Embedded newform 46.4.c.b.13.3

• Label: 46.4.c.b.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.b.39.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.30972 + 1.51150i) q^{2} +(7.23466 + 4.64943i) q^{3} +(-0.569259 + 3.95929i) q^{4} +(5.71615 - 12.5166i) q^{5} +(2.44777 + 17.0246i) q^{6} +(-32.6087 - 9.57479i) q^{7} +(-6.73003 + 4.32513i) q^{8} +(19.5068 + 42.7140i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9}+O(q^{10}) \)

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
							\(3\)	7.23466	+	4.64943i	1.39231	+	0.894783i	0.999690	−	0.0249170i	\(-0.00793214\pi\)
0.392621	+	0.919700i	\(0.371569\pi\)
\(5\)	5.71615	−	12.5166i	0.511268	−	1.11952i	−0.461373	−	0.887207i	\(-0.652643\pi\)
							0.972641	−	0.232315i	\(-0.0746299\pi\)
\(7\)	−32.6087	−	9.57479i	−1.76071	−	0.516990i	−0.768311	−	0.640077i	\(-0.778902\pi\)
							−0.992396	+	0.123087i	\(0.960721\pi\)
\(11\)	18.7232	−	21.6077i	0.513205	−	0.592270i	−0.438712	−	0.898628i	\(-0.644565\pi\)
							0.951916	+	0.306358i	\(0.0991105\pi\)
\(13\)	−30.5324	+	8.96511i	−0.651396	+	0.191267i	−0.590703	−	0.806889i	\(-0.701149\pi\)
							−0.0606935	+	0.998156i	\(0.519331\pi\)
\(17\)	11.0875	+	77.1152i	0.158183	+	1.10019i	0.901979	+	0.431780i	\(0.142114\pi\)
							−0.743796	+	0.668407i	\(0.766976\pi\)
\(19\)	1.30316	−	9.06368i	0.0157350	−	0.109440i	−0.980440	−	0.196817i	\(-0.936940\pi\)
							0.996175	+	0.0873774i	\(0.0278486\pi\)
\(23\)	−12.4127	−	109.603i	−0.112531	−	0.993648i
							\(29\)	18.5647	+	129.121i	0.118875	+	0.826796i	0.958798	+	0.284089i	\(0.0916913\pi\)
−0.839922	+	0.542706i	\(0.817400\pi\)
\(31\)	170.090	−	109.310i	0.985456	−	0.633314i	0.0545259	−	0.998512i	\(-0.482635\pi\)
							0.930930	+	0.365198i	\(0.118999\pi\)
\(37\)	123.629	+	270.711i	0.549312	+	1.20283i	0.957102	+	0.289750i	\(0.0935721\pi\)
							−0.407790	+	0.913076i	\(0.633701\pi\)
\(41\)	−7.14048	+	15.6355i	−0.0271989	+	0.0595573i	−0.922744	−	0.385414i	\(-0.874059\pi\)
							0.895545	+	0.444971i	\(0.146786\pi\)
\(43\)	−1.67987	−	1.07958i	−0.00595761	−	0.00382872i	0.537659	−	0.843163i	\(-0.319309\pi\)
							−0.543616	+	0.839334i	\(0.682945\pi\)
\(47\)	−341.720			−1.06053			−0.530265	−	0.847832i	\(-0.677908\pi\)
							−0.530265	+	0.847832i	\(0.677908\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.b.13.3	✓	30
23.4	even	11		1058.4.a.u.1.14		15
23.16	even	11	inner	46.4.c.b.39.3	yes	30
23.19	odd	22		1058.4.a.t.1.14		15

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.b.13.3	✓	30	1.1	even	1	trivial
46.4.c.b.39.3	yes	30	23.16	even	11	inner
1058.4.a.t.1.14		15	23.19	odd	22
1058.4.a.u.1.14		15	23.4	even	11