Embedded newform 141.2.g.a.11.6

• Label: 141.2.g.a.11.6
• Level: $141$
• Weight: $2$
• Character: 141.11
• Analytic conductor: $1.126$
• Analytic rank: $0$
• Dimension: $308$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 141 = 3 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	141.g (of order \(46\), degree \(22\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.12589066850\)
Analytic rank:	\(0\)
Dimension:	\(308\)
Relative dimension:	\(14\) over \(\Q(\zeta_{46})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{46}]$

Embedding invariants

Embedding label			11.6
Character	\(\chi\)	\(=\)	141.11
Dual form			141.2.g.a.77.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.596212 - 0.556824i) q^{2} +(-1.66862 - 0.464434i) q^{3} +(-0.0910680 - 1.33137i) q^{4} +(-1.53452 + 2.96148i) q^{5} +(0.736246 + 1.20603i) q^{6} +(-1.61001 + 0.699326i) q^{7} +(-1.71672 + 2.11013i) q^{8} +(2.56860 + 1.54993i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 308 q - 19 q^{3} - 26 q^{4} - 15 q^{6} - 42 q^{7} - 19 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/141\mathbb{Z}\right)^\times\).

\(n\)	\(52\)	\(95\)
\(\chi(n)\)	\(e\left(\frac{7}{46}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.596212	−	0.556824i	−0.421586	−	0.393734i	0.442753	−	0.896644i	\(-0.354002\pi\)
							−0.864339	+	0.502910i	\(0.832263\pi\)
\(3\)	−1.66862	−	0.464434i	−0.963380	−	0.268141i
							\(5\)	−1.53452	+	2.96148i	−0.686257	+	1.32442i	0.248328	+	0.968676i	\(0.420119\pi\)
−0.934585	+	0.355740i	\(0.884229\pi\)
\(7\)	−1.61001	+	0.699326i	−0.608527	+	0.264320i	−0.680105	−	0.733115i	\(-0.738066\pi\)
							0.0715785	+	0.997435i	\(0.477196\pi\)
\(11\)	−0.0868188	+	0.417795i	−0.0261769	+	0.125970i	−0.990144	−	0.140050i	\(-0.955274\pi\)
							0.963968	+	0.266020i	\(0.0857086\pi\)
\(13\)	−0.661787	+	1.08826i	−0.183547	+	0.301830i	−0.932759	−	0.360500i	\(-0.882606\pi\)
							0.749212	+	0.662330i	\(0.230432\pi\)
\(17\)	−5.04630	+	1.04863i	−1.22391	+	0.254331i	−0.770772	−	0.637111i	\(-0.780129\pi\)
							−0.453135	+	0.891442i	\(0.649694\pi\)
\(19\)	−2.97647	+	1.54228i	−0.682849	+	0.353824i	−0.766115	−	0.642704i	\(-0.777813\pi\)
							0.0832661	+	0.996527i	\(0.473465\pi\)
\(23\)	−4.12188	−	4.41345i	−0.859471	−	0.920268i	0.138066	−	0.990423i	\(-0.455912\pi\)
							−0.997536	+	0.0701548i	\(0.977651\pi\)
\(29\)	5.97850	−	3.63560i	1.11018	−	0.675115i	0.160093	−	0.987102i	\(-0.448821\pi\)
							0.950086	+	0.311987i	\(0.100995\pi\)
\(31\)	−0.492694	−	3.58461i	−0.0884904	−	0.643816i	−0.981173	−	0.193130i	\(-0.938136\pi\)
							0.892683	−	0.450686i	\(-0.148820\pi\)
\(37\)	3.12663	+	8.79751i	0.514016	+	1.44630i	0.861085	+	0.508462i	\(0.169786\pi\)
							−0.347069	+	0.937840i	\(0.612823\pi\)
\(41\)	−6.85266	+	5.57505i	−1.07021	+	0.870677i	−0.991997	−	0.126260i	\(-0.959702\pi\)
							−0.0782082	+	0.996937i	\(0.524920\pi\)
\(43\)	9.37275	−	0.641114i	1.42933	−	0.0977689i	0.667049	−	0.745014i	\(-0.267557\pi\)
							0.762282	+	0.647245i	\(0.224079\pi\)
\(47\)	−6.33015	−	2.63233i	−0.923348	−	0.383964i

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	141.2.g.a.11.6	✓	308
3.2	odd	2	inner	141.2.g.a.11.9	yes	308
47.30	odd	46	inner	141.2.g.a.77.9	yes	308
141.77	even	46	inner	141.2.g.a.77.6	yes	308

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
141.2.g.a.11.6	✓	308	1.1	even	1	trivial
141.2.g.a.11.9	yes	308	3.2	odd	2	inner
141.2.g.a.77.6	yes	308	141.77	even	46	inner
141.2.g.a.77.9	yes	308	47.30	odd	46	inner