Embedded newform 46.4.c.b.3.1

• Label: 46.4.c.b.3.1
• Level: $46$
• Weight: $4$
• Character: 46.3
• 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			3.1
Character	\(\chi\)	\(=\)	46.3
Dual form			46.4.c.b.31.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.284630 + 1.97964i) q^{2} +(-3.62606 + 7.93996i) q^{3} +(-3.83797 + 1.12693i) q^{4} +(6.91905 - 7.98501i) q^{5} +(-16.7504 - 4.91835i) q^{6} +(-16.1046 + 10.3498i) q^{7} +(-3.32332 - 7.27706i) q^{8} +(-32.2134 - 37.1762i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{8}{11}\right)\)

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
							\(3\)	−3.62606	+	7.93996i	−0.697835	+	1.52805i	0.144742	+	0.989469i	\(0.453765\pi\)
−0.842577	+	0.538576i	\(0.818962\pi\)
\(5\)	6.91905	−	7.98501i	0.618859	−	0.714201i	−0.356631	−	0.934245i	\(-0.616075\pi\)
							0.975490	+	0.220044i	\(0.0706202\pi\)
\(7\)	−16.1046	+	10.3498i	−0.869567	+	0.558837i	−0.897620	−	0.440770i	\(-0.854706\pi\)
							0.0280532	+	0.999606i	\(0.491069\pi\)
\(11\)	−4.92640	+	34.2639i	−0.135033	+	0.939177i	0.803823	+	0.594868i	\(0.202796\pi\)
							−0.938856	+	0.344309i	\(0.888113\pi\)
\(13\)	72.4658	+	46.5710i	1.54603	+	0.993574i	0.986312	+	0.164892i	\(0.0527277\pi\)
							0.559720	+	0.828682i	\(0.310909\pi\)
\(17\)	−19.8916	−	5.84070i	−0.283790	−	0.0833281i	0.136740	−	0.990607i	\(-0.456338\pi\)
							−0.420530	+	0.907279i	\(0.638156\pi\)
\(19\)	−37.3796	+	10.9756i	−0.451341	+	0.132526i	−0.499500	−	0.866314i	\(-0.666483\pi\)
							0.0481589	+	0.998840i	\(0.484665\pi\)
\(23\)	97.0422	+	52.4386i	0.879770	+	0.475400i
							\(29\)	193.682	+	56.8703i	1.24020	+	0.364157i	0.835092	−	0.550110i	\(-0.185414\pi\)
0.405112	+	0.914267i	\(0.367233\pi\)
\(31\)	−107.751	−	235.943i	−0.624282	−	1.36699i	−0.912364	−	0.409381i	\(-0.865745\pi\)
							0.288082	−	0.957606i	\(-0.406982\pi\)
\(37\)	−0.802954	−	0.926658i	−0.00356770	−	0.00411734i	0.753963	−	0.656917i	\(-0.228140\pi\)
							−0.757531	+	0.652800i	\(0.773594\pi\)
\(41\)	−25.4979	+	29.4262i	−0.0971246	+	0.112088i	−0.802231	−	0.597014i	\(-0.796354\pi\)
							0.705106	+	0.709102i	\(0.250899\pi\)
\(43\)	212.323	−	464.922i	0.752998	−	1.64884i	−0.00790405	−	0.999969i	\(-0.502516\pi\)
							0.760902	−	0.648867i	\(-0.224757\pi\)
\(47\)	393.293			1.22059			0.610294	−	0.792175i	\(-0.291051\pi\)
							0.610294	+	0.792175i	\(0.291051\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.b.3.1	✓	30
23.8	even	11	inner	46.4.c.b.31.1	yes	30
23.10	odd	22		1058.4.a.t.1.2		15
23.13	even	11		1058.4.a.u.1.2		15

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.b.3.1	✓	30	1.1	even	1	trivial
46.4.c.b.31.1	yes	30	23.8	even	11	inner
1058.4.a.t.1.2		15	23.10	odd	22
1058.4.a.u.1.2		15	23.13	even	11