Embedded newform 141.2.g.a.107.5

• Label: 141.2.g.a.107.5
• 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			107.5
Character	\(\chi\)	\(=\)	141.107
Dual form			141.2.g.a.29.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.00906 + 0.712272i) q^{2} +(1.57691 - 0.716494i) q^{3} +(-0.158889 + 0.447071i) q^{4} +(-1.67994 + 1.79878i) q^{5} +(-1.08086 + 1.84617i) q^{6} +(-2.17072 + 4.18929i) q^{7} +(-0.824573 - 2.94294i) q^{8} +(1.97327 - 2.25969i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 308 q - 19 q^{3} - 26 q^{4} - 15 q^{6} - 42 q^{7} - 19 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.00906	+	0.712272i	−0.713513	+	0.503653i	−0.875547	−	0.483133i	\(-0.839499\pi\)
							0.162034	+	0.986785i	\(0.448195\pi\)
\(3\)	1.57691	−	0.716494i	0.910428	−	0.413668i
							\(5\)	−1.67994	+	1.79878i	−0.751293	+	0.804438i	−0.985844	−	0.167666i	\(-0.946377\pi\)
0.234551	+	0.972104i	\(0.424638\pi\)
\(7\)	−2.17072	+	4.18929i	−0.820453	+	1.58340i	−0.00829512	+	0.999966i	\(0.502640\pi\)
							−0.812158	+	0.583437i	\(0.801707\pi\)
\(11\)	5.14853	+	3.13089i	1.55234	+	0.943999i	0.993389	+	0.114799i	\(0.0366224\pi\)
							0.558952	+	0.829200i	\(0.311204\pi\)
\(13\)	0.195603	−	0.450323i	0.0542505	−	0.124897i	−0.887958	−	0.459925i	\(-0.847876\pi\)
							0.942208	+	0.335028i	\(0.108746\pi\)
\(17\)	−2.05402	−	3.37768i	−0.498172	−	0.819209i	0.500752	−	0.865591i	\(-0.333057\pi\)
							−0.998924	+	0.0463821i	\(0.985231\pi\)
\(19\)	0.752170	−	0.702478i	0.172560	−	0.161159i	−0.591500	−	0.806305i	\(-0.701464\pi\)
							0.764060	+	0.645145i	\(0.223203\pi\)
\(23\)	−0.360216	+	0.510310i	−0.0751102	+	0.106407i	−0.852791	−	0.522253i	\(-0.825092\pi\)
							0.777681	+	0.628660i	\(0.216396\pi\)
\(29\)	1.09428	−	0.475311i	0.203202	−	0.0882630i	−0.294348	−	0.955698i	\(-0.595103\pi\)
							0.497550	+	0.867435i	\(0.334233\pi\)
\(31\)	3.25896	−	4.00579i	0.585326	−	0.719462i	−0.394594	−	0.918856i	\(-0.629115\pi\)
							0.979919	+	0.199394i	\(0.0638973\pi\)
\(37\)	5.67177	+	0.779567i	0.932433	+	0.128160i	0.586363	−	0.810049i	\(-0.300559\pi\)
							0.346070	+	0.938209i	\(0.387516\pi\)
\(41\)	−2.07583	−	0.581619i	−0.324190	−	0.0908337i	0.103852	−	0.994593i	\(-0.466883\pi\)
							−0.428041	+	0.903759i	\(0.640796\pi\)
\(43\)	−3.99085	−	1.41835i	−0.608598	−	0.216296i	0.0126368	−	0.999920i	\(-0.495977\pi\)
							−0.621235	+	0.783624i	\(0.713369\pi\)
\(47\)	3.28089	−	6.01961i	0.478567	−	0.878051i

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	141.2.g.a.107.5	yes	308
3.2	odd	2	inner	141.2.g.a.107.10	yes	308
47.29	odd	46	inner	141.2.g.a.29.10	yes	308
141.29	even	46	inner	141.2.g.a.29.5	✓	308

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
141.2.g.a.29.5	✓	308	141.29	even	46	inner
141.2.g.a.29.10	yes	308	47.29	odd	46	inner
141.2.g.a.107.5	yes	308	1.1	even	1	trivial
141.2.g.a.107.10	yes	308	3.2	odd	2	inner