Embedded newform 46.4.c.a.13.3

• Label: 46.4.c.a.13.3
• Level: $46$
• Weight: $4$
• Character: 46.13
• 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			13.3
Character	\(\chi\)	\(=\)	46.13
Dual form			46.4.c.a.39.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.30972 - 1.51150i) q^{2} +(7.02888 + 4.51719i) q^{3} +(-0.569259 + 3.95929i) q^{4} +(-7.76566 + 17.0044i) q^{5} +(-2.37815 - 16.5404i) q^{6} +(-9.77224 - 2.86939i) q^{7} +(6.73003 - 4.32513i) q^{8} +(17.7839 + 38.9414i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} + 6 q^{3} - 12 q^{4} + 10 q^{5} + 12 q^{6} + 107 q^{7} - 24 q^{8} - 63 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{7}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.30972	−	1.51150i	−0.463056	−	0.534396i
							\(3\)	7.02888	+	4.51719i	1.35271	+	0.869333i	0.997847	−	0.0655864i	\(-0.0208918\pi\)
0.354861	+	0.934919i	\(0.384528\pi\)
\(5\)	−7.76566	+	17.0044i	−0.694581	+	1.52092i	0.151839	+	0.988405i	\(0.451481\pi\)
							−0.846420	+	0.532516i	\(0.821247\pi\)
\(7\)	−9.77224	−	2.86939i	−0.527652	−	0.154932i	0.00704725	−	0.999975i	\(-0.497757\pi\)
							−0.534699	+	0.845043i	\(0.679575\pi\)
\(11\)	27.1128	−	31.2898i	0.743164	−	0.857657i	−0.250723	−	0.968059i	\(-0.580668\pi\)
							0.993887	+	0.110402i	\(0.0352138\pi\)
\(13\)	59.4488	−	17.4557i	1.26832	−	0.372412i	0.422734	−	0.906254i	\(-0.361071\pi\)
							0.845584	+	0.533842i	\(0.179252\pi\)
\(17\)	−4.50662	−	31.3442i	−0.0642950	−	0.447182i	−0.996385	−	0.0849544i	\(-0.972926\pi\)
							0.932090	−	0.362227i	\(-0.117984\pi\)
\(19\)	12.1457	−	84.4751i	0.146653	−	1.02000i	−0.774995	−	0.631968i	\(-0.782247\pi\)
							0.921648	−	0.388028i	\(-0.126843\pi\)
\(23\)	−0.295703	+	110.304i	−0.00268079	+	0.999996i
							\(29\)	37.7848	+	262.799i	0.241947	+	1.68278i	0.642327	+	0.766430i	\(0.277969\pi\)
−0.400380	+	0.916349i	\(0.631122\pi\)
\(31\)	64.2111	−	41.2660i	0.372021	−	0.239083i	−0.341249	−	0.939973i	\(-0.610850\pi\)
							0.713270	+	0.700890i	\(0.247213\pi\)
\(37\)	−80.9618	−	177.282i	−0.359731	−	0.787700i	−0.999812	−	0.0193931i	\(-0.993827\pi\)
							0.640081	−	0.768307i	\(-0.278901\pi\)
\(41\)	−56.9047	+	124.604i	−0.216757	+	0.474631i	−0.986508	−	0.163713i	\(-0.947653\pi\)
							0.769751	+	0.638344i	\(0.220380\pi\)
\(43\)	−235.783	−	151.529i	−0.836199	−	0.537393i	0.0510429	−	0.998696i	\(-0.483745\pi\)
							−0.887242	+	0.461304i	\(0.847382\pi\)
\(47\)	313.066			0.971604			0.485802	−	0.874069i	\(-0.338528\pi\)
							0.485802	+	0.874069i	\(0.338528\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.a.13.3	✓	30
23.4	even	11		1058.4.a.v.1.15		15
23.16	even	11	inner	46.4.c.a.39.3	yes	30
23.19	odd	22		1058.4.a.w.1.15		15

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.a.13.3	✓	30	1.1	even	1	trivial
46.4.c.a.39.3	yes	30	23.16	even	11	inner
1058.4.a.v.1.15		15	23.4	even	11
1058.4.a.w.1.15		15	23.19	odd	22