{8} +(2.28317 - 1.65882i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/151\mathbb{Z}\right)^\times\).

\(n\)	\(6\)
\(\chi(n)\)	\(e\left(\frac{11}{15}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.27637	+	2.21074i	0.902529	+	1.56323i	0.824200	+	0.566299i	\(0.191625\pi\)
							0.0783292	+	0.996928i	\(0.475041\pi\)
\(3\)	0.130320	+	0.401084i	0.0752403	+	0.231566i	0.981603	−	0.190936i	\(-0.0611522\pi\)
							−0.906362	+	0.422501i	\(0.861152\pi\)
\(5\)	−0.658964	−	0.293390i	−0.294698	−	0.131208i	0.254062	−	0.967188i	\(-0.418233\pi\)
							−0.548760	+	0.835980i	\(0.684900\pi\)
\(7\)	−1.31592	−	0.585885i	−0.497370	−	0.221444i	0.142691	−	0.989767i	\(-0.454424\pi\)
							−0.640061	+	0.768324i	\(0.721091\pi\)
\(11\)	2.41227	−	0.512744i	0.727327	−	0.154598i	0.170655	−	0.985331i	\(-0.445412\pi\)
							0.556671	+	0.830733i	\(0.312078\pi\)
\(13\)	3.18758	+	0.677540i	0.884075	+	0.187916i	0.627508	−	0.778610i	\(-0.284075\pi\)
							0.256567	+	0.966526i	\(0.417408\pi\)
\(17\)	−0.430810	+	4.09889i	−0.104487	+	0.994126i	0.809152	+	0.587599i	\(0.199927\pi\)
							−0.913639	+	0.406527i	\(0.866740\pi\)
\(19\)	−2.45867			−0.564058			−0.282029	−	0.959406i	\(-0.591008\pi\)
							−0.282029	+	0.959406i	\(0.591008\pi\)
\(23\)	−3.07198	−	5.32082i	−0.640552	−	1.10947i	−0.985310	−	0.170776i	\(-0.945372\pi\)
							0.344758	−	0.938691i	\(-0.387961\pi\)
\(29\)	0.584913	−	1.80018i	0.108616	−	0.334285i	−0.881946	−	0.471350i	\(-0.843767\pi\)
							0.990562	+	0.137065i	\(0.0437670\pi\)
\(31\)	0.762221	−	7.25205i	0.136899	−	1.30251i	−0.683177	−	0.730253i	\(-0.739402\pi\)
							0.820076	−	0.572254i	\(-0.193931\pi\)
\(37\)	−0.484846	+	0.538476i	−0.0797081	+	0.0885248i	−0.781680	−	0.623680i	\(-0.785637\pi\)
							0.701971	+	0.712205i	\(0.252303\pi\)
\(41\)	2.13287	+	6.56430i	0.333098	+	1.02517i	0.967651	+	0.252292i	\(0.0811843\pi\)
							−0.634553	+	0.772879i	\(0.718816\pi\)
\(43\)	−8.39593	+	3.73811i	−1.28037	+	0.570056i	−0.930345	−	0.366685i	\(-0.880493\pi\)
							−0.350022	+	0.936741i	\(0.613826\pi\)
\(47\)	8.77916	+	1.86607i	1.28057	+	0.272194i	0.797464	−	0.603366i	\(-0.206174\pi\)
							0.483108	+	0.875561i	\(0.339508\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.g.a.105.12	✓	96
151.128	even	15	inner	151.2.g.a.128.12	yes	96

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.g.a.105.12	✓	96	1.1	even	1	trivial
151.2.g.a.128.12	yes	96	151.128	even	15	inner