Embedded newform 46.4.c.b.29.3

• Label: 46.4.c.b.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.b.27.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.830830 + 1.81926i) q^{2} +(4.04264 + 1.18703i) q^{3} +(-2.61944 - 3.02300i) q^{4} +(17.3103 - 11.1246i) q^{5} +(-5.51826 + 6.36842i) q^{6} +(-4.23099 + 29.4272i) q^{7} +(7.67594 - 2.25386i) q^{8} +(-7.77992 - 4.99985i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9}+O(q^{10}) \)

Character values

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

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

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
							\(3\)	4.04264	+	1.18703i	0.778007	+	0.228443i	0.646543	−	0.762878i	\(-0.276214\pi\)
0.131464	+	0.991321i	\(0.458032\pi\)
\(5\)	17.3103	−	11.1246i	1.54828	−	0.995017i	0.562530	−	0.826777i	\(-0.309828\pi\)
							0.985746	−	0.168239i	\(-0.0538082\pi\)
\(7\)	−4.23099	+	29.4272i	−0.228452	+	1.58892i	0.476180	+	0.879348i	\(0.342021\pi\)
							−0.704632	+	0.709572i	\(0.748888\pi\)
\(11\)	11.8761	+	26.0051i	0.325526	+	0.712803i	0.999667	−	0.0257997i	\(-0.00821323\pi\)
							−0.674141	+	0.738603i	\(0.735486\pi\)
\(13\)	−5.03521	−	35.0206i	−0.107424	−	0.747152i	−0.970329	−	0.241786i	\(-0.922267\pi\)
							0.862905	−	0.505366i	\(-0.168642\pi\)
\(17\)	5.42123	−	6.25643i	0.0773436	−	0.0892593i	−0.715759	−	0.698348i	\(-0.753919\pi\)
							0.793102	+	0.609088i	\(0.208464\pi\)
\(19\)	−41.3286	−	47.6957i	−0.499022	−	0.575902i	0.449232	−	0.893415i	\(-0.351698\pi\)
							−0.948254	+	0.317513i	\(0.897152\pi\)
\(23\)	−86.6957	−	68.1972i	−0.785969	−	0.618265i
							\(29\)	−183.506	+	211.777i	−1.17504	+	1.35607i	−0.253712	+	0.967280i	\(0.581651\pi\)
−0.921327	+	0.388788i	\(0.872894\pi\)
\(31\)	102.623	−	30.1329i	0.594571	−	0.174582i	0.0294170	−	0.999567i	\(-0.490635\pi\)
							0.565154	+	0.824985i	\(0.308817\pi\)
\(37\)	73.1400	+	47.0042i	0.324977	+	0.208850i	0.692949	−	0.720987i	\(-0.256311\pi\)
							−0.367972	+	0.929837i	\(0.619948\pi\)
\(41\)	−36.1117	+	23.2076i	−0.137554	+	0.0884005i	−0.607608	−	0.794237i	\(-0.707871\pi\)
							0.470054	+	0.882638i	\(0.344234\pi\)
\(43\)	−134.644	−	39.5350i	−0.477512	−	0.140210i	0.0341151	−	0.999418i	\(-0.489139\pi\)
							−0.511627	+	0.859208i	\(0.670957\pi\)
\(47\)	33.4543			0.103826			0.0519128	−	0.998652i	\(-0.483468\pi\)
							0.0519128	+	0.998652i	\(0.483468\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.b.29.3	yes	30
23.2	even	11		1058.4.a.u.1.5		15
23.4	even	11	inner	46.4.c.b.27.3	✓	30
23.21	odd	22		1058.4.a.t.1.5		15

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.b.27.3	✓	30	23.4	even	11	inner
46.4.c.b.29.3	yes	30	1.1	even	1	trivial
1058.4.a.t.1.5		15	23.21	odd	22
1058.4.a.u.1.5		15	23.2	even	11