Embedded newform 141.2.g.a.107.12

• Label: 141.2.g.a.107.12
• Level: $141$
• Weight: $2$
• Character: 141.107
• 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			107.12
Character	\(\chi\)	\(=\)	141.107
Dual form			141.2.g.a.29.12

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.59407 - 1.12521i) q^{2} +(0.370083 - 1.69205i) q^{3} +(0.605180 - 1.70281i) q^{4} +(-1.77321 + 1.89865i) q^{5} +(-1.31398 - 3.11367i) q^{6} +(1.00489 - 1.93936i) q^{7} +(0.101518 + 0.362323i) q^{8} +(-2.72608 - 1.25240i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 308 q - 19 q^{3} - 26 q^{4} - 15 q^{6} - 42 q^{7} - 19 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(52\)	\(95\)
\(\chi(n)\)	\(e\left(\frac{11}{46}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.59407	−	1.12521i	1.12718	−	0.795647i	0.146099	−	0.989270i	\(-0.453328\pi\)
							0.981076	+	0.193623i	\(0.0620238\pi\)
\(3\)	0.370083	−	1.69205i	0.213668	−	0.976906i
							\(5\)	−1.77321	+	1.89865i	−0.793005	+	0.849101i	−0.991379	−	0.131025i	\(-0.958173\pi\)
0.198374	+	0.980126i	\(0.436434\pi\)
\(7\)	1.00489	−	1.93936i	0.379814	−	0.733008i	−0.618805	−	0.785545i	\(-0.712383\pi\)
							0.998619	+	0.0525365i	\(0.0167306\pi\)
\(11\)	2.72950	+	1.65985i	0.822976	+	0.500463i	0.866847	−	0.498574i	\(-0.166143\pi\)
							−0.0438706	+	0.999037i	\(0.513969\pi\)
\(13\)	−1.12368	+	2.58698i	−0.311654	+	0.717499i	−0.999969	−	0.00791323i	\(-0.997481\pi\)
							0.688315	+	0.725412i	\(0.258351\pi\)
\(17\)	−2.07333	−	3.40945i	−0.502857	−	0.826914i	0.496292	−	0.868156i	\(-0.334695\pi\)
							−0.999149	+	0.0412419i	\(0.986869\pi\)
\(19\)	−4.16422	+	3.88911i	−0.955338	+	0.892223i	−0.994257	−	0.107019i	\(-0.965869\pi\)
							0.0389192	+	0.999242i	\(0.487608\pi\)
\(23\)	1.55801	−	2.20719i	0.324867	−	0.460232i	−0.621458	−	0.783447i	\(-0.713460\pi\)
							0.946325	+	0.323216i	\(0.104764\pi\)
\(29\)	3.81591	−	1.65748i	0.708597	−	0.307787i	−0.0131795	−	0.999913i	\(-0.504195\pi\)
							0.721777	+	0.692126i	\(0.243326\pi\)
\(31\)	4.66115	−	5.72933i	0.837168	−	1.02902i	−0.161940	−	0.986801i	\(-0.551775\pi\)
							0.999108	−	0.0422173i	\(-0.0134422\pi\)
\(37\)	−11.8354	−	1.62674i	−1.94573	−	0.267435i	−0.947157	−	0.320770i	\(-0.896059\pi\)
							−0.998577	+	0.0533346i	\(0.983015\pi\)
\(41\)	−3.95021	−	1.10680i	−0.616919	−	0.172853i	−0.0528802	−	0.998601i	\(-0.516840\pi\)
							−0.564039	+	0.825748i	\(0.690753\pi\)
\(43\)	−3.24726	−	1.15408i	−0.495203	−	0.175995i	0.0755096	−	0.997145i	\(-0.475942\pi\)
							−0.570713	+	0.821150i	\(0.693333\pi\)
\(47\)	−6.76848	+	1.08982i	−0.987284	+	0.158966i

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	141.2.g.a.107.12	yes	308
3.2	odd	2	inner	141.2.g.a.107.3	yes	308
47.29	odd	46	inner	141.2.g.a.29.3	✓	308
141.29	even	46	inner	141.2.g.a.29.12	yes	308

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
141.2.g.a.29.3	✓	308	47.29	odd	46	inner
141.2.g.a.29.12	yes	308	141.29	even	46	inner
141.2.g.a.107.3	yes	308	3.2	odd	2	inner
141.2.g.a.107.12	yes	308	1.1	even	1	trivial