Embedded newform 46.4.c.b.9.1

• Label: 46.4.c.b.9.1
• Level: $46$
• Weight: $4$
• Character: 46.9
• 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			9.1
Character	\(\chi\)	\(=\)	46.9
Dual form			46.4.c.b.41.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.91899 - 0.563465i) q^{2} +(-3.58705 - 4.13968i) q^{3} +(3.36501 - 2.16256i) q^{4} +(-1.27675 - 8.88002i) q^{5} +(-9.21607 - 5.92281i) q^{6} +(1.52711 - 3.34391i) q^{7} +(5.23889 - 6.04600i) q^{8} +(-0.427496 + 2.97330i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.91899	−	0.563465i	0.678464	−	0.199215i
							\(3\)	−3.58705	−	4.13968i	−0.690328	−	0.796681i	0.297084	−	0.954851i	\(-0.403986\pi\)
−0.987412	+	0.158170i	\(0.949441\pi\)
\(5\)	−1.27675	−	8.88002i	−0.114196	−	0.794253i	−0.963761	−	0.266768i	\(-0.914044\pi\)
							0.849564	−	0.527485i	\(-0.176865\pi\)
\(7\)	1.52711	−	3.34391i	0.0824562	−	0.180554i	−0.863913	−	0.503641i	\(-0.831993\pi\)
							0.946369	+	0.323087i	\(0.104721\pi\)
\(11\)	15.1410	+	4.44581i	0.415017	+	0.121860i	0.482574	−	0.875855i	\(-0.339702\pi\)
							−0.0675564	+	0.997715i	\(0.521520\pi\)
\(13\)	22.1543	+	48.5111i	0.472653	+	1.03497i	0.984419	+	0.175841i	\(0.0562644\pi\)
							−0.511765	+	0.859125i	\(0.671008\pi\)
\(17\)	75.1229	+	48.2785i	1.07176	+	0.688780i	0.952640	−	0.304099i	\(-0.0983555\pi\)
							0.119123	+	0.992880i	\(0.461992\pi\)
\(19\)	−31.8031	+	20.4386i	−0.384007	+	0.246786i	−0.718375	−	0.695657i	\(-0.755114\pi\)
							0.334368	+	0.942443i	\(0.391477\pi\)
\(23\)	−47.5380	−	99.5346i	−0.430972	−	0.902365i
							\(29\)	123.602	+	79.4344i	0.791461	+	0.508641i	0.872819	−	0.488044i	\(-0.162289\pi\)
−0.0813578	+	0.996685i	\(0.525926\pi\)
\(31\)	−29.4250	+	33.9582i	−0.170480	+	0.196744i	−0.834560	−	0.550917i	\(-0.814278\pi\)
							0.664080	+	0.747662i	\(0.268823\pi\)
\(37\)	7.66648	−	53.3215i	0.0340638	−	0.236919i	−0.965675	−	0.259752i	\(-0.916359\pi\)
							0.999739	+	0.0228325i	\(0.00726844\pi\)
\(41\)	−35.1771	−	244.662i	−0.133993	−	0.931945i	−0.940276	−	0.340414i	\(-0.889433\pi\)
							0.806282	−	0.591531i	\(-0.201476\pi\)
\(43\)	−270.256	−	311.893i	−0.958459	−	1.10612i	−0.994285	−	0.106762i	\(-0.965952\pi\)
							0.0358259	−	0.999358i	\(-0.488594\pi\)
\(47\)	64.2627			0.199440			0.0997200	−	0.995016i	\(-0.468205\pi\)
							0.0997200	+	0.995016i	\(0.468205\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.b.9.1	✓	30
23.8	even	11		1058.4.a.u.1.12		15
23.15	odd	22		1058.4.a.t.1.12		15
23.18	even	11	inner	46.4.c.b.41.1	yes	30

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.b.9.1	✓	30	1.1	even	1	trivial
46.4.c.b.41.1	yes	30	23.18	even	11	inner
1058.4.a.t.1.12		15	23.15	odd	22
1058.4.a.u.1.12		15	23.8	even	11