Embedded newform 46.4.c.b.31.2

• Label: 46.4.c.b.31.2
• Level: $46$
• Weight: $4$
• Character: 46.31
• Analytic conductor: $2.714$
• Analytic rank: $0$
• Dimension: $30$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.71408786026\)
Analytic rank:	\(0\)
Dimension:	\(30\)
Relative dimension:	\(3\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.2
Character	\(\chi\)	\(=\)	46.31
Dual form			46.4.c.b.3.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.284630 - 1.97964i) q^{2} +(-0.493326 - 1.08023i) q^{3} +(-3.83797 - 1.12693i) q^{4} +(-10.8228 - 12.4902i) q^{5} +(-2.27889 + 0.669143i) q^{6} +(0.379417 + 0.243837i) q^{7} +(-3.32332 + 7.27706i) q^{8} +(16.7577 - 19.3394i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/46\mathbb{Z}\right)^\times\).

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{3}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.284630	−	1.97964i	0.100632	−	0.699909i
							\(3\)	−0.493326	−	1.08023i	−0.0949406	−	0.207891i	0.856203	−	0.516639i	\(-0.172817\pi\)
−0.951144	+	0.308748i	\(0.900090\pi\)
\(5\)	−10.8228	−	12.4902i	−0.968022	−	1.11716i	−0.993076	−	0.117471i	\(-0.962521\pi\)
							0.0250540	−	0.999686i	\(-0.492024\pi\)
\(7\)	0.379417	+	0.243837i	0.0204866	+	0.0131659i	0.550844	−	0.834608i	\(-0.314306\pi\)
							−0.530357	+	0.847774i	\(0.677942\pi\)
\(11\)	−1.47520	−	10.2602i	−0.0404354	−	0.281234i	0.959565	−	0.281488i	\(-0.0908281\pi\)
							−1.00000		0.000254396i	\(0.999919\pi\)
\(13\)	−24.9864	+	16.0578i	−0.533075	+	0.342586i	−0.779325	−	0.626620i	\(-0.784438\pi\)
							0.246250	+	0.969206i	\(0.420801\pi\)
\(17\)	80.4120	−	23.6111i	1.14722	−	0.336855i	0.347767	−	0.937581i	\(-0.386940\pi\)
							0.799455	+	0.600726i	\(0.205122\pi\)
\(19\)	109.322	+	32.0998i	1.32001	+	0.387589i	0.864495	−	0.502641i	\(-0.167638\pi\)
							0.455512	+	0.890230i	\(0.349456\pi\)
\(23\)	61.0735	−	91.8533i	0.553683	−	0.832727i
							\(29\)	−146.424	+	42.9939i	−0.937595	+	0.275303i	−0.714613	−	0.699520i	\(-0.753397\pi\)
−0.222982	+	0.974823i	\(0.571579\pi\)
\(31\)	45.7243	−	100.122i	0.264913	−	0.580080i	−0.729696	−	0.683772i	\(-0.760338\pi\)
							0.994609	+	0.103692i	\(0.0330657\pi\)
\(37\)	−217.095	+	250.541i	−0.964600	+	1.11321i	0.0289233	+	0.999582i	\(0.490792\pi\)
							−0.993524	+	0.113626i	\(0.963753\pi\)
\(41\)	−150.456	−	173.635i	−0.573103	−	0.661396i	0.393005	−	0.919536i	\(-0.371436\pi\)
							−0.966107	+	0.258141i	\(0.916890\pi\)
\(43\)	−26.5185	−	58.0675i	−0.0940474	−	0.205935i	0.856762	−	0.515712i	\(-0.172473\pi\)
							−0.950809	+	0.309777i	\(0.899745\pi\)
\(47\)	260.839			0.809516			0.404758	−	0.914424i	\(-0.367356\pi\)
							0.404758	+	0.914424i	\(0.367356\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.b.31.2	yes	30
23.3	even	11	inner	46.4.c.b.3.2	✓	30
23.7	odd	22		1058.4.a.t.1.7		15
23.16	even	11		1058.4.a.u.1.7		15

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.b.3.2	✓	30	23.3	even	11	inner
46.4.c.b.31.2	yes	30	1.1	even	1	trivial
1058.4.a.t.1.7		15	23.7	odd	22
1058.4.a.u.1.7		15	23.16	even	11