Embedded newform 46.4.c.a.29.3

• Label: 46.4.c.a.29.3
• Level: $46$
• Weight: $4$
• Character: 46.29
• 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			29.3
Character	\(\chi\)	\(=\)	46.29
Dual form			46.4.c.a.27.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.830830 - 1.81926i) q^{2} +(6.99711 + 2.05454i) q^{3} +(-2.61944 - 3.02300i) q^{4} +(2.74437 - 1.76370i) q^{5} +(9.55115 - 11.0226i) q^{6} +(-1.74684 + 12.1495i) q^{7} +(-7.67594 + 2.25386i) q^{8} +(22.0245 + 14.1543i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} + 6 q^{3} - 12 q^{4} + 10 q^{5} + 12 q^{6} + 107 q^{7} - 24 q^{8} - 63 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{9}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.830830	−	1.81926i	0.293743	−	0.643207i
							\(3\)	6.99711	+	2.05454i	1.34659	+	0.395396i	0.874018	−	0.485894i	\(-0.161506\pi\)
0.472576	+	0.881290i	\(0.343324\pi\)
\(5\)	2.74437	−	1.76370i	0.245464	−	0.157750i	−0.412124	−	0.911128i	\(-0.635213\pi\)
							0.657588	+	0.753378i	\(0.271577\pi\)
\(7\)	−1.74684	+	12.1495i	−0.0943205	+	0.656013i	0.886734	+	0.462280i	\(0.152969\pi\)
							−0.981054	+	0.193733i	\(0.937940\pi\)
\(11\)	−20.1674	−	44.1605i	−0.552792	−	1.21045i	−0.955466	−	0.295102i	\(-0.904646\pi\)
							0.402674	−	0.915344i	\(-0.368081\pi\)
\(13\)	0.229811	+	1.59837i	0.00490293	+	0.0341006i	0.992126	−	0.125243i	\(-0.0399712\pi\)
							−0.987223	+	0.159344i	\(0.949062\pi\)
\(17\)	−58.0997	+	67.0506i	−0.828896	+	0.956597i	−0.999587	−	0.0287272i	\(-0.990855\pi\)
							0.170691	+	0.985325i	\(0.445400\pi\)
\(19\)	7.24230	+	8.35806i	0.0874473	+	0.100920i	0.797787	−	0.602940i	\(-0.206004\pi\)
							−0.710340	+	0.703859i	\(0.751459\pi\)
\(23\)	−46.4083	+	100.066i	−0.420731	+	0.907186i
							\(29\)	182.064	−	210.113i	1.16581	−	1.34542i	0.238492	−	0.971145i	\(-0.423347\pi\)
0.927319	−	0.374272i	\(-0.122108\pi\)
\(31\)	19.1296	−	5.61696i	0.110832	−	0.0325431i	−0.225847	−	0.974163i	\(-0.572515\pi\)
							0.336678	+	0.941620i	\(0.390697\pi\)
\(37\)	10.5027	+	6.74967i	0.0466657	+	0.0299902i	0.563766	−	0.825935i	\(-0.309352\pi\)
							−0.517100	+	0.855925i	\(0.672988\pi\)
\(41\)	254.570	−	163.602i	0.969688	−	0.623181i	0.0430251	−	0.999074i	\(-0.486300\pi\)
							0.926663	+	0.375893i	\(0.122664\pi\)
\(43\)	−442.354	−	129.887i	−1.56880	−	0.460641i	−0.622149	−	0.782899i	\(-0.713740\pi\)
							−0.946652	+	0.322258i	\(0.895558\pi\)
\(47\)	508.441			1.57795			0.788977	−	0.614423i	\(-0.210611\pi\)
							0.788977	+	0.614423i	\(0.210611\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.a.29.3	yes	30
23.2	even	11		1058.4.a.v.1.2		15
23.4	even	11	inner	46.4.c.a.27.3	✓	30
23.21	odd	22		1058.4.a.w.1.2		15

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.a.27.3	✓	30	23.4	even	11	inner
46.4.c.a.29.3	yes	30	1.1	even	1	trivial
1058.4.a.v.1.2		15	23.2	even	11
1058.4.a.w.1.2		15	23.21	odd	22