Embedded newform 46.4.c.b.13.2

• Label: 46.4.c.b.13.2
• 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			13.2
Character	\(\chi\)	\(=\)	46.13
Dual form			46.4.c.b.39.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.30972 + 1.51150i) q^{2} +(2.26977 + 1.45869i) q^{3} +(-0.569259 + 3.95929i) q^{4} +(-3.30726 + 7.24189i) q^{5} +(0.767954 + 5.34124i) q^{6} +(19.2136 + 5.64162i) q^{7} +(-6.73003 + 4.32513i) q^{8} +(-8.19213 - 17.9383i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9}+O(q^{10}) \)

Character values

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

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

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
							\(3\)	2.26977	+	1.45869i	0.436818	+	0.280726i	0.740511	−	0.672044i	\(-0.234584\pi\)
−0.303693	+	0.952770i	\(0.598220\pi\)
\(5\)	−3.30726	+	7.24189i	−0.295810	+	0.647735i	−0.997929	−	0.0643256i	\(-0.979510\pi\)
							0.702119	+	0.712060i	\(0.252238\pi\)
\(7\)	19.2136	+	5.64162i	1.03744	+	0.304619i	0.755731	−	0.654882i	\(-0.227282\pi\)
							0.281706	+	0.959501i	\(0.409100\pi\)
\(11\)	−2.55857	+	2.95274i	−0.0701306	+	0.0809350i	−0.789731	−	0.613454i	\(-0.789780\pi\)
							0.719600	+	0.694389i	\(0.244325\pi\)
\(13\)	26.0126	−	7.63800i	0.554970	−	0.162954i	0.00779125	−	0.999970i	\(-0.497520\pi\)
							0.547179	+	0.837016i	\(0.315702\pi\)
\(17\)	−9.32407	−	64.8503i	−0.133025	−	0.925207i	−0.941581	−	0.336787i	\(-0.890660\pi\)
							0.808556	−	0.588419i	\(-0.200249\pi\)
\(19\)	9.63506	−	67.0133i	0.116339	−	0.809153i	−0.845193	−	0.534461i	\(-0.820515\pi\)
							0.961532	−	0.274693i	\(-0.0885761\pi\)
\(23\)	−41.7185	−	102.111i	−0.378214	−	0.925718i
							\(29\)	4.57432	+	31.8151i	0.0292907	+	0.203721i	0.999212	−	0.0396987i	\(-0.0126398\pi\)
−0.969921	+	0.243420i	\(0.921731\pi\)
\(31\)	−136.129	+	87.4849i	−0.788694	+	0.506863i	−0.871909	−	0.489669i	\(-0.837118\pi\)
							0.0832143	+	0.996532i	\(0.473481\pi\)
\(37\)	87.7575	+	192.162i	0.389926	+	0.853818i	0.998193	+	0.0600860i	\(0.0191375\pi\)
							−0.608268	+	0.793732i	\(0.708135\pi\)
\(41\)	−181.475	+	397.375i	−0.691260	+	1.51365i	0.158996	+	0.987279i	\(0.449174\pi\)
							−0.850256	+	0.526369i	\(0.823553\pi\)
\(43\)	109.592	+	70.4307i	0.388667	+	0.249781i	0.720351	−	0.693609i	\(-0.243981\pi\)
							−0.331685	+	0.943390i	\(0.607617\pi\)
\(47\)	−201.123			−0.624188			−0.312094	−	0.950051i	\(-0.601030\pi\)
							−0.312094	+	0.950051i	\(0.601030\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.b.13.2	✓	30
23.4	even	11		1058.4.a.u.1.10		15
23.16	even	11	inner	46.4.c.b.39.2	yes	30
23.19	odd	22		1058.4.a.t.1.10		15

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.b.13.2	✓	30	1.1	even	1	trivial
46.4.c.b.39.2	yes	30	23.16	even	11	inner
1058.4.a.t.1.10		15	23.19	odd	22
1058.4.a.u.1.10		15	23.4	even	11